1

                                                FILED PURSUANT TO RULE 424(b)(5)
                                                      REGISTRATION NO. 333-58604

            PROSPECTUS SUPPLEMENT TO PROSPECTUS DATED APRIL 12, 2001

                                  $400,000,000

                               [TRANSOCEAN LOGO]

                  1.5% Convertible Debentures due May 15, 2021

                               ------------------

     We will pay interest on the Debentures on May 15 and November 15 of each
year, beginning on November 15, 2001. The Debentures will rank equally with all
of the other unsecured and unsubordinated debt of Transocean Sedco Forex Inc.

     As a holder, you may convert the Debentures into our ordinary shares at a
conversion rate of 13.8627 ordinary shares per Debenture so long as specified
conditions are met and subject to adjustments in some circumstances. This rate
is equivalent to an initial conversion price of $72.136 per ordinary share based
on the $1,000 principal amount per Debenture. As a holder, you may surrender
Debentures for conversion at any time prior to maturity, unless they have been
previously repurchased or redeemed, but only if the closing sale price of our
ordinary shares is greater than 110% of the conversion price per ordinary share
for at least 20 trading days of the 30 trading days prior to conversion or if
other specified conditions are met. Our ordinary shares are listed on The New
York Stock Exchange under the symbol "RIG." On May 7, 2001, the closing price of
the ordinary shares as reported on the New York Stock Exchange was $50.800 per
ordinary share.

     We may redeem all or part of the Debentures at our option at any time after
May 20, 2006. As a holder, you have the right to require us to repurchase
Debentures on May 15, 2006, May 15, 2011 and May 15, 2016. The price per
redeemed or repurchased Debenture will be 100% of the principal amount of the
Debenture plus accrued interest up to but not including the date of repurchase.
If we exercise our redemption right, we must pay the redemption price in cash.
If a holder exercises the right to require us to repurchase a Debenture, we may
choose to pay the repurchase price in cash or our ordinary shares, or any
combination of cash and our ordinary shares.

     INVESTING IN THE DEBENTURES INVOLVES RISKS. SEE "RISK FACTORS" BEGINNING ON
PAGE S-3 OF THIS PROSPECTUS SUPPLEMENT.



                                                                        UNDERWRITING      PROCEEDS TO
                                                         PRICE TO       DISCOUNT AND       TRANSOCEAN
                                                        PUBLIC(1)        COMMISSIONS      SEDCO FOREX
                                                       ------------   -----------------   ------------
                                                                                 
Per Debenture........................................          100%           1.50%             98.50%
Total................................................  $400,000,000      $6,000,000       $394,000,000


(1) Plus accrued interest, if any, from May 11, 2001.

     Delivery of the Debentures in book-entry form only will be made on or about
May 11, 2001.

     Neither the Securities and Exchange Commission nor any state securities
commission has approved or disapproved of these securities or determined if this
prospectus supplement or the prospectus to which it relates is truthful or
complete. Any representation to the contrary is a criminal offense.

                           CREDIT SUISSE FIRST BOSTON

             The date of this prospectus supplement is May 8, 2001.
   2

                               ------------------

                               TABLE OF CONTENTS


                                     
PROSPECTUS SUPPLEMENT                   Page
ENFORCEABILITY OF CIVIL LIABILITIES
  AGAINST FOREIGN PERSONS............    S-3
RISK FACTORS.........................    S-3
SPECIAL NOTE REGARDING FORWARD-
  LOOKING STATEMENTS.................    S-8
USE OF PROCEEDS......................    S-9
PRICE RANGES AND DIVIDENDS...........    S-9
RATIO OF EARNINGS TO FIXED CHARGES...   S-10
DESCRIPTION OF THE DEBENTURES........   S-11
CERTAIN UNITED STATES FEDERAL
  INCOME TAX CONSIDERATIONS..........   S-18
CAYMAN ISLANDS TAX CONSEQUENCES......   S-22
UNDERWRITING.........................   S-23
NOTICE TO CANADIAN RESIDENTS.........   S-24
LEGAL MATTERS........................   S-25
PROSPECTUS                              Page
ABOUT THIS PROSPECTUS................      1
FORWARD-LOOKING STATEMENTS...........      1
ABOUT TRANSOCEAN SEDCO FOREX INC.....      2
WHERE YOU CAN FIND MORE
  INFORMATION........................      2
USE OF PROCEEDS......................      3
RATIO OF EARNINGS TO FIXED CHARGES...      3
DESCRIPTION OF DEBT SECURITIES.......      4
DESCRIPTION OF SHARE CAPITAL.........     13
DESCRIPTION OF ORDINARY SHARES.......     13
DESCRIPTION OF PREFERENCE SHARES.....     16
DESCRIPTION OF WARRANTS..............     17
ANTI-TAKEOVER PROVISIONS.............     18
PLAN OF DISTRIBUTION.................     19
LEGAL OPINIONS.......................     21
EXPERTS..............................     21


                               ------------------

     YOU SHOULD RELY ONLY ON THE INFORMATION CONTAINED IN THIS PROSPECTUS
SUPPLEMENT OR THE ACCOMPANYING PROSPECTUS OR TO WHICH WE HAVE REFERRED YOU. WE
HAVE NOT AUTHORIZED ANYONE TO PROVIDE YOU WITH INFORMATION THAT IS DIFFERENT.
THIS PROSPECTUS SUPPLEMENT AND THE ACCOMPANYING PROSPECTUS MAY ONLY BE USED
WHERE IT IS LEGAL TO SELL THE DEBENTURES. THE INFORMATION IN THIS PROSPECTUS
SUPPLEMENT OR THE ACCOMPANYING PROSPECTUS MAY ONLY BE ACCURATE ON THE DATE OF
THIS PROSPECTUS SUPPLEMENT.

     This document is in two parts. The first part is the prospectus supplement,
which describes the specific terms of the Debentures we are offering and certain
other matters relating to our business. The second part, the accompanying
prospectus, gives more general information, some of which does not apply to this
series of Debentures we are offering. Generally, when we refer to the
prospectus, we are referring to both parts combined. If the description of the
Debentures varies between the prospectus supplement and the accompanying
prospectus, you should rely on the information in the prospectus supplement.

                                       S-2
   3

          ENFORCEABILITY OF CIVIL LIABILITIES AGAINST FOREIGN PERSONS

     Transocean Sedco Forex Inc. is a Cayman Islands exempted company and
certain of our officers and directors may be residents of various jurisdictions
outside the United States. All or a substantial portion of our assets and the
assets of these persons may be located outside the United States. As a result,
it may be difficult for investors to effect service of process within the United
States upon these persons or to enforce any U.S. court judgment obtained against
these persons that is predicated upon the civil liability provisions of the
Securities Act of 1933. We have agreed to be served with process with respect to
actions based on offers and sales of the Debentures. To bring a claim against
us, you may serve our Corporate Secretary, c/o Transocean Sedco Forex Inc., 4
Greenway Plaza, Houston, Texas 77046, our U.S. agent appointed for that purpose.

     Walkers, our Cayman Islands legal counsel, has advised us that there is
doubt as to whether Cayman Islands courts would enforce (1) judgments of U.S.
courts obtained in actions against us or other persons that are predicated upon
the civil liability provisions of the Securities Act of 1933 or (2) original
actions brought against us or other persons predicated upon the Securities Act
of 1933. There is no treaty between the United States and the Cayman Islands
providing for enforcement of judgments, and there are grounds upon which Cayman
Islands courts may not enforce judgments of U.S. courts. In general, Cayman
Islands courts would not enforce any remedies if they are deemed to be
penalties, fines, taxes or similar remedies.

                                  RISK FACTORS

     In considering whether to purchase the Debentures, you should consider
carefully the following matters, in addition to the other information included
or incorporated by reference in this prospectus supplement and the accompanying
prospectus. If any of the following risks occur, our business, financial
condition or results of operations could be materially adversely affected.

OUR BUSINESS DEPENDS ON THE LEVEL OF ACTIVITY IN THE OIL AND GAS INDUSTRY, WHICH
IS SIGNIFICANTLY AFFECTED BY VOLATILE OIL AND GAS PRICES.

     Our business depends on the level of activity in oil and gas exploration,
development and production in markets worldwide, with the U.S. and international
offshore and U.S. inland marine areas being our primary markets. Oil and gas
prices, market expectations of potential changes in these prices and a variety
of political and economic factors significantly affect this level of activity.
Oil and gas prices are extremely volatile and are affected by numerous factors,
including the following:

     - worldwide demand for oil and gas,

     - the ability of the Organization of Petroleum Exporting Countries,
       commonly called "OPEC," to set and maintain production levels and
       pricing,

     - the level of production in non-OPEC countries,

     - the policies of various governments regarding exploration and development
       of their oil and gas reserves,

     - advances in exploration and development technology, and

     - the political environment in oil-producing regions.

THE LEVEL OF ACTIVITY IN THE OIL AND GAS INDUSTRY HAS NOT FULLY RECOVERED FROM
THE RECENT DOWNTURN, WHICH CONTINUES TO ADVERSELY AFFECT OUR DAYRATES AND RIG
UTILIZATION.

     The global reduction in exploration and development spending by our
customers, resulting from the sustained period of significantly lower oil and
gas prices from late 1997 through early 1999 and consolidation activity among
major oil producers over the same period, resulted in lower utilization and
dayrates for our drilling rigs during that period. Despite a recovery in crude
oil and gas prices that began in the latter part of 1999, worldwide customer
spending levels have only recently begun to appreciably increase from spending
levels during 1999 and there remains surplus rig capacity, particularly in the
lower specification semisubmersible and

                                       S-3
   4

some jackup markets. A decline in oil or gas prices could reduce demand for our
drilling services and adversely affect both utilization and dayrates.

OUR INDUSTRY IS HIGHLY COMPETITIVE AND CYCLICAL, WITH INTENSE PRICE COMPETITION.

     The offshore and inland marine contract drilling industry is highly
competitive with numerous industry participants, none of which has a dominant
market share. Drilling contracts are traditionally awarded on a competitive bid
basis. Intense price competition is often the primary factor in determining
which qualified contractor is awarded a job, although rig availability and the
quality and technical capability of service and equipment may also be
considered.

     Our industry has historically been cyclical. There have been periods of
high demand, short rig supply and high dayrates, followed by periods of low
demand, excess rig supply and low dayrates. The industry experienced a period of
moderately increased demand on a global basis during 2000 as a result of
relatively strong oil and gas prices during the year. However, our clients did
not significantly increase their spending, except in the United States. Changes
in commodity prices can have a dramatic effect on rig demand, and periods of
excess rig supply intensify the competition in the industry and often result in
rigs being idle for long periods of time.

OUR DRILLING CONTRACTS MAY BE TERMINATED DUE TO A NUMBER OF EVENTS.

     Our customers may terminate some of our term drilling contracts under
various circumstances such as the loss or destruction of the drilling unit or
the suspension of drilling operations for a specified period of time as a result
of a breakdown of major equipment. Some drilling contracts permit the customer
to terminate the contract at the customer's option without paying a termination
fee. In addition, the drilling contracts for the Sedco Express-class newbuild
rigs contain termination or term reduction provisions tied to late delivery of
these rigs and a unit of TotalFinaElf cancelled the Sedco Express contract
because of late delivery. If our customers cancel some of our significant
contracts and we are unable to secure new contracts on substantially similar
terms, it could adversely affect our results of operations. In reaction to
depressed market conditions, our customers may also seek renegotiation of firm
drilling contracts to reduce their obligations.

OUR SHIPYARD PROJECTS ARE SUBJECT TO DELAYS AND COST OVERRUNS.

     We currently have two new rigs in the testing and commissioning phase and
plans for significant shipyard upgrade and maintenance projects for at least six
rigs during 2001. These shipyard projects are subject to the risks of delay or
cost overruns inherent in any large construction project resulting from numerous
factors, including the following:

     - engineering, software or systems problems, including those relating to
       the commissioning of newly designed equipment,

     - shortages of equipment, materials or skilled labor,

     - unscheduled delays in the delivery of ordered materials and equipment,

     - work stoppages,

     - shipyard unavailability,

     - weather interference,

     - unanticipated cost increases, and

     - difficulty in obtaining necessary permits or approvals.

     These factors may contribute to cost variations and delays in the
completion of our shipyard projects. Delays in delivery of the newbuild units
would result in delays in contract commencements, resulting in a loss of revenue
to us, and may also cause clients to terminate or shorten the term of the
drilling contracts for these rigs, as described above. In the event of the
termination of a drilling contract for one of these rigs, there can be no
assurance that we would be able to secure a replacement contract on as favorable
terms.
                                       S-4
   5

WE MAY FACE DIFFICULTIES IN INTEGRATING OUR COMBINED OPERATIONS.

     We have been involved in two merger transactions in the last two years. We
may not be able to integrate the operations of the merged or acquired companies
without a loss of employees, customers or suppliers, a loss of revenues, an
increase in operating or other costs or other difficulties. In addition, we may
not be able to realize the operating efficiencies, synergies, cost savings or
other benefits expected from these transactions.

     We plan to restructure the ownership of a portion of the assets currently
held by R&B Falcon and its subsidiaries. This restructuring is intended to lower
the worldwide effective corporate tax rate from what that rate would have been
in the absence of the restructuring and to achieve operational efficiencies,
including improved worldwide cash management and increased flexibility for
operating rigs in various jurisdictions. Any transfers of assets by R&B Falcon
or one of its subsidiaries to Transocean Sedco Forex or one of its non-U.S.
subsidiaries in this restructuring could, in some cases, result in the
imposition of additional taxes.

WE ACQUIRED A SIGNIFICANT AMOUNT OF DEBT IN THE MERGER WITH R&B FALCON.

     R&B Falcon was subject to a significant amount of debt. Our overall debt
level increased as a result of this R&B Falcon debt after the merger. Some of
this debt has relatively high interest rates. Some of the R&B Falcon debt
agreements also contain restrictions and requirements that may limit our
flexibility in conducting our operations.

OUR BUSINESS INVOLVES NUMEROUS OPERATING HAZARDS.

     Our operations are subject to the usual hazards inherent in the drilling of
oil and gas wells, such as blowouts, reservoir damage, loss of production, loss
of well control, punchthroughs, craterings and fires. The occurrence of these
events could result in the suspension of drilling operations, damage to or
destruction of the equipment involved and injury or death to rig personnel. We
may also be subject to personal injury and other claims of rig personnel as a
result of our drilling operations. Operations also may be suspended because of
machinery breakdowns, abnormal drilling conditions, failure of subcontractors to
perform or supply goods or services or personnel shortages. In addition,
offshore drilling operators are subject to perils peculiar to marine operations,
including capsizing, grounding, collision and loss or damage from severe
weather. Damage to the environment could also result from our operations,
particularly through oil spillage or extensive uncontrolled fires. We may also
be subject to property, environmental and other damage claims by oil and gas
companies. Our insurance policies and contractual rights to indemnity may not
adequately cover losses, and we may not have insurance coverage or rights to
indemnity for all risks. If a significant accident or other event occurs and is
not fully covered by insurance or a recoverable indemnity from a client, it
could adversely affect our consolidated financial position or results of
operations.

     In March 2001, a production facility located offshore Brazil sank in
approximately 4000 feet of water, resulting in loss of life and equipment, and
the release of hydrocarbons into the water. We had no interest in this facility
nor any personnel or property involved in the accident, but we do have 15 rigs
working in Brazil including two rigs working in the same field in which this
facility was located. There can be no assurance that this event will not result
in delays or other changes in the development or exploration efforts offshore of
Brazil or other areas and thereby affect our operations.

OUR NON-U.S. OPERATIONS WILL INVOLVE ADDITIONAL RISKS NOT ASSOCIATED WITH OUR
U.S. OPERATIONS.

     We operate in various regions throughout the world that may expose us to
political and other uncertainties, including risks of:

     - war and civil disturbances,

     - expropriation of equipment,

     - the inability to repatriate income or capital, and

     - changing taxation policies.

                                       S-5
   6

     Many governments favor or effectively require the awarding of drilling
contracts to local contractors or require foreign contractors to employ citizens
of, or purchase supplies from, a particular jurisdiction. These practices may
adversely affect our ability to compete.

