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                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
                            -------------------------
                                   SCHEDULE TO
                                (Amendment No. 1)
                             Tender Offer Statement
    Under Section 14(d)(1) or 13(e)(1) of the Securities Exchange Act of 1934
                            -------------------------
                              Triton Energy Limited
                            (Name of Subject Company)
                            -------------------------
                            Amerada Hess Corporation
                          Amerada Hess (Cayman) Limited
                            (Names of Filing Persons)

                   Ordinary Shares, Par Value $0.01 Per Share
                         (Title of Class of Securities)

                           G90751101: Ordinary Shares
                    ----------------------------------------
                      (CUSIP Number of Class of Securities)
                            -------------------------
                           J. Barclay Collins II, Esq.
                  Executive Vice President and General Counsel
                            Amerada Hess Corporation
                           1185 Avenue of the Americas
                            New York, New York 10036
                                 (212) 997-8500
            (Name, Address and Telephone Number of Person Authorized
       to Receive Notices and Communications on Behalf of Filing Persons)
                            -------------------------
                                   Copies to:
                            Timothy B. Goodell, Esq.
                               Gregory Pryor, Esq.
                                White & Case LLP
                           1155 Avenue of the Americas
                            New York, New York 10036
                                 (212) 819-8200

CALCULATION OF FILING FEE

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       Transaction Valuation*                     Amount of Filing Fee
--------------------------------------------------------------------------------
          $ 2,891,688,585                            $ 578,337.78
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*  Based on the product of (i) $45.00 per  ordinary  share and (ii)  64,259,753,
   the estimated  maximum number of Triton Energy Limited  ordinary shares to be
   received by the Offeror in the Offer.

|X| Check the box if any part of the fee is offset as  provided by Rule 0-11 (a)
(2) and identify the filing with which the offsetting  fee was previously  paid.
Identify the previous filing by registration  statement  number,  or the Form or
Schedule and the date of its filing.
          Amount Previously Paid:  $578,337.78
          Form or Registration No:  005-49539
          Filing Parties:  Amerada Hess Corporation  and  Amerada  Hess (Cayman)
                           Limited
          Date Filed:  July 17, 2001
|_|  Check the box if the filing relates  solely to  preliminary  communications
     made before the commencement of a tender offer.
Check the appropriate boxes  below  to  designate  any transactions to which the
statement relates:
|X|     third-party tender offer subject to Rule 14d-1.
|_|     issuer tender offer subject to Rule 13e-4.
|_|     going-private transaction subject to Rule 13e-3.
|X|     amendment to Schedule 13D under Rule 13d-2.
Check the following box if the filing is a final amendment reporting the results
of the tender offer:  |_|
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     This  Amendment No. 1 to Tender Offer  Statement on Schedule TO ("Amendment
No. 1") amends and  supplements  the Tender Offer Statement on Schedule TO filed
with the Securities and Exchange  Commission on July 17, 2001 ("Schedule TO") by
Amerada  Hess  (Cayman)  Limited  ("Purchaser"),  a  company  limited  by shares
organized under the laws of the Cayman Islands and a wholly-owned  subsidiary of
Amerada Hess Corporation ("Amerada Hess"), a Delaware  corporation,  relating to
the offer to  purchase  all  unconditionally  allotted  or issued and fully paid
ordinary shares,  par value $0.01 per share, of Triton Energy Limited ("Triton")
and any further ordinary shares which are unconditionally allotted or issued and
fully  paid  before  the date and time on which  the Offer  (as  defined  below)
expires (including the associated Series A junior participating  preferred share
purchase rights issued pursuant to the Rights  Agreement,  dated as of March 25,
1996, by and between Triton and Mellon  Investor  Services LLC, as  amended)(the
"Ordinary  Shares"),  at a price of U.S. $45.00 per Ordinary Share, on the terms
and subject to the conditions set forth in the Offer to Purchase, dated July 17,
2001 (the "Offer to Purchase"), a copy of which is attached as Exhibit (a)(1) to
the Schedule TO, and in the related  Letter of  Transmittal,  a copy of which is
attached as Exhibit (a)(2) to the Schedule TO (which, as they may be amended and
supplemented from time to time, together constitute the "Offer"). This Amendment
No. 1 is being filed on behalf of Purchaser and Amerada Hess.

Item 2.   Subject Company Information

     The second sentence of the third  paragraph  under the caption  "Cautionary
Statements Concerning Projections" in Section 7--"Certain Information Concerning
the  Company" on page 25 of the Offer to  Purchase is hereby  amended to read in
its entirety as follows:

     "Neither  Amerada  Hess  nor  the  Purchaser  nor any of  their  respective
     affiliates  or   representatives   assumes  any   responsibility   for  the
     reasonableness, completeness, accuracy or reliability of such Projections."

Item 4.   Terms of the Transaction

     The second  sentence of the first paragraph of Section  2--"Acceptance  for
Payment and Payment for Ordinary Shares" on pages 11-12 of the Offer to Purchase
is hereby amended to read in its entirety as follows:

     "Subject  to  applicable  rules  of the  Commission  and the  terms  of the
     Acquisition  Agreement,  the Purchaser expressly reserves the right, in its
     sole  discretion,  to delay  acceptance  for  payment  of, or payment  for,
     Ordinary Shares, pending receipt of any governmental regulatory approvals."

     The following text is added to Section 14--"Conditions of the Offer" of the
Offer to Purchase:

     "Notwithstanding  the fact that the Purchaser  reserves the right to assert
     the  existence of any  condition  set forth in this Section 14, in order to
     postpone its obligation to pay for Ordinary Shares