     Our non-U.S. contract drilling operations are subject to various laws and
regulations in countries in which we operate, including laws and regulations
relating to the equipment and operation of drilling units, currency conversions
and repatriation, oil and gas exploration and development and taxation of
offshore earnings and earnings of expatriate personnel. Governments in some
foreign countries have become increasingly active in regulating and controlling
the ownership of concessions and companies holding concessions, the exploration
of oil and gas and other aspects of the oil and gas industries in their
countries. In addition, government action, including initiatives by OPEC, may
continue to cause oil or gas price volatility. In some areas of the world, this
governmental activity has adversely affected the amount of exploration and
development work done by major oil companies and may continue to do so.

     Another risk inherent in our operations is the possibility of currency
exchange losses where revenues are received and expenses are paid in foreign
currencies. We may also incur losses as a result of an inability to collect
revenues because of a shortage of convertible currency available to, or transfer
or exchange by, the country of operation.

FAILURE TO RETAIN KEY PERSONNEL COULD HURT OUR OPERATIONS.

     We require highly skilled personnel to operate and provide technical
services and support for our drilling units. To the extent that demand for
drilling services and the size of the worldwide industry fleet increase,
shortages of qualified personnel could arise, creating upward pressure on wages.

     On a worldwide basis, we had approximately 14 percent of our employees
working under collective bargaining agreements on March 1, 2001, most of whom
were working in Norway, Nigeria, Trinidad and Venezuela. Of these represented
employees, a majority are working under agreements that are subject to salary
negotiation in 2001. In addition, the Company has signed a recognition agreement
requiring negotiation with a labor union representing employees in the U.K.
These negotiations could result in collective bargaining agreements covering
these employees, which could result in higher personnel expenses, other
increased costs or increased operating restrictions.

GOVERNMENTAL LAWS AND REGULATIONS MAY ADD TO OUR COSTS OR LIMIT DRILLING
ACTIVITY.

     Our operations are affected from time to time in varying degrees by
governmental laws and regulations. The drilling industry is dependent on demand
for services from the oil and gas exploration industry and, accordingly, is also
affected by changing tax and other laws relating to the energy business
generally. We may be required to make significant capital expenditures to comply
with laws and regulations. It is also possible that these laws and regulations
may in the future add significantly to operating costs or may limit drilling
activity.

COMPLIANCE WITH OR BREACH OF ENVIRONMENTAL LAWS CAN BE COSTLY AND COULD LIMIT
OUR OPERATIONS.

     Our operations are subject to regulations controlling the discharge of
materials into the environment, requiring removal and cleanup of materials that
may harm the environment or otherwise relating to the protection of the
environment. For example, as an operator of mobile offshore drilling units in
navigable U.S. waters and some offshore areas, we may be liable for damages and
costs incurred in connection with oil spills related to those operations. Laws
and regulations protecting the environment have become more stringent in recent
years, and may in some cases impose strict liability, rendering a person liable
for environmental damage without regard to negligence. These laws and
regulations may expose us to liability for the conduct of or conditions caused
by others or for acts that were in compliance with all applicable laws at the
time they were performed. The application of these requirements or the adoption
of new requirements could have a material adverse effect on our financial
position and results of our operations.

                                       S-6
   7

OUR HOLDING COMPANY STRUCTURE RESULTS IN SUBSTANTIAL STRUCTURAL SUBORDINATION
AND MAY AFFECT OUR ABILITY TO MAKE PAYMENTS ON THE DEBENTURES.

     The Debentures are obligations exclusively of Transocean Sedco Forex. We
are a holding company and, accordingly, substantially all of our operations are
conducted through our subsidiaries. As a result, our cash flow and our ability
to service our debt, including the Debentures, is dependent upon the earnings of
our subsidiaries and on the distribution of earnings, loans or other payments by
our subsidiaries to us.

WE MAY NOT HAVE THE FUNDS NECESSARY TO FINANCE A REPURCHASE REQUIRED BY THE
INDENTURE IN THE EVENT OF A CHANGE IN CONTROL OR AT THE OPTION OF A HOLDER OF
DEBENTURES.

     Upon the occurrence of specific change in control events and on the May 15,
2006, May 15, 2011 and May 15, 2016 repurchase dates, holders of Debentures will
have the right to require us to repurchase their Debentures. However, it is
possible that we will not have sufficient funds at such time to make the
required repurchase of Debentures or that restrictions in our credit agreements
or other indebtedness will not allow such repurchases. Our failure to purchase
all validly tendered Debentures would constitute an event of default under the
indenture under which the Debentures are issued. In addition, certain important
corporate events, such as leveraged recapitalizations that would increase the
level of our indebtedness, would not constitute a "Change in Control" under the
indenture. See "Description of the Debentures -- Repurchase Rights" and
"-- Change in Control."

NO MARKET CURRENTLY EXISTS FOR THE DEBENTURES AND WE CANNOT ASSURE YOU THAT AN
ACTIVE TRADING MARKET FOR THE DEBENTURES WILL DEVELOP.

     The Debentures comprise a new issue of securities for which there is
currently no public market and we do not currently intend to apply to list the
Debentures on any securities exchange or public market. If the Debentures are
traded after their initial issuance, they may trade at a discount from their
initial public offering price, depending on prevailing interest rates, the
market for similar securities, our performance and other factors. To the extent
that an active trading market for the Debentures does not develop, the liquidity
and trading prices for the Debentures may be harmed.

                                       S-7
   8

               SPECIAL NOTE REGARDING FORWARD-LOOKING STATEMENTS

     This prospectus supplement and the documents incorporated by reference in
the accompanying prospectus contain both historical and forward-looking
statements. All statements other than statements of historical fact are, or may
be deemed to be, forward-looking statements within the meaning of Section 27A of
the Securities Act of 1933 and Section 21E of the Securities Exchange Act of
1934. Forward-looking statements include the information concerning possible or
assumed future results of operations of our company, including statements about
the following subjects:

     - business strategy,

     - expected capital expenditures,

     - adequacy of source of funds for liquidity needs,

     - results and effects of legal proceedings,

     - liabilities for tax issues,

     - adequacy of insurance coverage,

     - the timing and cost of completion of capital projects,

     - timing of delivery of drilling units,

     - expiration of rig contracts,

     - potential revenues,

     - potential timing and proceeds of asset sales,

     - increased expenses,

     - customer drilling programs,

     - utilization rates,

     - dayrates,

     - other expectations with regard to outlook,

     - number and timing of idle rig days,

     - timing of the sale of the land and barge drilling business in Venezuela,

     - refinancing of indebtedness,

     - loss contingencies and charges, and

     - the potential savings and effects of our merger transaction with R&B
       Falcon.

     Forward-looking statements in this prospectus supplement or incorporated by
reference are identifiable by use of the following words and other similar
expressions, among others:

     - "anticipate"

     - "believe"

     - "budget"

     - "could"

     - "estimate"

     - "expect"

     - "forecast"

     - "intend"

     - "may"

     - "might"

     - "plan"

     - "predict"

     - "project"

     - "should"

     The factors discussed above under "Risk Factors" and in the documents we
incorporate by reference into the accompanying prospectus could affect our
future results of operations and could cause those results to differ materially
from those expressed in the forward-looking statements included in this
prospectus supplement or incorporated by reference.

     You should not place undue reliance on forward-looking statements. Each
forward-looking statement speaks only as of the date of the particular
statement, and we undertake no obligation to publicly update or revise any
forward-looking statements.

                                       S-8
   9

                                USE OF PROCEEDS

     We intend to use the net proceeds from the offering of the Debentures to
provide a portion of the funding for the redemption by our subsidiary, Cliffs
Drilling Company, of its 10.25% Senior Notes due 2003, Series B and Series D, to
repay all or a portion of our outstanding commercial paper indebtedness and for
general corporate purposes. As of May 4, 2001, a total of $254.8 million face
amount of our commercial paper indebtedness was outstanding. This indebtedness
had a weighted average maturity of 7.5 days and a weighted average yield of
approximately 4.98 percent. Proceeds from commercial paper issuances were used
to repay indebtedness under our revolving credit agreements and for general
corporate purposes. Pending use of the net proceeds from this offering, we may
invest the funds in short-term, interest bearing, investment grade, marketable
securities.

                           PRICE RANGES AND DIVIDENDS

     Our ordinary shares are listed on the New York Stock Exchange under the
symbol "RIG." The following table sets forth the high and low sales prices of
our ordinary shares for the periods indicated as reported on the NYSE Composite
Tape.



                                                                    PRICE
                                                              -----------------
                                                               HIGH       LOW
                                                              -------   -------
                                                                  
1999
  First Quarter.............................................  $31.563   $19.625
  Second Quarter............................................   32.500    22.625
  Third Quarter.............................................   36.500    25.563
  Fourth Quarter............................................   34.375    23.875
2000
  First Quarter.............................................   53.125    29.250
  Second Quarter............................................   56.188    41.250
  Third Quarter.............................................   64.625    45.625
  Fourth Quarter............................................   65.500    34.375
2001
  First Quarter.............................................   54.500    43.344
  Second Quarter (through May 7)............................   54.480    40.350


     On May 7, 2001, the last reported sales price of our ordinary shares on the
New York Stock Exchange was $50.800 per ordinary share. On such date, there were
approximately 318 million ordinary shares outstanding.

     We have paid quarterly cash dividends of $0.03 per ordinary share since the
fourth quarter of 1993. Any future declaration and payment of dividends will be:

     - dependent upon our results of operations, financial condition, cash
       requirements and other relevant factors,

     - subject to the discretion of our Board of Directors,

     - subject to restrictions contained in our bank credit agreements, note
       purchase agreement and indentures (see "Item 7. Management's Discussion
       and Analysis of Financial Condition and Results of
       Operations -- Liquidity and Capital Resources -- Debt" in our Annual
       Report on Form 10-K for the year ended December 31, 2000), and

     - payable only out of our profits or share premium account in accordance
       with Cayman Islands law.

                                       S-9
   10

                       RATIO OF EARNINGS TO FIXED CHARGES

     Our ratio of earnings to fixed charges for each of the periods shown is as
follows:



                                                          YEAR ENDED DECEMBER 31,
                                                --------------------------------------------
                                                2000   1999(A)   1998(A)   1997(A)   1996(A)
                                                ----   -------   -------   -------   -------
                                                                      
Historical ratio of earnings to fixed
  charges.....................................  1.5      1.4       9.7      10.3      12.6
Supplemental pro forma ratio of earnings to
  fixed charges(b)............................   --
Supplemental pro forma as adjusted ratio of
  earnings to fixed charges(b)................   --


---------------

(a)  The ratios for each of the years in the four year period ended December 31,
     1999 include only the earnings and fixed charges of Sedco Forex, not those
     of Transocean Offshore Inc.

(b)  Supplemental pro forma earnings and supplemental pro forma as adjusted
     earnings were insufficient to cover fixed charges by $141.3 million and
     $117.6 million, respectively.

     We have computed the ratios of earnings to fixed charges shown above by
dividing earnings available for fixed charges by fixed charges. For this
purpose, "earnings available for fixed charges" consist of pretax income (loss)
from continuing operations before extraordinary items plus fixed charges,
distributed earnings of unconsolidated joint ventures and amortization of
capitalized interest, less capitalized interest and undistributed equity in
earnings of joint ventures. "Fixed charges" consist of interest expense,
capitalized interest and an estimate of the interest within rental expense.

     On January 31, 2001, we completed our merger transaction with R&B Falcon.
The merger was accounted for as a purchase, with our company as the acquiror for
accounting purposes. The historical ratios of earnings to fixed charges for the
year ended December 31, 2000 include only the earnings and fixed charges of
Transocean Sedco Forex. On December 31, 1999, we completed our merger with Sedco
Forex Holdings Limited, the former offshore contract drilling business of
Schlumberger Limited. The merger was accounted for as a purchase, with Sedco
Forex as the acquiror for accounting purposes. The historical ratios of earnings
to fixed charges for the four year period ended December 31, 1999 include only
the earnings and fixed charges of Sedco Forex.

     On April 5, 2001, we completed a debt offering that consisted of $700
million aggregate principal amount of 6.625% notes due April 15, 2011 and $600
million aggregate principal amount of 7.500% notes due April 15, 2031. The net
proceeds from the April 2001 debt offering were used to provide funding for the
tender offer for the 11.375% Senior Secured Notes due 2009 of RBF Finance Co.,
the redemption of the 11% Senior Secured Notes due 2006 of RBF Finance Co. and
the redemption of the 12.25% Senior Notes due 2006 of R&B Falcon Corporation.

     The supplemental pro forma ratio of earnings to fixed charges for the year
ended December 31, 2000 assumes that we completed the merger transaction with
R&B Falcon and the April 2001 debt offering on January 1, 2000. This pro forma
information does not necessarily reflect what the ratio of earnings to fixed
charges would have been if the merger and the April 2001 debt offering had been
completed on that date nor does it necessarily reflect any future ratio of
earnings to fixed charges.

     The supplemental pro forma as adjusted ratio of earnings to fixed charges
for the year ended December 31, 2000 reflects the supplemental pro forma ratio
shown above, as adjusted to reflect this offering and assuming that the net
proceeds will be used to provide all of the funding for the redemption by our
subsidiary, Cliffs Drilling Company, of its 10.25% Senior Notes due 2003 and the
repayment of approximately $189 million of indebtedness under our revolving
credit agreements with an average interest rate of 6.3 percent. Our actual
intended use of the net proceeds from this offering is described under "Use of
Proceeds."

                                       S-10
   11

                         DESCRIPTION OF THE DEBENTURES

GENERAL

     We will issue the Debentures under the senior indenture referred to in the
accompanying prospectus, as supplemented by a fourth supplemental indenture
dated the date of the closing of the offering. We will issue Debentures in an
aggregate principal amount of $400,000,000. The Debentures will rank equally
with all of our other unsecured and unsubordinated debt. The Debentures will
mature on May 15, 2021. We will issue the Debentures only in book-entry form in
denominations of $1,000 and integral multiples of $1,000.

INTEREST

     The Debentures will bear interest at the annual rate shown on the front
cover of this prospectus supplement and will accrue interest from May 11, 2001
or from the most recent date to which interest has been paid or provided for. We
will pay interest on the Debentures twice a year, on May 15 and November 15,
beginning on November 15, 2001, to the person in whose name a Debenture is
registered at the close of business on the May 1 or November 1 that immediately
precedes the date on which interest will be paid. Interest will cease to accrue
on a Debenture upon its maturity, conversion, purchase by us at the option of a
holder or redemption. We will calculate interest on the basis of a 360-day year
composed of twelve 30-day months.

CONVERSION RIGHTS

     You have the right to convert a Debenture into our ordinary shares, par
value $0.01 per share, at any time until the close of business on the fourth
trading day prior to the earlier of May 15, 2021 and the date on which the
Debenture is redeemed, if any of the following conditions are satisfied:

     - if the closing sale price of our ordinary shares is greater than 110% of
       the conversion price per ordinary share for at least 20 trading days of
       the 30 trading days prior to conversion,

     - if we have called Debentures for redemption, or

     - upon the occurrence of specified corporate transactions.

     We describe each of these conditions in greater detail below. Our ordinary
shares are described in the accompanying prospectus.

  Conversion Upon Satisfaction of Market Price Condition

     You may only surrender Debentures for conversion into our ordinary shares
if the closing sale price per ordinary share on the principal national
securities exchange on which the ordinary shares are listed exceeds 110% of the
conversion price per ordinary share for at least 20 trading days in a period of
30 consecutive trading days ending on the trading day immediately prior to the
conversion date. For purposes of this determination, the conversion price per
ordinary share as of any day equals the quotient of:

     - the principal amount of a Debenture, divided by

     - the number of our ordinary shares issuable upon conversion of that
       Debenture on that day.

     The conversion agent designated by us will, on our behalf, determine daily
if the Debentures are convertible as a result of the closing sale price of our
ordinary shares and will notify us accordingly.

  Conversion Upon Notice of Redemption

     If a Debenture has been called for redemption, you will be entitled to
convert the Debenture until close of business on the fourth trading day prior to
the date of redemption, even if it is not otherwise convertible at such time.
You may convert fewer than all of your Debentures so long as the Debentures
converted are an integral multiple of $1,000 principal amount.

                                       S-11
   12

  Conversion Upon Specified Corporate Transactions

     If we elect to:

     - distribute to all holders of our ordinary shares certain rights entitling
       them to purchase, for a period expiring within 60 days, ordinary shares
       at less than the quoted price of the ordinary shares at the time, or

     - distribute to all holders of our ordinary shares assets, debt securities
       or certain rights to purchase our securities, which distribution has a
       per share value exceeding 15% of the closing price of our ordinary shares
       on the day preceding the declaration date for such distribution,

we must notify the holders of Debentures at least 20 days prior to the
ex-dividend date for such distribution. Once we have given such notice, you may
surrender your Debentures for conversion at any time until the earlier of the
close of business on the business day immediately prior to the ex-dividend date
or our announcement that such distribution will not take place.

     In addition, if we are a party to a reclassification, consolidation, merger
or scheme of arrangement under Cayman Islands law, or a sale of all or
substantially all of our assets to another person, pursuant to which our
ordinary shares would be converted into cash, securities or other property, you
may surrender Debentures for conversion at any time from and after the date
which is 15 days prior to the date we announce as the anticipated effective date
of the transaction until 15 days after the actual date of such transaction. If
we are a party to a reclassification, consolidation, merger or scheme of
arrangement under Cayman Islands law, or a sale of all or substantially all of
our assets to another person, pursuant to which our ordinary shares are
converted into cash, securities or other property, then at the effective time of
the transaction, the right to convert a Debenture into our ordinary shares will
be changed into a right to convert it into the kind and amount of shares or
stock and other securities and property (including cash) receivable immediately
prior to the transaction by a holder of the number of ordinary shares
deliverable upon conversion of the Debenture. If the transaction also
constitutes a "change in control," as defined below, you can alternatively
require us to purchase all or a portion of your Debentures as described under
"Change in Control" below.

  Conversion Rate and Delivery of Ordinary Shares

     The initial conversion rate is 13.8627 ordinary shares for each Debenture.
This rate is equivalent to an initial conversion price of $72.136 per ordinary
share, based on the $1,000 principal amount per Debenture. Upon conversion we
will deliver to you a fixed number of ordinary shares and any cash payment to
account for fractional shares. The cash payment for fractional shares will be
based on the closing price of the ordinary shares on the trading day immediately
prior to the conversion date. We will not adjust the conversion price to account
for accrued and unpaid interest.

     The conversion rate will be subject to adjustment upon the following
events:

     - issuance of ordinary shares as a dividend or distribution on the ordinary
       shares,

     - subdivision or combination of the outstanding ordinary shares,

     - issuance to all ordinary shareholders of rights or warrants that allow
       the shareholders, for a period ending not more than 60 days after the
       record date for such issuance, to purchase ordinary shares at less than
       the current market price,

     - distribution to all ordinary shareholders of debt or other assets but
       excluding distributions of rights and warrants described above and
       all-cash distributions,

                                       S-12
   13

     - distribution to all or substantially all ordinary shareholders of
       all-cash distributions in an aggregate amount that together with (1) any
       cash and the fair market value of any other consideration payable in
       respect of any tender offer by us or any of our subsidiaries for ordinary
       shares consummated within the preceding 12 months not triggering a
       conversion price adjustment and (2) all other all-cash distributions to
       all or substantially all ordinary shareholders made within the preceding
       12 months not triggering a conversion price adjustment, exceeds an amount
       equal to 12.5% of the market capitalization of our ordinary shares on the
       business day immediately preceding the day on which we declare such
       distribution, and

     - purchase of ordinary shares pursuant to a tender offer made by us or any
       of our subsidiaries to the extent that the tender offer involves
       aggregate consideration that together with (1) any cash and the fair
       market value of any other consideration payable in respect of any tender
       offer by us or any of our subsidiaries for ordinary shares consummated
       within the preceding 12 months not triggering a conversion price
       adjustment and (2) any all-cash distributions to all or substantially all
       ordinary shareholders made within the preceding 12 months not triggering
       a conversion price adjustment, exceeds an amount equal to 12.5% of the
       market capitalization of our ordinary shares on the expiration date of
       such tender offer.

     We may increase the conversion rate as permitted by law for at least 20
days, so long as the increase is irrevocable during that period. We are not
required to adjust the conversion rate until adjustments greater than 1% have
occurred.

     If you submit your Debentures for conversion between the closing of
business on a record date and the opening of business on the next interest
payment date (except for Debentures or portions of Debentures called for
redemption on a redemption date occurring during this period), you must pay
funds equal to the interest payable on the converted principal amount, but we
will pay the interest payable on that interest payment date to the holder of
Debentures on that record date.

REDEMPTION RIGHTS

     We may redeem all or part of the Debentures at our option at any time after
May 20, 2006, upon not less than 20 nor more than 60 days' notice by mail to
holders of Debentures. The redemption price will be equal to 100% of the
principal amount plus accrued and unpaid interest up to but not including the
redemption date.

     If we decide to redeem fewer than all of the outstanding Debentures, the
trustee will select the Debentures to be redeemed by lot, pro rata or by another
method the trustee considers fair and appropriate.

     If the trustee selects a portion of your Debentures for partial redemption
and you convert a portion of the same Debentures, the converted portion will be
deemed to be from the portion selected for redemption.

REPURCHASE RIGHTS

     You have the right to require us to repurchase the Debentures on May 15,
2006, May 15, 2011 and May 15, 2016. We will be required to repurchase any
outstanding Debenture for which you deliver a written repurchase notice to the
paying agent designated by us. This notice must be delivered during the period
beginning at the opening of business on the date that is 20 business days prior
to the repurchase date and ending on the close of business on the repurchase
date. If a repurchase notice has been given but is subsequently withdrawn during
that period, we will not be obligated to repurchase the related Debentures. Our
repurchase obligation will be subject to certain additional conditions described
below.

     The repurchase price payable by us will be equal to the principal amount
plus accrued and unpaid interest up to and including the repurchase date.
Because each repurchase date is on an interest payment date, interest will be
paid to the record holder on the relevant record date.

     We may, at our option, choose to pay the repurchase price in cash or our
ordinary shares, or any combination of cash and our ordinary shares. For a
discussion of the tax treatment of a holder receiving cash, ordinary shares or
any combination of both, see "Certain United States Federal Income Tax
Considerations -- U.S. Holders."

                                       S-13
   14

     We will be required to give notice on a date not less than 20 business days
prior to each repurchase date to all holders of Debentures at their addresses
shown in the register maintained by the registrar under the indenture, and to
beneficial owners as required by applicable law, stating among other things:

     - whether we will pay the repurchase price of the Debentures in cash or
       ordinary shares or any combination of both, specifying the percentages of
       each,

     - if we elect to pay in ordinary shares the method of calculating the
       market price of the ordinary shares, and

     - the procedures that holders must follow to require us to repurchase their
       Debentures.

     Your notice electing to require us to repurchase your Debentures must
state:

     - if certificated Debentures have been issued, the Debenture certificate
       numbers, or if no certificated Debentures have been issued, your notice
       must comply with appropriate Depository Trust Company procedures,

     - the portion of the principal amount of Debentures to be repurchased, in
       multiples of $1,000,

     - that the Debentures are to be repurchased by us pursuant to the
       applicable provisions of the senior indenture, and

     - in the event that we choose, pursuant to the notice that we are required
       to give, to pay the repurchase price in our ordinary shares, in whole or
       in part, but the repurchase price is ultimately to be paid to the holder
       of Debentures entirely in cash because any of the conditions to payment
       of the repurchase price or portion of the repurchase price in ordinary
       shares is not satisfied prior to the close of business on the repurchase
       date, as described below, whether the holder elects:

          (1) to withdraw the repurchase notice as to some or all of the
     Debentures to which it relates, or

          (2) to receive cash in respect of the entire repurchase price for all
     Debentures or portions of Debentures to which such repurchase notice
     relates.

     If the holder fails to indicate the holder's choice with respect to the
election described in the final bullet point above, the holder will be deemed to
have elected to receive cash in respect of the entire repurchase price for all
Debentures subject to the repurchase notice in the circumstances described. For
a discussion of the tax treatment of a holder receiving cash instead of ordinary
shares, see "Certain United States Federal Income Tax Considerations -- U.S.
Holders -- Sale, Exchange or Retirement of the Debentures."

     You may withdraw any repurchase notice by a written notice of withdrawal
delivered to the paying agent prior to the close of business on the repurchase
date. The notice of withdrawal must state:

     - the principal amount of the withdrawn Debentures,

     - if certificated Debentures have been issued, the certificate numbers of
       the withdrawn Debentures, or if no certificated Debentures have been
       issued, your notice must comply with appropriate Depository Trust Company
       procedures, and

     - the principal amount, if any, which remains subject to the repurchase
       notice.

     If we choose to pay the repurchase price, in whole or in part, in our
ordinary shares, the number of ordinary shares to be delivered by us will be
equal to the portion of the repurchase price to be paid in ordinary shares
divided by the market price of one ordinary share.

     We will pay cash for all fractional ordinary shares in the event that we
choose to deliver our ordinary shares in payment, in whole or in part, of the
repurchase price. This cash payment will be based on the market price of our
ordinary shares.

     The "market price" means the average of the sale prices of our ordinary
shares for the five trading day period ending on the third business day prior to
the applicable repurchase date (or if the third business day prior

                                       S-14
   15

to the applicable repurchase date is not a trading day, then on the last trading
day prior to the third business day), appropriately adjusted to take into
account the occurrence, during the period commencing on the first of such
trading days during such five trading day period and ending on such repurchase
date, of certain events that would result in an adjustment of the conversion
rate with respect to the ordinary shares.

     The "sale price" of the ordinary shares on any date means the closing sale
price per ordinary share (or if no closing sale price is reported, the average
of the closing bid and ask prices or, if more than one in either case, the
average of the average closing bid and the average closing ask prices) on such
date as reported in composite transactions for the principal U.S. securities
exchange on which our ordinary shares are traded or, if the ordinary shares are
not listed on a U.S. national or regional securities exchange, as reported by
the Nasdaq system.

     Because the market price of our ordinary shares is determined prior to the
applicable repurchase date, holders of Debentures bear the market risk with
respect to the value of the ordinary shares to be received from the date such
market price is determined to such repurchase date. We may pay the repurchase
price or any portion of the repurchase price in ordinary shares only if the
information necessary to calculate the market price is published in a daily
newspaper of national circulation.

     Upon determination of the actual number of ordinary shares in accordance
with the foregoing provisions, we will publish such information on our web site
on the World Wide Web or through such other public medium as we may use at that
time.

     Our right to repurchase Debentures, in whole or in part, with our ordinary
shares is subject to our satisfying various conditions, including:

     - the registration of our ordinary shares under the Securities Act of 1933
       and the Securities Exchange Act of 1934, if required, and

     - any necessary qualification or registration under applicable state
       securities law or the availability of an exemption from such
       qualification and registration.

     If these conditions are not satisfied with respect to a holder prior to the
close of business on the repurchase date, we will pay the repurchase price of
the Debentures of the holder entirely in cash. See "Certain United States
Federal Income Tax Considerations -- U.S. Holders -- Sale, Exchange or
Retirement of the Debentures." We may not change the form or components or
percentages of components of consideration to be paid for the Debentures once we
have given the notice that we are required to give to holders of Debentures,
except under circumstances where we are required by the indenture to pay cash
instead of our ordinary shares.

     Our ability to repurchase Debentures with cash at any time may be limited
by the terms of our then existing borrowing agreements. The indenture will
prohibit us from repurchasing Debentures for cash in connection with the
holders' repurchase rights if any event of default under the indenture has
occurred and is continuing, except for a default in the payment of the
repurchase price with respect to the Debentures.

     In order to receive payment of the repurchase price, a holder must either
effect a book-entry transfer or deliver the corresponding Debenture or
Debentures, together with necessary endorsements, to the office of the paying
agent, after delivery of the repurchase notice. You will receive payment in cash
promptly after the later of (1) the repurchase date or (2) the time of
book-entry transfer or the delivery of the Debenture. If the paying agent holds
money or securities sufficient to pay the repurchase price of the Debenture on
the repurchase date, then:

     - the Debenture will cease to be outstanding,

     - interest will cease to accrue, and

     - all other rights of the holder will terminate.

     This will be the case whether or not a book-entry transfer is effected or
whether or not the Debenture or Debentures are delivered to the paying agent.

                                       S-15
   16

     We will comply with the provisions of Rule 13e-4 and any other tender offer
rules under the Securities Exchange Act of 1934 which may be applicable at the
time. We will file Schedule TO or any other schedule required in connection with
any offer by us to repurchase the Debentures at your option.

CHANGE IN CONTROL

     If we undergo a change in control after the first issuance of the
Debentures, you will have the option to require us to purchase your Debentures
within 35 business days after the change in control. We will pay a purchase
price equal to 100% of the principal amount of your Debentures plus accrued and
unpaid interest up to but not including the date of purchase. You may require us
to purchase all or any part of the Debentures so long as the principal amount at
maturity of the Debentures being purchased is an integral multiple of $1,000.

     A change in control occurs in the following situations:

     - any person or group (1) becomes the beneficial owner of our voting shares
       representing 50% or more of the total voting power of all of our
       outstanding classes of voting shares or (2) has the power, directly or
       indirectly, to elect a majority of the members of our board of directors
       (but specifically excluding rights to designate directors pursuant to the
       agreement implementing the Sedco Forex merger),

     - we consolidate with or merge with or into another person, we sell,
       assign, convey, transfer, lease or otherwise dispose of all or
       substantially all of our assets, any person consolidates with or merges
       with or into our company or we complete a scheme of arrangement under
       Cayman Islands law with any person, but none of these circumstances will
       constitute a change in control if the persons that beneficially own our
       voting shares immediately prior to the relevant transaction beneficially
       own shares with a majority of the total voting power of all outstanding
       voting shares of the surviving or transferee person, or

     - our company liquidates or dissolves.

     In order to exercise your repurchase right in the case of a change in
control, you must deliver a written notice to the paying agent prior to the
close of business on the business day prior to the date on which the Debentures
are to be purchased. This notice must specify the Debentures submitted for
repurchase. You may withdraw this notice by delivering a written notice of
withdrawal to the paying agent before the same date.

     Within 15 business days after a change in control, we will mail to the
trustee and to each holder of the Debentures a written notice of the change in
control which specifies the terms and conditions and the procedures required for
exercise of a holder's right to require us to purchase your Debentures.

     For purposes of defining a change of control:

     - the terms "person" and "group" have the meanings given to them in
       Sections 13(d) and 14(d) of the Securities Exchange Act of 1934 or any
       successor provisions,

     - the term "group" includes any group acting for the purpose of acquiring,
       holding or disposing of securities within the meaning of Rule 13d-5(b)(1)
       under the Securities Exchange Act of 1934 or any successor provision, and

     - the term "beneficial owner" is determined in accordance with Rule 13d-3
       under the Securities Exchange Act of 1934, as in effect on the date of
       this prospectus supplement.

TAX ADDITIONAL AMOUNTS

     We will pay any amounts due with respect to the Debentures without
deduction or withholding for any and all present and future withholding taxes,
levies, imposts and charges (a "withholding tax") imposed by or for the account
of the Cayman Islands. If the Cayman Islands require us to deduct or withhold
any of these taxes, levies, imposts or charges, we will (subject to compliance
by the holder of a Debenture with any relevant administrative requirements) pay
these additional amounts in respect of principal amount, redemption price,
repurchase price and interest (if any), in accordance with the terms of the
Debentures and the indenture, as may be necessary so that the net amounts paid
to the holder or the trustee after such deduction or withholding will equal the
principal

                                       S-16
   17

amount, redemption price, repurchase price and interest (if any), on the
Debentures. However, we will not pay any additional amounts in the following
instances:

     - if any withholding would not be payable or due but for the fact that (1)
       the holder of a Debenture (or a fiduciary, settlor, beneficiary of,
       member or shareholder of, the holder, if the holder is an estate, trust,
       partnership or corporation), is a domiciliary, national or resident of,
       or engaging in business or maintaining a permanent establishment or being
       physically present in, the Cayman Islands or otherwise having some
       present or former connection with the Cayman Islands other than the
       holding or ownership of the Debenture or the collection of principal
       amount, redemption price, repurchase price and interest (if any), in
       accordance with the terms of the Debentures and the indenture, or the
       enforcement of the Debenture or (2) where presentation is required, the
       Debenture was presented more than 30 days after the date such payment
       became due or was provided for, whichever is later,

     - if any withholding tax is attributable to any estate, inheritance, gift,
       sales, transfer, excise, personal property or similar tax, levy, impost
       or charge,

     - if any withholding tax is attributable to any tax, levy, impost or charge
       which is payable otherwise than by withholding from payment of principal
       amount, redemption price, repurchase price and interest (if any),

     - if any withholding tax would not have been imposed but for the failure to
       comply with certification, information, documentation or other reporting
       requirements concerning the nationality, residence, identity or
       connections with the relevant tax authority of the holder or beneficial
       owner of the Debenture, if this compliance is required by statute or by
       regulation as a precondition to relief or exemption from such withholding
       tax, or

     - any combination of the instances described in the preceding bullet
       points.

     We also will not pay any additional amounts to any holder who is a
fiduciary or partnership or other than the sole beneficial owner of the
Debenture to the extent that a beneficiary or settlor with respect to such
fiduciary, or a member or such partnership or a beneficial owner thereof, would
not have been entitled to the payment of such additional amounts had such
beneficiary settlor, member or beneficial owner been the holder of the
Debenture.

COVENANTS RELATING TO THE DEBENTURES

     The Debentures will be entitled to the benefit of covenants included in the
indenture regarding limitations on liens and limitations on sale and lease-back
transactions as described under "Description of Debt Securities -- Provisions
Applicable Solely to Senior Debt Securities" in the accompanying prospectus.

CONVERSION AGENT/PAYING AGENT

     We have designated the trustee as conversion agent and paying agent for the
Debentures.

BOOK-ENTRY SYSTEM

     The Debentures will be represented by one or more global securities. A
global security is a special type of indirectly held security. Each global
security will be deposited with, or on behalf of, The Depository Trust Company
("DTC") and be registered in the name of a nominee of DTC. Except under the
circumstances described below, the Debentures will not be issued in definitive
form in the name of individual holders.

     Upon the issuance of a global security, DTC will credit on its book-entry
registration and transfer system the accounts of persons designated by the
initial purchaser with the respective principal amounts of the Debentures
represented by the global security. Ownership of beneficial interests in a
global security will be limited to DTC participants (i.e., persons that have
accounts with DTC or its nominee) or persons that may hold interests through DTC
participants. Ownership of beneficial interests in a global security will be
shown on, and the transfer of that ownership will be effected only through,
records maintained by DTC or its nominee (except with respect to persons that
are themselves DTC participants).

                                       S-17
   18

     So long as DTC or its nominee is the registered owner of a global security,
DTC or the nominee will be considered the sole owner or holder of the Debentures
represented by that global security under the indenture. Except as described
below, owners of beneficial interests in a global security will not be entitled
to have Debentures represented by that global security registered in their
names, will not receive or be entitled to receive physical delivery of
Debentures in definitive form and will not be considered the owners or holders
of the Debentures under the indenture. Principal and interest payments on
Debentures registered in the name of DTC or its nominee will be made to DTC or
the nominee, as the registered owner. Neither our company, the trustee, any
paying agent or the registrar for the Debentures will have any responsibility or
liability for any aspect of the records relating to or payments made on account
of beneficial interests in a global security or for maintaining, supervising or
reviewing any records relating to such beneficial interests. The laws of some
states require that certain purchasers of securities take physical delivery of
such securities in definitive form. Those limits and laws may impair the ability
to transfer beneficial interests in a global security.

     We expect that DTC or its nominee, upon receipt of any payment of principal
or interest, will credit immediately the participants' accounts with payments in
amounts proportionate to their beneficial interests in the principal amount of
the relevant global security as shown on the records of DTC or its nominee. We
also expect that payments by participants to owners of beneficial interests in a
global security held through those participants will be governed by standing
instructions and customary practices, as is the case with securities held for
the accounts of customers in bearer form or registered in "street name," and
will be the responsibility of those participants.

     If DTC is at any time unwilling or unable to continue as a depositary and a
successor depositary is not appointed by us within 90 days, we will issue
Debentures in definitive form in exchange for the entire global security for the
Debentures. In addition, we may at any time choose not to have Debentures
represented by a global security and will then issue Debentures in definitive
form in exchange for the entire global security relating to the Debentures. In
any such instance, an owner of a beneficial interest in a global security will
be entitled to physical delivery in definitive form of Debentures represented by
the global security equal in principal amount to that beneficial interest and to
have the Debentures registered in its name. Debentures so issued in definitive
form will be issued as registered Debentures in denominations of $1,000 and
integral multiples thereof, unless otherwise specified by us.

            CERTAIN UNITED STATES FEDERAL INCOME TAX CONSIDERATIONS

     The following is a description of the material U.S. federal income tax
considerations relating to the purchase, ownership and disposition of the
Debentures or ordinary shares to initial purchasers of the Debentures who are
U.S. holders (as described below), and the material U.S. federal income and
estate tax considerations relating to the purchase, ownership and disposition of
the Debentures or ordinary shares to initial purchasers who are non-U.S. holders
(as described below). This discussion does not address all tax considerations
that may be important to you in light of your particular circumstances (such as
the alternative minimum tax provisions) or under certain special rules. Special
rules may apply, for instance, to banks, tax-exempt organizations, dealers in
securities or currencies, persons who hold Debentures or ordinary shares as part
of a hedge, conversion or constructive sale transaction, or straddle or other
risk reduction transaction, traders in securities that elect to use a
mark-to-market method of accounting for their securities holdings, persons whose
functional currency for tax purposes is not the U.S. dollar, U.S. holders who
own or have previously owned, actually or constructively, stock possessing 5% or
more of the voting power or value of our Company, or persons who have ceased to
be United States citizens or to be taxed as resident aliens. This discussion is
limited to holders of Debentures or our ordinary shares who purchase the
Debentures at their "issue price" and hold the Debentures and any ordinary
shares into which the Debentures are converted or for which the Debentures are
exchanged as capital assets. For this purpose only, the "issue price" of the
Debentures is the first price at which a substantial portion of the Debentures
is sold to the public (not including sales to underwriters or placement agents).
Except as described below with respect to certain Cayman Islands tax
consequences, this discussion also does not address the tax consequences arising
under the laws of any foreign, state or local jurisdiction.

                                       S-18
   19

     This discussion is based upon the Internal Revenue Code of 1986, as amended
(the "Code"), its legislative history, existing and proposed U.S. Treasury
regulations, and judicial decisions and administrative interpretations
thereunder, as of the date hereof, all of which are subject to change or
different interpretations, possibly with retroactive effect. We cannot assure
you that the Internal Revenue Service (the "IRS") will not challenge one or more
of the tax results described herein, and we have not obtained, nor do we intend
to obtain, a ruling from the IRS with respect to the U.S. federal tax
consequences of acquiring, holding or disposing of the Debentures or our
ordinary shares.

     PLEASE CONSULT YOUR OWN TAX ADVISORS AS TO THE PARTICULAR TAX CONSEQUENCES
TO YOU OF ACQUIRING, HOLDING, CONVERTING OR OTHERWISE DISPOSING OF THE
DEBENTURES AND ORDINARY SHARES, INCLUDING THE EFFECT AND APPLICABILITY OF STATE,
LOCAL OR FOREIGN TAX LAWS.

U.S. HOLDERS

     You are a U.S. holder for purposes of this discussion if you are a holder
of a Debenture or an ordinary share that is, for U.S. federal income tax law
purposes:

     - a citizen or resident of the United States,

     - a corporation organized in or under the laws of the United States or of
       any political subdivision thereof,

     - an estate the income of which is subject to U.S. federal income taxation
       regardless of its source, or

     - a trust if a U.S. court can exercise primary supervision over the trust's
       administration and one or more U.S. persons are authorized to control all
       substantial decisions of the trust.

In the case of a holder of a Debenture or an ordinary share which is a
partnership, the tax consequences will generally affect the partner rather than
the partnership, but special considerations not here set forth may apply.

     Taxation of Interest.  In general, you will be required to include interest
received on a Debenture as ordinary income at the time it accrues or is
received, in accordance with your regular method of accounting for U.S. federal
income tax purposes.

     Sale, Exchange or Retirement of the Debentures.  Upon the sale, exchange or
retirement of a Debenture (other than a conversion or exchange for ordinary
shares), you will recognize gain or loss equal to the difference between the
sale or redemption proceeds and your adjusted tax basis in the Debenture. Your
adjusted tax basis in a Debenture will generally equal your cost for the
Debenture. Gain or loss realized on the sale, exchange or retirement of a
Debenture will generally be capital gain or loss and will be long-term capital
gain or loss if the Debenture is held for more than one year. You should consult
your tax advisors regarding the treatment of capital gains (which may be taxed
at lower rates than ordinary income for taxpayers who are individuals) and
losses (the deductibility of which is subject to limitations). Payments for
accrued interest not previously included in income will be treated as ordinary
interest income.

     Conversion of Debentures.  The conversion of a Debenture into our ordinary
shares will generally not be a taxable event, except with respect to cash
received in lieu of a fractional share. Your basis in the ordinary shares
received on conversion of a Debenture will be the same as your basis in the
Debenture at the time of conversion (exclusive of any tax basis allocable to a
fractional share), and your holding period for the ordinary shares received on
conversion will include the holding period of the Debenture converted. The
receipt of cash in lieu of a fractional ordinary share will generally result in
capital gain or loss (measured by the difference between the cash received for
the fractional share interest and your tax basis in the fractional share
interest).

     Exercise of Repurchase Right.  If you require us to repurchase a Debenture
on a repurchase date and if we issue ordinary shares in full satisfaction of the
purchase price, the exchange of a Debenture for ordinary shares will be treated
the same as a conversion. If you require us to repurchase a Debenture on a
repurchase date and if we deliver cash in full satisfaction of the purchase
price, the exchange of a Debenture for cash will be treated the same as a sale,
exchange or retirement. If you require us to repurchase a Debenture on a
repurchase date and if we deliver a combination of cash and ordinary shares in
payment of the purchase price, then, in general, (1) you
                                       S-19
   20

will recognize gain (but not loss) to the extent that the cash and the value of
the ordinary shares exceeds your adjusted tax basis in the Debenture, but in no
event will the amount of recognized gain exceed the amount of cash received, (2)
your basis in the ordinary shares received will be the same as your basis in the
Debenture repurchased by us (exclusive of any basis allocable to a fractional
share), decreased (but not below zero) by the amount of cash received (other
than cash received in lieu of a fractional share), and increased by the amount
of gain, if any, recognized by you (other than gain with respect to a fractional
share), and (3) the holding period of the ordinary shares received in the
exchange will include the holding period for the Debenture which was
repurchased. Payments for accrued interest not previously included in income
will be treated as ordinary interest income.

     Adjustment of Conversion Rate.  If at any time we make a distribution of
property to shareholders that would be taxable to such shareholders as a
dividend for federal income tax purposes (for example, distributions of cash,
evidences of our indebtedness or assets, but generally not share dividends or
rights to subscribe for ordinary shares) and, pursuant to the anti-dilution
provisions of the senior indenture, the conversion rate of the Debentures is
increased, such increase may be deemed to be the payment of a taxable dividend
to you. If the conversion rate is increased at our discretion or in certain
other circumstances, such increase also may be deemed to be the payment of a
taxable dividend to you.

     Ownership and Disposition of Ordinary Shares.  Dividends, if any, paid on
the ordinary shares generally will be includable in your income as ordinary
income to the extent of your ratable share of our current or accumulated
earnings and profits. Upon the sale, exchange or other disposition of ordinary
shares, you generally will recognize capital gain or capital loss equal to the
difference between the amount realized on such sale or exchange and your
adjusted tax basis in such shares. You should consult your tax advisors
regarding the treatment of capital gains (which may be taxed at lower rates than
ordinary income for taxpayers who are individuals) and losses (the deductibility
of which is subject to limitations).

     Status of Transocean Sedco Forex as a Foreign Corporation.  Special
considerations apply by reason of the fact that we are a foreign corporation.
These include the following:

     - We do not expect that dividends on our ordinary shares will be eligible
       for the dividends received deduction which is generally allowed to U.S.
       corporate shareholders on dividends received from a domestic corporation.

     - If we were classified as a "passive foreign investment company," there
       could be various adverse consequences to U.S. holders of Debentures and
       ordinary shares, including taxation of gain on a sale or other
       disposition of the Debentures or ordinary shares at ordinary income
       rates, imposition of an interest charge on distributions to U.S. holders
       and on gain on dispositions, and the requirement that gain be recognized
       on dispositions which would otherwise qualify for nonrecognition
       treatment. We believe that we will not be a passive foreign investment
       company following the offering of the Debentures, but the tests for
       determining passive foreign investment company status are applied
       annually, and it is difficult accurately to predict future income and
       assets relevant to this determination. If we should determine in the
       future that we are a passive foreign investment company, we will endeavor
       to notify U.S. holders, although there can be no assurance that we will
       be able to do so in a timely manner. U.S. holders should consult their
       own tax advisors about the passive foreign investment company rules,
       including elections which are available with respect to passive foreign
       investment companies.

                                       S-20
   21

NON-U.S. HOLDERS

     You are a Non-U.S. holder for purposes of this discussion if you are a
holder of a Debenture or an ordinary share that is not a U.S. person for U.S.
federal income tax purposes.

     Withholding Tax on Payments of Principal and Interest on Debentures.  As
long as we are not engaged in the conduct of any trade or business in the United
States, the payment of principal and interest on a Debenture by us or any paying
agent of ours to you will not be subject to U.S. federal withholding tax. Even
if we were engaged in the conduct of a trade or business in the U.S., payments
would not be subject to U.S. federal withholding tax, provided that in the case
of payment of interest:

     - you do not actually or constructively own 10% or more of the total
       combined voting power of all classes of our shares,

     - you are not a controlled foreign corporation that is related to us within
       the meaning of the Code, and

     - the U.S. payor does not have actual knowledge or reason to know that you
       are a U.S. person and either (1) the beneficial owner of the Debenture
       certifies to the applicable payor or its agent, under penalties of
       perjury, that it is not a U.S. holder and provides its name and address
       on U.S. Treasury Form W-8 BEN (or a suitable substitute form), or (2) a
       securities clearing organization, bank or other financial institution,
       that holds customers' securities in the ordinary course of its trade or
       business (a "financial institution") and holds the Debenture, certifies
       under penalties of perjury that a Form W-8 BEN (or a suitable substitute
       form) has been received from the beneficial owner by it or by a financial
       institution between it and the beneficial owner and furnishes the payor
       with a copy of the form or the U.S. payor otherwise possesses
       documentation upon which it may rely to treat the payment as made to a
       non-U.S. person in accordance with U.S. Treasury regulations.

     Except to the extent otherwise provided under an applicable tax treaty, you
generally will be taxed in the same manner as a U.S. holder with respect to
interest on a Debenture if such interest is effectively connected with a U.S.
trade or business of yours. Effectively connected interest received by a
corporate Non-U.S. holder may also, under certain circumstances, be subject to
an additional "branch profits tax" at a 30% rate (or, if applicable, a lower
treaty rate), subject to certain adjustments. Such effectively connected
interest will not be subject to withholding tax if the holder delivers the
appropriate form (currently a Form W-8 ECI) to the payor.

     Dividends.  While the matter may not be entirely free from doubt, we do not
anticipate that dividends paid on the ordinary shares to you will be subject to
U.S. federal withholding tax. Except to the extent otherwise provided under an
applicable tax treaty, you generally will be taxed in the same manner as a U.S.
holder on dividends paid (or deemed paid) that are effectively connected with
your conduct of a trade or business in the United States. If you are a foreign
corporation, you may also be subject to a U.S. branch profits tax on such
effectively connected income at a 30% rate or such lower rate as may be
specified by an applicable income tax treaty, subject to certain adjustments.

     Gain on Disposition of the Debentures and Ordinary Shares.  You generally
will not be subject to U.S. federal income tax on gain realized on the sale,
exchange or redemption of a Debenture, including the exchange of a Debenture for
ordinary shares, or the sale or exchange of ordinary shares unless:

     - you are an individual present in the United States for 183 days or more
       in the year of such sale, exchange or redemption and either (A) you have
       a "tax home" in the United States and certain other requirements are met
       or (B) the gain from the disposition is attributable to an office or
       other fixed place of business maintained by you in the United States, or

     - the gain is effectively connected with your conduct of a U.S. trade or
       business.

     However, in some instances you may be required to establish an exemption
from United States federal income and withholding tax. See "-- Withholding Tax
on Payments of Principal and Interest on Debentures."

                                       S-21
   22

     U.S. Federal Estate Tax.  A Debenture or ordinary shares held by an
individual who at the time of death is not a citizen or resident of the United
States (as specially defined for U.S. federal estate tax purposes) will not be
subject to U.S. federal estate tax.

BACKUP WITHHOLDING AND INFORMATION REPORTING

     U.S. Holders.  Payments of interest or dividends made by us on, or the
proceeds of the sale or other disposition of, the Debentures or our ordinary
shares may be subject to information reporting and U.S. federal backup
withholding tax at the rate of 31% if the recipient of those payments fails to
supply an accurate taxpayer identification number or otherwise fails to comply
with applicable United States information reporting or certification
requirements. Any amount withheld from a payment to a U.S. holder under the
backup withholding rules is allowable as a credit against the holder's federal
income tax, provided that the required information is furnished to the IRS.

     Non-U.S. Holders.  Non-U.S. holders of Debentures or ordinary shares should
consult their tax advisers regarding the application of information reporting
and backup withholding in their particular situations, the availability of
exemptions and the procedure for obtaining such an exemption, if available. Any
amount withheld from a payment to a non-U.S. holder under the backup withholding
rules is allowable as a credit against the holder's federal income tax, provided
that the required information is furnished to the IRS.

                        CAYMAN ISLANDS TAX CONSEQUENCES

     According to our Cayman Islands counsel, Walkers, there is currently no
Cayman Islands income or profits tax, withholding tax, capital gains tax,
capital transfer tax, estate duty or inheritance tax payable by a holder in
respect of any income, gain or loss derived from holding Debentures or ordinary
shares. We have obtained an undertaking from the Governor-in-Council of the
Cayman Islands under the Tax Concession Law (1995 Revision) that, in the event
that any legislation is enacted in the Cayman Islands imposing tax computed on
profits or income, or computed on any capital assets, gain or appreciation, or
any tax in the nature of estate duty or inheritance tax, that tax will not until
June 1, 2019 apply to us or to any of our operations or our shares, notes,
debentures or other obligations. Therefore, there should be no Cayman Islands
tax consequences with respect to holding Debentures or ordinary shares; however,
if Debentures are taken into the Cayman Islands in original form, they will be
subject to stamp duty in the amount of 1/4 of 1% of the face value thereof,
subject to a maximum of CI$250.00 per Debenture.

                                       S-22
   23

                                  UNDERWRITING

     Under the terms and subject to the conditions contained in an underwriting
agreement dated May 8, 2001, we have agreed to sell to Credit Suisse First
Boston Corporation all of the Debentures.

     The underwriting agreement provides that the underwriter is obligated to
purchase all of the Debentures if any are purchased.

     The underwriter proposes to offer the Debentures initially at the public
offering price on the cover page of this prospectus supplement and to selling
group members at that price less a concession of $9.00 per Debenture. After the
initial public offering the underwriter may change the public offering price and
concession.

     We estimate that our out of pocket expenses for this offering will be
approximately $400,000.

     The Debentures are a new issue of securities with no established trading
market. The underwriter intends to make a secondary market for the Debentures.
However, it is not obligated to do so and may discontinue making a secondary
market for the Debentures at any time without notice. No assurance can be given
as to how liquid the trading market for the Debentures will be.

     We have agreed to indemnify the underwriter against liabilities under the
Securities Act, or contribute to payments which the underwriter may be required
to make in that respect.

     We have agreed that we will not offer, sell, contract to sell, pledge or
otherwise dispose of, or file with the Securities and Exchange Commission a
registration statement under the Securities Act of 1933 relating to, any
additional ordinary shares or securities convertible into or exchangeable or
exercisable for any ordinary shares, or publicly disclose our intention to make
any such offer, sale, pledge, disposition or filing, without the prior written
consent of the underwriter for a period of 90 days after the date of this
prospectus supplement. We may, however, make grants of employee or director
stock options, stock appreciation rights or restricted stock grants under the
terms of an existing plan, issue ordinary shares upon the exercise of such
options or the exercise or conversion of any other options, warrants or
convertible securities currently outstanding or under our savings plan. We may
also take any of these actions in connection with any merger or acquisition. The
underwriter may waive these restrictions in its sole discretion at any time
without public notice.

     In connection with the offering the underwriter may engage in stabilizing
transactions and over-allotment in accordance with Regulation M under the
Securities Exchange Act of 1934.

     - Stabilizing transactions permit bids to purchase the Debentures or the
       underlying ordinary shares so long as the stabilizing bids do not exceed
       a specified maximum.

     - Over-allotment involves sales by the underwriter in excess of the
       principal amount of the Debentures the underwriter is obligated to
       purchase, which creates a short position.

These stabilizing transactions may have the effect of raising or maintaining the
market price of the Debentures or preventing or retarding a decline in the
market price of the Debentures. As a result, the price of the Debentures may be
higher than the price that might otherwise exist in the open market. These
transactions, if commenced, may be discontinued at any time.

     The underwriter and its affiliates regularly engage in various general
banking, financing and/or investment banking transactions with us and our
affiliates. An affiliate of the underwriter is a lender under our five-year
revolving credit facility. A portion of the proceeds of this offering will be
used to repay commercial paper indebtedness, a portion of the proceeds of which
were used to repay amounts outstanding under that facility.

                                       S-23
   24

                          NOTICE TO CANADIAN RESIDENTS

RESALE RESTRICTIONS

     The distribution of the Debentures in Canada is being made only on a
private placement basis exempt from the requirement that we prepare and file a
prospectus with the securities regulatory authorities in each province where
trades of Debentures are made. Any resale of the Debentures in Canada must be
made under applicable securities laws which will vary depending on the relevant
jurisdiction and which may require resales to be made in accordance with
available statutory exemptions or under a discretionary exemption granted by the
applicable Canadian securities regulatory authority. Purchasers are advised to
seek legal advice prior to any resale of the Debentures or, if applicable, the
ordinary shares.

REPRESENTATIONS OF PURCHASERS

     By purchasing Debentures in Canada and accepting a purchase confirmation, a
purchaser is representing to us and the dealer from whom such purchase
confirmation is received that:

     - the purchaser is entitled under applicable provincial securities laws to
       purchase the Debentures without the benefit of a prospectus qualified
       under such securities laws,

     - where required by law, the purchaser is purchasing as principal and not
       as agent, and

     - the purchaser has reviewed the text above under Resale Restrictions.

RIGHTS OF ACTION (ONTARIO PURCHASERS)

     The securities being offered are those of a foreign issuer and Ontario
purchasers will not receive the contractual right of action prescribed by
Ontario securities law. As a result, Ontario purchasers must rely on other
remedies that may be available, including common law rights of action for
damages or rescission or rights of action under the civil liability provisions
of the U.S. federal securities laws.

ENFORCEMENT OF LEGAL RIGHTS

     All of the issuer's directors and officers as well as the experts named
herein may be located outside of Canada and, as a result, it may not be possible
for Canadian purchasers to effect service of process within Canada upon the
issuer or such persons. All or a substantial portion of the assets of the issuer
and such persons may be located outside of Canada and, as a result, it may not
be possible to satisfy a judgment against the issuer or such persons in Canada
or to enforce a judgment obtained in Canadian courts against such issuer or
persons outside of Canada.

NOTICE TO BRITISH COLUMBIA RESIDENTS

     A purchaser of Debentures to whom the Securities Act (British Columbia)
applies is advised that the purchaser is required to file with the British
Columbia Securities Commission a report within ten days of the sale of any
Debentures and, if applicable, the ordinary shares acquired by the purchaser in
this offering. The report must be in the form attached to British Columbia
Securities Commission Blanket Order BOR #95/17, a copy of which may be obtained
from us. Only one report must be filed in respect of Debentures acquired on the
same date and under the same prospectus exemption.

TAXATION AND ELIGIBILITY FOR INVESTMENT

     Canadian purchasers of Debentures should consult their own legal and tax
advisors with respect to the tax consequences of an investment in the Debentures
in their particular circumstances and about the eligibility of the Debentures
and, if applicable, the ordinary shares for investment by the purchaser under
relevant Canadian legislation.

                                       S-24
   25

                                 LEGAL MATTERS

     Certain legal matters in connection with the Debentures offered by this
prospectus supplement and the accompanying prospectus will be passed upon for us
by our general counsel, Eric B. Brown, Esq., and by our outside counsel, Baker
Botts L.L.P., Houston, Texas. Walkers, Cayman Islands will pass upon certain
matters for us relating to Cayman Islands law. Sullivan & Cromwell, New York,
New York, will pass upon certain legal matters for the underwriter.

                                       S-25
   26

PROSPECTUS

                                 $2,000,000,000

                               [TRANSOCEAN LOGO]

                                DEBT SECURITIES
                               PREFERENCE SHARES
                                ORDINARY SHARES
                                    WARRANTS

     We may offer from time to time our

     - unsecured debt securities, which may be either senior or subordinated and
       may be convertible into or exchangeable for our preference shares,
       ordinary shares or other debt securities,

     - preference shares, which may be convertible into or exchangeable for our
       debt securities, ordinary shares or other preference shares,

     - ordinary shares, and

     - warrants to purchase debt securities, preference shares, ordinary shares
       or other securities.

     The aggregate initial offering price of the securities that we offer will
not exceed $2,000,000,000. We will offer the securities in amounts, at prices
and on terms to be determined at the time of our offering.

     We will provide the specific terms of the securities in supplements to this
prospectus. You should read this prospectus and any supplement carefully before
you invest.

NEITHER THE SECURITIES AND EXCHANGE COMMISSION NOR ANY STATE SECURITIES
COMMISSION HAS APPROVED OR DISAPPROVED OF THESE SECURITIES OR DETERMINED IF THIS
PROSPECTUS IS TRUTHFUL OR COMPLETE. ANY REPRESENTATION TO THE CONTRARY IS A
CRIMINAL OFFENSE.

                 The date of this prospectus is April 12, 2001
   27

                               TABLE OF CONTENTS


                                                           
About This Prospectus.......................................    1
Forward-Looking Statements..................................    1
About Transocean Sedco Forex Inc. ..........................    2
Where You Can Find More Information.........................    2
Use of Proceeds.............................................    3
Ratio of Earnings to Fixed Charges..........................    3
Description of Debt Securities..............................    4
Description of Share Capital................................   13
Description of Ordinary Shares..............................   13
Description of Preference Shares............................   16
Description of Warrants.....................................   17
Anti-takeover Provisions....................................   18
Plan of Distribution........................................   19
Legal Opinions..............................................   21
Experts.....................................................   21


                             ABOUT THIS PROSPECTUS

     This prospectus is part of a registration statement that we have filed with
the Securities and Exchange Commission under a "shelf" registration process.
Using this process, we may offer the securities this prospectus describes in one
or more offerings with a total initial offering price of up to $2,000,000,000.
This prospectus provides you with a general description of the securities we may
offer. Each time we use this prospectus to offer securities, we will provide a
prospectus supplement and, if applicable, a pricing supplement. The prospectus
supplement and any pricing supplement will describe the specific terms of that
offering, the offered securities, any material United States federal income tax
consequences and other special considerations. The prospectus supplement and any
pricing supplement also may add to, update or change the information contained
in this prospectus. Please carefully read this prospectus, the prospectus
supplement and any pricing supplement, in addition to the information contained
in the documents we refer to under the heading "Where You Can Find More
Information."

                           FORWARD-LOOKING STATEMENTS

     This prospectus includes or incorporates by reference forward-looking
statements that reflect our current view of future events and financial
performance. These forward-looking statements are subject to numerous risks and
uncertainties, including those factors discussed elsewhere in or incorporated by
reference into this prospectus, any prospectus supplement and our other filings
with the SEC. These risks and uncertainties could cause actual results or events
to differ materially from historical results or those anticipated. You can
identify forward-looking statements by the use of words like "anticipate,"
"believe," "budget," "estimate," "expect," "forecast," "intend," "plan,"
"predict," "project" and similar expressions. Any statement that is not a
historical fact is a forward-looking statement. We caution you not to place
undue reliance on these forward-looking statements, which speak only as of their
dates. Nothing in this document is intended to provide guidance for financial
results for future periods for Transocean Sedco Forex Inc. Any actual or
purported guidance given prior to the date of this registration statement,
including in any document we filed with the SEC prior to this date, spoke only
as of the date such statement was made and no obligation to update was
undertaken. We undertake no obligation to update or revise publicly any
forward-looking statements, whether as a result of new information, future
events or otherwise.
   28

                       ABOUT TRANSOCEAN SEDCO FOREX INC.

     We are a leading international provider of offshore contract drilling
services for oil and gas wells. On March 1, 2001, we owned, had partial
ownership interests in, operated or had under construction 166 mobile offshore
and barge drilling units. As of that date, our active fleet included 13
high-specification drillships, three other drillships, 20 high-specification
semisubmersibles (including four under construction), 30 other semisubmersibles,
55 jackup rigs, 37 drilling barges, five tenders and three submersible rigs. The
fleet also included four mobile offshore production units, two multi-purpose
service vessels and three platform drilling rigs. We also have a fleet of land
and barge drilling rigs in Venezuela consisting of 11 wholly owned and two
partially owned land rigs and three lake barges.

     Our core business is to contract these drilling rigs, related equipment and
work crews primarily on a dayrate basis to drill oil and gas wells. We
specialize in technically demanding segments of the offshore drilling business
with a particular focus on deepwater and harsh environment drilling services. We
also provide additional services, including management of third-party well
service activities. Our ordinary shares are listed on the New York Stock
Exchange under the symbol "RIG."

     Our principal executive offices in the U.S. are located at 4 Greenway
Plaza, Houston, Texas 77046, and our telephone number at that location is (713)
232-7500. As used in this prospectus, "we" means Transocean Sedco Forex Inc., a
Cayman Islands exempted company, and its subsidiaries, unless we state otherwise
or the context indicates otherwise.

                      WHERE YOU CAN FIND MORE INFORMATION

     We file annual, quarterly and current reports, proxy statements and other
information with the SEC. You can read and copy these materials at the SEC's
public reference room at 450 Fifth Street, N.W., Washington, D.C. 20549 and at
the SEC's regional offices located at Seven World Trade Center, New York, New
York 10048 and at 500 West Madison Street, 14th Floor, Chicago, Illinois 60661.
You can obtain information about the operation of the SEC's public reference
room by calling the SEC at 1-800-SEC-0330. The SEC also maintains a Web site
that contains information we file electronically with the SEC, which you can
access over the Internet at http://www.sec.gov. You can obtain information about
us at the offices of the New York Stock Exchange, 20 Broad Street, New York, New
York 10005.

     This prospectus is part of a registration statement we have filed with the
SEC relating to the securities. As permitted by SEC rules, this prospectus does
not contain all of the information we have included in the registration
statement and the accompanying exhibits and schedules. You may refer to the
registration statement, exhibits and schedules for more information about us and
our securities. The registration statement, exhibits and schedules are available
at the SEC's public reference room or through its Web site.

     The SEC allows us to "incorporate by reference" the information we file
with them, which means that we can disclose important information to you by
referring you to those documents. The information we incorporate by reference is
an important part of this prospectus, and later information that we file with
the SEC will automatically update and supersede this information. We incorporate
by reference the documents listed below and any future filings we make with the
SEC under Sections 13(a), 13(c), 14 or 15(d) of the Securities Exchange Act of
1934 until we sell all the offered securities. The documents we incorporate by
reference are:

     - our Annual Report on Form 10-K for the year ended December 31, 2000,

     - our Current Reports on Form 8-K filed with the SEC on February 7, 2001
       (as amended on March 23, 2001), February 26, 2001 and April 9, 2001, and

     - the description of our ordinary shares contained in our Current Report on
       Form 8-K dated May 14, 1999

                                        2
   29

     You may request a copy of these filings (other than an exhibit to those
filings unless we have specifically incorporated that exhibit by reference into
the filing), which we will provide at no cost, by writing or telephoning us at
the following address:

           Transocean Sedco Forex Inc.
           4 Greenway Plaza
           Houston, Texas 77046
           Attention: Vice President of Investor Relations and Communications
           Telephone: (713) 232-7500

     You should rely only on the information contained or incorporated by
reference in this prospectus or any prospectus supplement. We have not
authorized any person (including any salesman or broker) to provide information
other than that provided in this prospectus or any prospectus supplement. We
have not authorized anyone to provide you with different information. We are not
making an offer of these securities in any state where the offer is not
permitted. You should not assume that the information in this prospectus or any
prospectus supplement is accurate as of any date other than the date on its
cover page or that any information contained in any document we have
incorporated by reference is accurate as of any date other than the date of the
document incorporated by reference.

                                USE OF PROCEEDS

     Unless we inform you otherwise in the prospectus supplement, we will use
the net proceeds from the sale of the offered securities for general corporate
purposes. These purposes may include repayment or refinancing of indebtedness,
working capital, capital expenditures, acquisitions and repurchases and
redemptions of securities. Pending any specific application, we may initially
invest funds in short-term marketable securities or apply them to the reduction
of short-term indebtedness.

                       RATIO OF EARNINGS TO FIXED CHARGES

     Our ratio of earnings to fixed charges for each of the periods shown is as
follows:



                                                        Year Ended December 31,
                                              --------------------------------------------
                                              2000   1999(a)   1998(a)   1997(a)   1996(a)
                                              ----   -------   -------   -------   -------
                                                                    
Historical ratio of earnings to fixed
  charges...................................  1.5      1.4       9.7      10.3      12.6


---------------

(a)  The ratios for each of the years in the four year period ended December 31,
     1999 include only the earnings and fixed charges of Sedco Forex Holdings
     Limited, not those of Transocean Offshore Inc.

     We have computed the ratios of earnings to fixed charges shown above by
dividing earnings available for fixed charges by fixed charges. For this
purpose, "earnings available for fixed charges" consist of pretax income (loss)
from continuing operations before extraordinary items plus fixed charges,
distributed earnings of unconsolidated joint ventures and amortization of
capitalized interest, less capitalized interest and undistributed equity in
earnings of joint ventures. "Fixed charges" consist of interest expense,
capitalized interest and an estimate of the interest within rental expense.

     On January 31, 2001, we completed our merger transaction with R&B Falcon
Corporation. The merger was accounted for as a purchase, with our company as the
acquiror for accounting purposes. The historical ratios of earnings to fixed
charges for the year ended December 31, 2000 include only the earnings and fixed
charges of Transocean Sedco Forex. On December 31, 1999, we completed our merger
with Sedco Forex Holdings Limited, the former offshore contract drilling
business of Schlumberger Limited. The merger was accounted for as a purchase,
with Sedco Forex as the acquiror for accounting purposes. The historical ratios
of earnings to fixed charges for the four year period ended December 31, 1999
include only the earnings and fixed charges of Sedco Forex.

                                        3
   30

     For the year ended December 31, 2000, our pro forma earnings were
inadequate to cover pro forma fixed charges by $130.5 million, assuming our
merger with R&B Falcon occurred on January 1, 2000. This pro forma information
does not necessarily reflect what the ratio of earnings to fixed charges would
have been if the merger had been completed on that date, nor does it necessarily
reflect any future ratio of earnings to fixed charges.

     Our ratio of earnings to combined fixed charges and preferred stock
dividends for each of the five years in the period ended December 31, 2000 is
the same as those reflected above for the ratio of earnings to fixed charges
because we had no preferred stock dividend requirements.

     For the year ended December 31, 2000, our pro forma earnings were
inadequate to cover pro forma combined fixed charges and preferred stock
dividends by $278.2 million, assuming our merger with R&B Falcon occurred on
January 1, 2000. This pro forma information does not necessarily reflect what
the ratio of earnings to combined fixed charges and preferred stock dividends
would have been if the merger had been completed on that date nor does it
necessarily reflect any future ratio of earnings to combined fixed charges and
preferred stock dividends.

                         DESCRIPTION OF DEBT SECURITIES

     We may issue two types of debt securities, senior or subordinated. When we
issue them, we will file a prospectus supplement describing the exact terms of
the debt securities. The senior debt securities will be issued under an
indenture dated April 15, 1997 with Chase Bank of Texas, N.A. (now known as The
Chase Manhattan Bank), as trustee, as supplemented. The subordinated debt
securities will be issued under an indenture that will be entered into with a
trustee and will be described in the prospectus supplement for those debt
securities. We sometimes call the senior indenture and the subordinated
indenture the indentures. We have summarized selected provisions of the debt
securities and the indentures below. In this summary, "we" or "our" means
Transocean Sedco Forex Inc. only, unless we state otherwise or the context
indicates otherwise. The summary is not complete. For a complete description,
you should refer to the indentures and the terms of the debt securities, which
we have filed or which we will file with the SEC. Please read "Where You Can
Find More Information."

     The indentures do not limit the amount of debt securities we can issue and
do not limit the amount of other indebtedness we may incur. We may issue debt
securities under the indentures from time to time in separate series, each up to
the aggregate amount we authorize from time to time for that series.

     The indentures do not contain any covenants or other provisions designed to
protect holders of the debt securities in the event of a highly leveraged
transaction. The indentures also do not contain provisions that give holders of
the debt securities the right to require us to repurchase their securities in
the event of a decline in our credit rating resulting from a takeover,
recapitalization or similar restructuring or otherwise.

     The prospectus supplement relating to any series of debt securities being
offered will include specific terms relating to the offering. These terms will
include some or all of the following:

     - the title of the debt securities,

     - the total principal amount of the debt securities,

     - whether the debt securities are senior debt securities or subordinated
       debt securities,

     - whether we will issue the debt securities in individual certificates to
       each holder or in the form of temporary or permanent global securities
       held by a depository on behalf of holders,

     - the date or dates on which the principal of and any premium on the debt
       securities will be payable,

     - any interest rate, the date from which interest will accrue, interest
       payment dates and record dates for interest payments,

                                        4
   31

     - whether and under what circumstances any additional amounts with respect
       to the debt securities will be payable,

     - the place or places where payments on the debt securities will be
       payable,

     - any optional redemption provisions,

     - any sinking fund or other provisions that would obligate us to redeem,
       purchase or repay debt securities,

     - the denominations in which debt securities will be issuable,

     - whether payments on the debt securities will be payable in foreign
       currency or currency units or another form and whether payments will be
       payable by reference to any index or formula,

     - the portion of the principal amount of debt securities that will be
       payable if the maturity is accelerated, if other than the entire
       principal amount,

     - any additional means of defeasance of the debt securities and any
       additional conditions to defeasance of the debt securities,

     - any changes or additions to events of default or covenants,

     - any restrictions or other provisions relating to the transfer or exchange
       of debt securities,

     - any terms for the conversion or exchange of the debt securities for our
       preference shares, ordinary shares or other debt securities, or

     - any other terms of the debt securities.

     We may sell the debt securities at a discount (which may be substantial)
below their stated principal amount. These debt securities may bear no interest
or interest at a rate that at the time of issuance is below market rates.

     If we sell any of the debt securities for any foreign currency or currency
unit or if payments on the debt securities are payable in any foreign currency
or currency unit, we will describe in the prospectus supplement the
restrictions, elections, tax consequences, specific terms and other information
relating to those debt securities and the foreign currency or currency unit.

RANKING

     The debt securities will be our unsecured obligations. The senior debt
securities will rank equal in right of payment with all of our other unsecured
and unsubordinated indebtedness. The subordinated debt securities will rank in
right of payment below any senior debt securities and below our other senior
debt. For a more detailed description of the subordination of the subordinated
debt securities, see "-- Provisions Applicable Solely to Subordinated Debt
Securities." The indentures do not limit the amount of debt that we or any of
our subsidiaries may incur or issue, nor do they restrict transactions between
us and our affiliates or dividends and other distributions by us or our
subsidiaries.

     We conduct a substantial portion of our total operations through
subsidiaries, and a substantial portion of our operating income and cash flow is
generated by our subsidiaries. As a result, distributions or advances from our
subsidiaries are important sources of funds necessary to meet our debt service
obligations. Contractual provisions or laws, as well as our subsidiaries'
financial condition and operating requirements, may limit our ability to obtain
from our subsidiaries the cash we need to pay our debt service obligations,
including payments on the debt securities. In addition, holders of the debt
securities will have a junior position to the claims of creditors and
securityholders of our subsidiaries (including the holders of debt issued by R&B
Falcon and its subsidiaries) on their assets and earnings.

                                        5
   32

EVENTS OF DEFAULT

     Unless we inform you otherwise in the prospectus supplement, the following
are events of default with respect to a series of debt securities:

     - our failure to pay interest on or any additional amounts with respect to
       any debt securities of that series for 30 days,

     - our failure to pay principal of or any premium on any debt securities of
       that series when due,

     - our failure to make any required sinking fund payment for that series of
       debt securities for 30 days,

     - our failure to perform any of our other covenants in the indenture (other
       than a covenant included in the indenture solely for the benefit of
       another series of debt securities) for 90 days after written notice by
       the trustee or by the holders of at least 25% in principal amount of all
       outstanding debt securities under the indenture,

     - various events involving a bankruptcy, insolvency or reorganization of
       the Company, and

     - any other event of default provided for that series of debt securities.

     A default under an indenture with respect to one series of debt securities
issued under the indenture will not necessarily be a default under another
series. The trustee may withhold notice to the holders of the debt securities of
any default or event of default (except for a default in any payment on the debt
securities) if the trustee considers it in the interest of the holders of the
debt securities to do so.

     In the case of an event of default for any series of debt securities issued
under an indenture, the trustee or the holders of at least 25% in principal
amount of the outstanding debt securities of the series affected by the default
(or, in some cases, of all outstanding debt securities under the indenture,
voting as one class) may declare the principal of those debt securities to be
due and payable immediately. If an event of default relating to events of
bankruptcy, insolvency or reorganization occurs, the principal of all the debt
securities will become immediately due and payable without any action on the
part of the trustee or any holder. The holders of a majority in principal amount
of the outstanding debt securities of the series affected by the default (or, in
some cases, of all outstanding debt securities under the indenture, voting as
one class) may in some cases rescind this accelerated payment requirement.
Depending on the terms of our other indebtedness, an event of default under the
indentures may give rise to cross defaults on our other indebtedness.

     In most cases, the trustee will be under no obligation to exercise any of
its rights or powers under the indenture at the request or direction of any of
the holders, unless those holders have offered to the trustee reasonable
indemnity. The holders of a majority in principal amount of the outstanding debt
securities of any series (or, in some cases, of all outstanding debt securities
under the indenture) may direct the time, method and place of:

     - conducting any proceeding for any remedy available to the trustee, or

     - exercising any trust or power conferred on the trustee with respect to
       the debt securities of that series.

     In the case of an event of default, the trustee will be required to use the
degree of care and skill of a prudent man in the conduct of his own affairs.

     A holder of a debt security may not individually pursue any remedy under
the indenture unless all of the following conditions are met:

     - the holder has previously given written notice to the trustee of an event
       of default with respect to that series of debt securities,

     - the holders of not less than 25% in principal amount of the outstanding
       debt securities of that series have made a written request to the trustee
       to institute proceedings in its own name,
                                        6
   33

     - the holder has offered the trustee reasonable indemnity,

     - the trustee has failed to act within 60 days after receipt of the notice
       and indemnity, and

     - the holders of a majority in principal amount of the outstanding debt
       securities of that series have given no direction inconsistent with the
       request.

     The foregoing limitations with respect to remedies do not, however, affect
the right of a holder of any debt security to sue for the enforcement of any
overdue payment.

CONSOLIDATION, MERGER AND SALE OF ASSETS

     The indentures generally permit a consolidation or merger between us and
another entity. The indentures also permit our transfer or disposal of all or
substantially all of our assets. We have agreed, however, that we will
consolidate with or merge into any entity, or transfer or dispose of all or
substantially all of our assets to any entity, only if:

     - the resulting entity assumes the due and punctual payments of the debt
       securities issued under the indentures and the performance of our
       covenants under the indentures, and

     - immediately after giving effect to the transaction, no event of default,
       and no event that, after notice or lapse of time, would become an event
       of default, would occur and be continuing.

If a resulting entity assumes the debt securities and the indentures as
described above, we will be relieved of our obligations under the debt
securities and indentures, except in the case of our transfer or disposal of
assets by lease.

DEFEASANCE

     When we use the term "defeasance," we mean discharge from some or all of
our obligations under the applicable indenture. If we deposit with the trustee
money or U.S. government securities sufficient to make payments on the debt
securities of a series on the dates those payments are due and payable, then at
our option either of the following will occur:

     - we will no longer have any obligation to the holders of the debt
       securities to comply with the restrictive covenants under the indenture,
       and the related events of default will no longer apply to us ("covenant
       defeasance"), but our other obligations under the indenture and the debt
       securities of that series, including our obligations to make payments on
       the debt securities, to register the transfer or exchange of debt
       securities of that series, to replace stolen, lost or mutilated debt
       securities of that series, to maintain paying agencies and to hold monies
       for payment in trust, will continue, or

     - if permitted by the terms of that series of debt securities, we will be
       discharged from all of our obligations with respect to the debt
       securities of that series ("legal defeasance and discharge") and holders
       of the debt securities of that series would be entitled to claim payments
       on their debt securities only from the trust fund.

     Unless we inform you otherwise in the prospectus supplement, we will be
required to deliver to the trustee an opinion of counsel that the deposit and
related defeasance would not cause the holders of the debt securities to
recognize income, gain or loss for federal income tax purposes. If we elect
legal defeasance and discharge, that opinion of counsel must be based upon a
ruling from the U.S. Internal Revenue Service or a change in law to that effect.

PAYMENT AND PAYING AGENTS

     Unless we inform you otherwise in the prospectus supplement, we will make
payments on the debt securities at the office of the paying agents we designate
from time to time. We may make, at our option,

                                        7
   34

interest payments by check mailed to the person entitled to the payment as it
appears on the security register. Unless we inform you otherwise in the
prospectus supplement, we will make interest payments to the person in whose
name the debt security is registered at the close of business on the record date
for the interest payment, even if that person no longer owns the debt security
on the interest payment date.

     We have designated the corporate trust office of the trustee as a paying
agent for payments on the senior debt securities. We may at any time designate
additional paying agents, rescind the designation of any paying agent or approve
a change in the office through which any paying agent acts. We will, however, be
required to maintain a paying agent in each place of payment for a series of
debt securities.

     Any funds we pay to a paying agent for payments on any debt security that
remain unclaimed for three years after the payments become due and payable will
be repaid to us, subject to applicable escheat laws. After repayment to us, the
holder of that debt security can claim payment only from us and not from the
paying agent.

MODIFICATION AND WAIVER

     We may modify or amend the indenture if the holders of a majority in
principal amount of the outstanding debt securities of all series issued under
the indenture (acting as one class) affected by the modification or amendment
consent to it. Without the consent of the holder of each outstanding debt
security affected, however, no modification may:

     - change the stated maturity of the principal of or any installment of
       principal of or interest on any debt security,

     - reduce the principal amount of, the interest rate on, any additional
       amount with respect to or the premium payable upon redemption of any debt
       security,

     - change the subordination provisions of the subordinated indenture in a
       manner that is adverse to the holders of subordinated debt securities,

     - make the debt security payable in a currency other than originally stated
       in the debt security,

     - change the place where the principal of, any additional amounts with
       respect to or any premium or interest on any debt security is payable,

     - impair the right to institute suit for the enforcement of any payment on
       any debt security,

     - reduce the percentage in principal amount of outstanding debt securities
       necessary to modify the indenture, waive compliance with the provisions
       of the indenture or waive defaults, or

     - modify any of the above provisions.

     We and the trustee may agree to modify, amend or supplement the indenture
without the consent of any holders of the debt securities in certain
circumstances, including:

     - to evidence the assumption of our obligations under the indenture and the
       debt securities issued under the indenture by a successor,

     - to add covenants or events of default or to surrender any of our rights
       under the indenture,

     - to provide security for any series of debt securities issued under the
       indenture,

     - to make any change that does not adversely affect any outstanding debt
       securities of a series,

     - to establish the terms of any series of debt securities,

     - to add provisions necessary to permit or facilitate defeasance of any
       series of debt securities if we have received an opinion of counsel that
       those provisions do not materially adversely affect the holders of any
       series of debt securities,

                                        8
   35

     - to provide for a successor trustee, or

     - to cure any ambiguity, defect or inconsistency.

     The holders of a majority in principal amount of the outstanding debt
securities of any series (or, in some cases, of all outstanding debt securities
under the indenture or of all series affected) may waive past defaults under the
indenture and compliance by us with our covenants under the indenture. Those
holders may not, however, waive any default in any payment on any debt security
of that series or compliance with a provision that cannot be modified or amended
without the consent of each holder affected.

BOOK-ENTRY DEBT SECURITIES

     We may issue the debt securities of a series in the form of one or more
global debt securities that would be deposited with a depositary or its nominee
identified in the prospectus supplement. We may issue global debt securities in
either temporary or permanent form. We will describe in the prospectus
supplement the terms of any depositary arrangement and the rights and
limitations of owners of beneficial interests in any global debt security. The
prospectus supplement will also describe the form, exchange, registration and
transfer of debt securities we may issue in temporary or permanent global forms.

TRANSFER AND EXCHANGE

     We have appointed the trustee as security registrar for the senior debt
securities. We will appoint the trustee under the subordinated indenture as the
security registrar for the subordinated debt securities, unless we indicate
otherwise in the prospectus supplement. We are required to maintain an office or
agency for transfers and exchanges in each place of payment. We may at any time
designate additional transfer agents for any series of debt securities or
rescind the designation of any transfer agent.

     In the case of any redemption of debt securities, we will not be required:

     - to issue, register the transfer of or exchange debt securities of a
       series during a period beginning 15 days before the day of mailing of the
       relevant notice of redemption and ending on the close of business on the
       day of mailing of the relevant notice of redemption, or

     - to register the transfer or exchange of any debt security, or portion of
       any debt security, selected for redemption, except the unredeemed portion
       of any debt security we are redeeming in part.

MEETINGS

     Meetings may be convened on notice:

     - by the trustee,

     - by us, if we ask the trustee to call a meeting and it fails to do so, or

     - by the holders of 10% in principal amount of the debt securities of a
       series, if they ask the trustee to call a meeting and it fails to do so.

     Holders entitled to vote a majority in principal amount of the outstanding
debt securities of a series constitute a quorum at any meeting. Except for
actions requiring the consent of all holders of debt securities affected by the
action, any action at a meeting adopted by the holders of a majority in
principal amount of the debt securities of any series (or a lesser percentage
required for the action by the indenture) will be binding on all holders of the
debt securities of that series.

NOTICES

     Notices to holders of debt securities will be given by mail to the holder's
address as it appears in the security register.

                                        9
   36

GOVERNING LAW

     New York law governs the indentures and the debt securities.

THE TRUSTEE

     The Chase Manhattan Bank is the trustee under the senior indenture. We may
borrow money and maintain other banking relationships, in the ordinary course of
business, with any trustee and its affiliates under any indenture. The
indentures, however, contain limitations on the right of the trustee, if it
becomes one of our creditors, to obtain payment of claims or to realize on
certain property received for any such claim, as security or otherwise. If the
trustee acquires any conflicting interest, it must eliminate that conflict or
resign.

PROVISIONS APPLICABLE SOLELY TO SENIOR DEBT SECURITIES

     The following provisions are included in the senior indenture and apply to
any series of senior debt securities, unless we indicate otherwise in the
prospectus supplement. In the following discussion, "we" or "our" means
Transocean Sedco Forex Inc. and its subsidiaries, unless the context indicates
otherwise. When we refer to our "drilling rigs and drillships," we mean any
drilling rig or drillship (or the stock or indebtedness of any subsidiary owning
such a drilling rig or drillship) that we lease or own all or part of and that
our board of directors deems of material importance to us. No drilling rig or
drillship that has a gross book value of less than 2% of consolidated net
tangible assets will be deemed of material importance. When we refer to
"consolidated net tangible assets," we mean the total amount of our assets (less
reserves and other properly deductible items) after deducting current
liabilities (other than those that are extendable at our option to a date more
than 12 months after the date the amount is determined), goodwill and other
intangible assets shown in our most recent consolidated balance sheet prepared
in accordance with accounting principles generally accepted in the United
States.

  Limitation on Liens

     In the senior indenture, we have agreed that we will not create, assume or
allow to exist any debt secured by a lien upon any of our drilling rigs or
drillships, unless we secure each series of senior debt securities equally and
ratably with the secured debt. This covenant has exceptions that permit:

     - liens already existing on the date the applicable series of senior debt
       securities is issued,

     - liens already existing on a particular drilling rig or drillship at the
       time we acquire that drilling rig or drillship, and liens already
       existing on drilling rigs or drillships of a corporation or other entity
       at the time it becomes our subsidiary,

     - liens securing debt incurred to finance the acquisition, completion of
       construction and commencement of commercial operation, alteration, repair
       or improvement of any drilling rig or drillship, if the debt was incurred
       prior to, at the time of or within 12 months after that event, and liens
       securing debt in excess of the purchase price or cost if recourse on the
       debt is only against the drilling rig or drillship in question,

     - liens securing intercompany debt,

     - liens in favor of a governmental entity to secure either (1) payments
       under any contract or statute or (2) industrial development, pollution
       control or similar indebtedness,

     - liens imposed by law such as mechanics' or workmen's liens,

     - governmental liens under contracts for the sale of products or services,

     - liens under workers compensation laws or similar legislation,

     - liens in connection with legal proceedings or securing taxes or
       assessments,

     - good faith deposits in connection with bids, tenders, contracts or
       leases,
                                        10
   37

     - deposits made in connection with maintaining self-insurance, to obtain
       the benefits of laws, regulations or arrangements relating to
       unemployment insurance, old age pensions, social security or similar
       matters or to secure surety, appeal or customs bonds, and

     - any extensions, renewals or replacements of the above-described liens if
       both of the following conditions are met:

      (1) the amount of debt secured by the new lien does not exceed the amount
          of debt secured by the existing lien, plus any additional debt used to
          complete a specific project, and

      (2) the new lien is limited to all or a part of the drilling rigs or
          drillships (plus any improvements) secured by the original lien issued
          under the senior indenture.

     In addition, without securing the senior debt securities as described
above, we may create, assume or allow to exist secured debt that would otherwise
be prohibited, in an aggregate amount that does not exceed a "basket" equal to
10% of our consolidated net tangible assets. When determining whether secured
debt is permitted by this exception, we must include in the calculation of the
"basket" amount all of our other secured debt that would otherwise be prohibited
and the present value of lease payments in connection with sale and lease-back
transactions that would be prohibited by the "Limitation on Sale and Lease-Back
Transactions" covenant described below if this exception did not apply.

  Limitation on Sale and Lease-Back Transactions

     We have agreed that we will not enter into a sale and lease-back
transaction covering any drilling rig or drillship, unless one of the following
applies:

     - we could incur debt secured by the leased property in an amount at least
       equal to the present value of the lease payments in connection with that
       sale and lease-back transaction without violating the "Limitation on
       Liens" covenant described above, or

     - within six months of the effective date of the sale and lease-back
       transaction, we apply an amount equal to the present value of the lease
       payments in connection with the sale and lease-back transaction to (1)
       the acquisition of any drilling rig or drillship or (2) the retirement of
       long-term debt ranking at least equally with the debt securities issued
       under the senior indenture.

     When we use the term "sale and lease-back transaction," we mean any
arrangement by which we sell or transfer to any person any drilling rig or
drillship that we then lease back from them. This term excludes leases shorter
than three years, intercompany leases, leases executed within 12 months of the
acquisition, construction, improvement or commencement of commercial operation
of the drilling rig or drillship, and arrangements pursuant to any provision of
law with an effect similar to the former Section 168(f)(8) of the Internal
Revenue Code of 1954 (which permitted the lessor to recognize depreciation on
the property).

PROVISIONS APPLICABLE SOLELY TO SUBORDINATED DEBT SECURITIES

     Under the subordinated indenture, payment of the principal, interest, any
additional amounts and any premium on the subordinated debt securities will
generally be subordinated and junior in right of payment to the prior payment in
full of all of our senior debt. The subordinated indenture provides that we may
not pay principal, interest, any additional amounts or any premium on the
subordinated debt securities, and we may not acquire any subordinated debt
securities (other than for our junior securities), if:

     - we fail to pay the principal, interest or premium on the senior debt when
       due, or

     - we default in performing any other covenant (a "covenant default") in any
       senior debt that we designate for this purpose in the instrument creating
       that senior debt, if the covenant default allows the holders of that
       senior debt to accelerate the maturity of the senior debt they hold.

                                        11
   38

     A covenant default will only prevent us from paying the subordinated debt
securities for up to 179 days after holders of the senior debt give the trustee
for the subordinated debt securities notice of the covenant default, unless that
senior debt has been declared due and payable in its entirety.

     The subordination does not affect our obligation to pay, when due,
principal, interest, any additional amounts and any premium on the subordinated
debt securities. In addition, the subordination does not prevent the occurrence
of any default under the subordinated indenture.

     If we distribute our assets or dissolve, liquidate or reorganize in
bankruptcy, insolvency or similar proceedings:

     - the holders of all of our senior indebtedness will first be entitled to
       receive payment in full before the holders of subordinated debt
       securities are entitled to receive any payment (other than payments of
       our junior securities), and

     - any payment or distribution of assets (other than our junior securities)
       that the holders of subordinated debt securities or the trustee would
       otherwise be entitled to receive will be paid directly to the holders of
       our senior indebtedness or their representatives, to the extent necessary
       to pay in full all of our senior indebtedness.

     As a result of the subordination of the subordinated debt securities, if we
distribute our assets, dissolve, liquidate or become insolvent or bankrupt,
holders of subordinated debt securities may receive less on a proportionate
basis than holders of our senior indebtedness and other creditors.

     If the trustee or the holders of subordinated debt securities receive any
payment or distribution of assets (other than our junior securities) that is
prohibited by the foregoing provisions, then the trustee or the holders of
subordinated debt securities will hold those amounts for the benefit of the
holders of our senior indebtedness and will be obligated to pay or deliver those
amounts to the holders of our senior indebtedness or their representatives.

     The subordinated indenture does not limit the amount of senior debt that we
may incur. Unless we inform you otherwise in the prospectus supplement, "senior
debt" will mean the following types of indebtedness, unless that indebtedness
states that it is not senior to the subordinated debt securities or our other
junior debt:

     - all of our liabilities and obligations (1) in respect of borrowed money,
       (2) evidenced by bonds, notes, debentures or similar instruments, (3)
       representing the balance of the purchase price of any property or
       services, (4) evidenced by bankers' acceptances or similar instruments
       issued or accepted by banks, (5) for the payment of money relating to a
       capitalized lease obligation or (6) evidenced by a letter of credit or a
       reimbursement obligation with respect to any letter of credit,

     - all of our net obligations under interest swap and hedging obligations,

     - all liabilities of others of the kind described in the preceding two
       clauses that we have guaranteed or are otherwise our legal liability,

     - all obligations to purchase, redeem or acquire any of our share capital
       or rights to purchase our share capital (other than convertible or
       exchangeable indebtedness), and

     - all amendments, deferrals, renewals, extensions, refinancings or
       refundings of any liability of the kind described above.

     However, "senior indebtedness" will not include:

     - indebtedness to any of our subsidiaries, officers, directors or
       employees,

     - indebtedness to trade creditors, or

     - any liability for taxes.
                                        12
   39

                          DESCRIPTION OF SHARE CAPITAL

     We are a Cayman Islands exempted company. Our authorized share capital is
$13,000,000, divided into:

     - 800,000,000 ordinary shares, par value $0.01, and

     - 50,000,000 other shares, par value $0.10, which shares may be designated
       and created as shares of any other classes or series of shares with the
       respective rights and restrictions determined by action of the board of
       directors.

     As of March 31, 2001, 317,799,390 ordinary shares and no other class or
series of shares had been issued.

     The following description of our share capital is a summary. This summary
is not complete and is subject to the complete text of our memorandum of
association (the "memorandum") and articles of association (the "articles"). Our
memorandum and articles are exhibits to the registration statement and are
incorporated herein by reference. We encourage you to read those documents
carefully.

                         DESCRIPTION OF ORDINARY SHARES

VOTING

     The holders of ordinary shares are entitled to one vote per share other
than on the election of directors.

     With respect to the election of directors, each holder of ordinary shares
entitled to vote at the election has the right to vote, in person or by proxy,
the number of shares held by him for as many persons as there are directors to
be elected and for whose election that holder has a right to vote. The directors
are divided into three classes, with only one class being up for election each
year. Directors are elected by a plurality of the votes cast in the election.
Cumulative voting for the election of directors is prohibited by our articles.

     There are no limitations imposed by Cayman Islands law or our articles on
the right of nonresident shareholders to hold or vote their ordinary shares.

     The rights attached to any separate class or series of shares, unless
otherwise provided by the terms of the shares of that class or series, may be
varied only with the consent in writing of the holders of all of the issued
shares of that class or series or by a special resolution passed at a separate
general meeting of holders of the shares of that class or series. The necessary
quorum for that meeting is the presence of holders of at least a majority of the
shares of that class or series. Each holder of shares of the class or series
present, in person or by proxy, will have one vote for each share of the class
or series of which he is the holder. Outstanding shares will not be deemed to be
varied by the creation or issuance of additional shares that rank in any respect
prior to or equivalent with those shares.

     Under Cayman Islands law, some matters, like altering the memorandum or the
articles, changing the name of a company, voluntarily winding up a company or
resolving to be registered by way of continuation in a jurisdiction outside the
Cayman Islands, require approval of shareholders by a special resolution. A
special resolution is a resolution (1) passed by the holders of two-thirds of
the shares voted at a general meeting or (2) approved in writing by all
shareholders entitled to vote at a general meeting of the company.

QUORUM FOR GENERAL MEETINGS

     The presence of shareholders, in person or by proxy, holding at least a
majority of the issued shares generally entitled to vote at a meeting, is a
quorum for the transaction of most business. However, different quorums are
required in some cases to approve a change in our articles.

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     Shareholders present, in person or by proxy, holding at least 95% of the
issued shares entitled to vote at a meeting constitute the required quorum at a
general meeting to consider or adopt a special resolution to amend, vary,
suspend the operation of or cause any of the following provisions of the
articles to cease to apply:

     - Section 17 -- which relates to the convening of general meetings,

     - Section 19 -- which relates to proceedings and procedures at general
       meetings,

     - Section 21.1 -- which relates to the election and appointment of
       directors,

     - Section 26 -- which requires shareholders to approve the sale, lease or
       exchange of all or substantially all of our property or assets, or

     - Section 27 -- which generally requires shareholders to approve business
       combinations with interested shareholders (with the exceptions described
       below).

     However, the presence of shareholders, in person or by proxy, holding at
least a majority of the issued shares entitled to vote at the meeting, is a
quorum if:

     - a majority of the board of directors has, at or prior to the meeting,
       recommended a vote in favor of the special resolution, and

     - in the case of a special resolution to amend, vary, suspend the operation
       of or disapply Section 27 of the articles, other than a special
       resolution referred to below, the favorable board of directors'
       recommendation is made at a time when a majority of the board of
       directors then in office were directors prior to any person becoming an
       interested shareholder during the previous three years or were
       recommended for election or elected to succeed those directors by a
       majority of those directors.

     In addition, the presence of shareholders, in person or by proxy, holding
at least a majority of the issued shares entitled to vote at a meeting, is also
the required quorum to consider or adopt a special resolution to delete Section
27 of the articles if:

     - the resolution will not be effective until 12 months after the passing of
       the resolution, and

     - the restriction in Section 27 of the articles will otherwise continue to
       apply to any business combination between us and any person who became an
       interested shareholder on or before the passing of the resolution.

     The shareholders present at a duly constituted general meeting may continue
to transact business until adjournment, despite the withdrawal of shareholders
that leaves less than a quorum.

DIVIDEND RIGHTS

     Subject to any rights and restrictions of any other class or series of
shares, the board of directors may, from time to time, declare dividends on the
shares issued and authorize payment of the dividends out of our lawfully
available funds. The board of directors may declare that any dividend be paid
wholly or partly by the distribution of our shares and/or specific assets.

RIGHTS UPON LIQUIDATION

     Upon our liquidation, after the full amounts that holders of any issued
shares ranking senior to the ordinary shares as to distribution on liquidation
or winding-up are entitled to receive have been paid or set aside for payment,
the holders of ordinary shares are entitled to receive, pro rata, any remaining
assets available for distribution to the holders of ordinary shares. The
liquidator may deduct from the amount payable in respect of those ordinary
shares any liabilities the holder has to or with us. The assets received

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by the holders of ordinary shares in a liquidation may consist in whole or in
part of property. That property is not required to be of the same kind for all
shareholders.

NO SINKING FUND

     The ordinary shares have no sinking fund provisions.

NO LIABILITY FOR FURTHER CALLS OR ASSESSMENTS

     The ordinary shares that have been issued to date are fully paid and
nonassessable. Any ordinary shares we offer under this prospectus will be fully
paid and nonassessable.

NO PREEMPTIVE RIGHTS

     Holders of ordinary shares will have no preemptive or preferential right to
purchase any of our securities.

REDEMPTION AND CONVERSION

     The ordinary shares are not convertible into shares of any other class or
series or subject to redemption either by us or the holder of the shares.

REPURCHASE

     Under our articles, we may purchase any issued ordinary shares in the
circumstances and on the terms agreed by us and the holder of the shares,
whether or not we have made a similar offer to any of the other holders of
ordinary shares.

RESTRICTIONS ON TRANSFER

     Subject to the rules of any stock exchange on which the ordinary shares may
be listed, the board of directors may, in its absolute discretion and without
assigning any reason, decline to register any transfer of shares.

OTHER CLASSES OR SERIES OF SHARES

     The board of directors is authorized, without obtaining any vote or consent
of the holders of any class or series of shares unless expressly provided by the
terms of issue of that class or series, to provide from time to time for the
issuance of other classes or series of shares and to establish the
characteristics of each class or series, including the number of shares,
designations, relative voting rights, dividend rights, liquidation and other
rights, redemption, repurchase or exchange rights and any other preferences and
relative, participating, optional or other rights and limitations not
inconsistent with applicable law.

COMPULSORY ACQUISITION OF SHARES HELD BY MINORITY HOLDERS

     An acquiring party is generally able to acquire compulsorily the ordinary
shares of minority holders in one of two ways:

     - By a procedure under the Companies Law (2000 Revision) of the Cayman
       Islands known as a "scheme of arrangement." A scheme of arrangement is
       made by obtaining the consent of the Cayman Islands company, the consent
       of a Cayman Islands court and approval of the arrangement by holders of
       ordinary shares (1) representing a majority in number of the shareholders
       present, in person or by proxy, at the meeting held to consider the
       arrangement and (2) holding at least 75% of all the issued ordinary
       shares other than those held by the acquiring party, if any. If a scheme
       of arrangement receives all necessary consents, all holders of ordinary
       shares of the company would be compelled to sell their shares under the
       terms of the scheme of arrangement, or

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   42

     - By acquiring pursuant to a tender offer 90% of the ordinary shares not
       already owned by the acquiring party. If the acquiring party has, within
       four months after the making of an offer for all the ordinary shares not
       owned by the acquiring party, obtained the approval of not less than 90%
       of all the shares to which the offer relates, the acquiring party may, at
       any time within two months after the end of that four-month period,
       require any nontendering shareholder to transfer its shares on the same
       terms as the original offer. In those circumstances, nontendering
       shareholders will be compelled to sell their shares, unless within one
       month from the date on which the notice to compulsorily acquire was given
       to the nontendering shareholder, the nontendering shareholder is able to
       convince a Cayman Islands court to order otherwise.

STOCK EXCHANGE LISTING

     The ordinary shares are listed on the New York Stock Exchange and trade
under the symbol "RIG."

TRANSFER AGENT

     The transfer agent and registrar for the ordinary shares is The Bank of New
York.

                        DESCRIPTION OF PREFERENCE SHARES

     The board of directors is authorized, without obtaining any vote or consent
of the holders of any class or series of shares unless expressly provided by the
terms of issue of that class or series, to provide from time to time for the
issuance of up to 50,000,000 preference shares in one or more classes or series
of shares. The board of directors can also establish the characteristics of each
class or series, including the number of shares, designations, relative voting
rights, dividend rights, liquidation and other rights, redemption, repurchase or
exchange rights and any other preferences and relative, participating, optional
or other rights and limitations not inconsistent with applicable law.

     We have summarized selected provisions of the preference shares in this
section. This summary is not complete. If we offer any preference shares, we
will file the form of the preference shares with the SEC, and you should read it
for provisions that may be important to you.

     The prospectus supplement relating to any series of preference shares being
offered will describe that series of preference shares and include specific
terms relating to the offering. The prospectus supplement will include some or
all of the following:

     - the title of the preference shares,

     - the maximum number of shares of the series,

     - the dividend rate or the method of calculating the dividend, the date
       from which dividends will accrue and whether dividends will be
       cumulative,

     - procedures for any auctioning or remarketing of the preference shares,

     - any liquidation preference,

     - any optional redemption provisions,

     - any sinking fund or other provisions that would obligate us to redeem or
       purchase the preference shares,

     - any terms for the conversion or exchange of the preference shares for our
       debt securities, ordinary shares or other preference shares,

     - any voting rights, or

     - any other preferences and relative, participating, optional or other
       special rights and limitations.

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   43

     Any preference shares we offer under this prospectus will be fully paid and
nonassessable. The transfer agent and registrar for each series will be
described in the related prospectus supplement.

                            DESCRIPTION OF WARRANTS

     We may issue warrants to purchase debt securities, preference shares,
ordinary shares or other securities. We may issue warrants independently or
together with other securities, and warrants sold with other securities may be
attached to or separate from the other securities. Warrants will be issued under
one or more warrant agreements between us and a warrant agent that we will name
in the prospectus supplement.

     We have summarized selected provisions of the warrants and the warrant
agreements below. This summary is not complete. If we offer any warrants, we
will file the form of any warrant certificate and warrant agreement with the
SEC, and you should read the warrant certificate and warrant agreement for
provisions that may be important to you.

     The prospectus supplement relating to any warrants being offered will
describe the warrants and include specific terms relating to the offering. The
prospectus supplement will include some or all of the following:

     - the title of the warrants,

     - the aggregate number of warrants offered,

     - the designation, number and terms of the debt securities, preference
       shares, ordinary shares or other securities purchasable upon exercise of
       the warrants, and procedures that will result in the adjustment of those
       numbers,

     - the exercise price of the warrants,

     - the dates or periods during which the warrants are exercisable,

     - the designation and terms of any securities with which the warrants are
       issued,

     - if the warrants are issued as a unit with another security, the date on
       and after which the warrants and the other security will be separately
       transferable,

     - if the exercise price is not payable in U.S. dollars, the foreign
       currency, currency unit or composite currency in which the exercise price
       is denominated,

     - any minimum or maximum amount of warrants that may be exercised at any
       one time,

     - any terms, procedures and limitations relating to the transferability,
       exchange or exercise of the warrants, or

     - any other terms of the warrants.

     Warrant certificates will be exchangeable for new warrant certificates of
different denominations at the office indicated in the prospectus supplement.
Prior to the exercise of their warrants, holders of warrants will not have any
of the rights of holders of the securities subject to the warrants.

MODIFICATIONS

     We may amend the warrant agreements and the warrants, without the consent
of the holders of the warrants, to cure any ambiguity, to cure, correct or
supplement any defective or inconsistent provision, or in any other manner that
will not materially and adversely affect the interests of holders of outstanding
warrants.

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   44

ENFORCEABILITY

     The warrant agent will act solely as our agent. The warrant agent will not
have any duty or responsibility if we default under the warrant agreements or
the warrant certificates. A warrant holder may, without the consent of the
warrant agent, enforce by appropriate legal action on its own behalf the
holder's right to exercise the holder's warrants.

                            ANTI-TAKEOVER PROVISIONS

     Our articles have provisions that could have an anti-takeover effect. These
provisions are intended to enhance the likelihood of continuity and stability in
the composition of the board of directors and in the policies formulated by the
board of directors, and may have the effect of discouraging actual or threatened
changes of control.

     The articles provide that our board of directors will be divided into three
classes serving staggered three-year terms. Directors can be removed from office
only for cause, as defined in the articles, by the affirmative vote of the
holders of a majority of the issued shares generally entitled to vote. The board
of directors does not have the power to remove directors. Vacancies on the board
of directors may be filled only by the remaining directors and not by the
shareholders. Each of these provisions can delay a shareholder from obtaining
majority representation on the board of directors.

     The articles provide that the board of directors will consist of at least
two and not more than thirteen persons. The exact number of directors is to be
set from time to time by a majority of the whole board of directors.
Accordingly, the board of directors, and not the shareholders, has the authority
to determine the number of directors and could delay any shareholder from
obtaining majority representation on the board of directors by enlarging the
board of directors and filling the new vacancies with its own nominees until a
general meeting at which directors are to be appointed.

     The articles establish an advance notice procedure that must be followed by
shareholders if they wish to nominate candidates for election as directors or
propose any business at an annual general meeting of shareholders. The articles
provide generally that, if a shareholder desires to nominate candidates for
election as directors or propose any business at an annual general meeting, that
shareholder must give us notice not less than 90 days prior to the anniversary
of the originally scheduled date of the immediately preceding annual general
meeting. However, if the date of the forthcoming annual general meeting is more
than 30 days before or after the anniversary date, the deadline is the close of
business on the tenth day after we publicly disclose the meeting date. In each
case, the notice must contain specified information concerning the shareholder
submitting the proposal.

     Subject to the terms of any other class of shares in issue, any action
required or permitted to be taken by the holders of ordinary shares must be
taken at a duly called annual or special general meeting of shareholders unless
taken by written consent of all holders of ordinary shares. Special general
meetings may be called only by a majority of the entire board of directors.

     The board of directors is authorized, without obtaining any vote or consent
of the holders of any class or series of shares unless expressly provided by the
terms of issue of a class or series, to issue from time to time any other
classes or series of shares with the designations and relative powers,
preferences, conversion or other rights, voting powers, restrictions,
limitations as to dividends or terms or conditions of redemption as it considers
fit. The board of directors could authorize the issuance of preference shares
with terms and conditions that could discourage a takeover or other transaction
that holders of some or a majority of the ordinary shares might believe to be in
their best interests or in which holders might receive a premium for their
shares over the then market price of the shares. No preference shares have been
established as of the date of this prospectus.

     The special quorum provisions contained in the articles require the holders
of 95% of all the voting shares to be present, in person or by proxy, at a
general meeting to consider or adopt a special resolution to amend, vary,
suspend the operation of or cease the application of the following provisions of
the articles,

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unless a majority of the board of directors has recommended that the
shareholders vote in favor of the special resolution:

     - Section 17 -- which relates to the convening of general meetings,

     - Section 19 -- which relates to proceedings and procedures at general
       meetings,

     - Section 21.1 -- which relates to the election and appointment of
       directors,

     - Section 26 -- which requires shareholders to approve the sale, lease or
       exchange of all or substantially all of our property or assets, or

     - Section 27 -- which generally requires shareholders to approve business
       combinations with interested shareholders.

     For a description of exceptions to the quorum requirements to amend Section
27, see the discussion under the heading "Description of Ordinary
Shares -- Quorum for General Meetings."

     Our articles generally prohibit "business combinations" between us and an
"interested shareholder." Specifically, "business combinations" between an
interested shareholder and us are prohibited for a period of three years after
the time the interested shareholder acquired its shares, unless:

     - the business combination or the transaction resulting in the person
       becoming an interested shareholder is approved by the board of directors
       prior to the date the interested shareholder acquired shares,

     - the interested shareholder acquired at least 85% of our shares in the
       transaction in which it became an interested shareholder, or

     - the business combination is approved by a majority of the board of
       directors and by the affirmative vote of disinterested shareholders
       holding at least two-thirds of the shares generally entitled to vote.

     "Business combinations" is defined broadly to include mergers,
consolidations of majority owned subsidiaries, sales or other dispositions of
assets having an aggregate value in excess of 10% of our consolidated assets,
and most transactions that would increase the interested shareholder's
proportionate share ownership.

     "Interested shareholder" is defined as a person who, together with any
affiliates and/or associates of that person, beneficially owns, directly or
indirectly, 15% or more of our issued voting shares.

                              PLAN OF DISTRIBUTION

     We may sell the offered securities in and outside the United States (1)
through underwriters or dealers, (2) directly to purchasers or (3) through
agents. The prospectus supplement will set forth the following information:

     - the terms of the offering,

     - the names of any underwriters or agents,

     - the purchase price,

     - the net proceeds to us,

     - any delayed delivery arrangements,

     - any underwriting discounts and other items constituting underwriters'
       compensation,

     - any initial public offering price, and

     - any discounts or concessions allowed or reallowed or paid to dealers.

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   46

SALE THROUGH UNDERWRITERS OR DEALERS

     If we use underwriters in the sale, the underwriters will acquire the
securities for their own account. The underwriters may resell the securities
from time to time in one or more transactions, including negotiated
transactions, at a fixed public offering price or at varying prices determined
at the time of sale. Underwriters may offer securities to the public either
through underwriting syndicates represented by one or more managing underwriters
or directly by one or more firms acting as underwriters. Unless we inform you
otherwise in the prospectus supplement, the obligations of the underwriters to
purchase the securities will be subject to certain conditions, and the
underwriters will be obligated to purchase all the offered securities if they
purchase any of them. The underwriters may change from time to time any initial
public offering price and any discounts or concessions allowed or reallowed or
paid to dealers.

     During and after an offering through underwriters, the underwriters may
purchase and sell the securities in the open market. These transactions may
include overallotment and stabilizing transactions and purchases to cover
syndicate short positions created in connection with the offering. The
underwriters may also impose a penalty bid, in which selling concessions allowed
to syndicate members or other broker-dealers for the offered securities sold for
their account may be reclaimed by the syndicate if such offered securities are
repurchased by the syndicate in stabilizing or covering transactions. These
activities may stabilize, maintain or otherwise affect the market price of the
offered securities, which may be higher than the price that might otherwise
prevail in the open market. If commenced, these activities may be discontinued
at any time.

     If we use dealers in the sale of securities, we will sell the securities to
them as principals. They may then resell those securities to the public at
varying prices determined by the dealers at the time of resale. We will include
in the prospectus supplement the names of the dealers and the terms of the
transaction.

DIRECT SALES AND SALES THROUGH AGENTS

     We may sell the securities directly. In that event, no underwriters or
agents would be involved. We may also sell the securities through agents we
designate from time to time. In the prospectus supplement, we will name any
agent involved in the offer or sale of the offered securities, and we will
describe any commissions payable by us to the agent. Unless we inform you
otherwise in the prospectus supplement, any agent will agree to use its
reasonable best efforts to solicit purchases for the period of its appointment.

     We may sell the securities directly to institutional investors or others
who may be deemed to be underwriters within the meaning of the Securities Act of
1933 with respect to any sale of those securities. We will describe the terms of
any such sales in the prospectus supplement.

DELAYED DELIVERY CONTRACTS

     If we so indicate in the prospectus supplement, we may authorize agents,
underwriters or dealers to solicit offers from certain types of institutions to
purchase securities from us at the public offering price under delayed delivery
contracts. These contracts would provide for payment and delivery on a specified
date in the future. The contracts would be subject only to those conditions
described in the prospectus supplement. The prospectus supplement will describe
the commission payable for solicitation of those contracts.

GENERAL INFORMATION

     We may have agreements with the agents, dealers and underwriters to
indemnify them against certain civil liabilities, including liabilities under
the Securities Act of 1933, or to contribute with respect to payments that the
agents, dealers or underwriters may be required to make. Agents, dealers and
underwriters may be our customers, may engage in transactions with us, or may
perform services for us in the ordinary course of their businesses.

     The securities may or may not be listed on a national securities exchange.
We cannot assure you that there will be a market for the securities.
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   47

                                 LEGAL OPINIONS

     The validity of the debt securities offered hereby will be passed upon by
Baker Botts L.L.P. The validity of the ordinary shares, preference shares and
warrants offered hereby will be passed upon by our Cayman Islands counsel,
Walkers, Cayman Islands. Any underwriters will be advised about issues relating
to any offering by their own legal counsel.

                                    EXPERTS

     The consolidated financial statements of Transocean Sedco Forex Inc. and
Subsidiaries appearing in Transocean Sedco Forex's Annual Report (Form 10-K) for
the year ended December 31, 2000 (and the financial statement schedule) have
been audited by Ernst & Young LLP, independent auditors, as set forth in their
report included therein and incorporated herein by reference. Such consolidated
financial statements are incorporated herein by reference in reliance upon such
report given on the authority of such firm as experts in accounting and
auditing.

     The financial statements of Transocean Sedco Forex Inc. (previously Sedco
Forex Holdings Limited) for the year ended December 31, 1998 incorporated in
this Prospectus by reference to the Annual Report on Form 10-K for the year
ended December 31, 2000 have been so incorporated in reliance on the report of
PricewaterhouseCoopers LLP, independent accountants, given on the authority of
said firm as experts in auditing and accounting.

     The consolidated balance sheets of R&B Falcon as of December 31, 2000 and
1999 and the related consolidated statements of operations, cash flows and
stockholders' equity for each of the three years in the period ended December
31, 2000, incorporated by reference in this prospectus and elsewhere in the
registration statement, have been audited by Arthur Andersen LLP, independent
public accountants, as indicated in their report with respect thereto, and are
included herein in reliance upon the authority of said firm as experts in giving
said report.

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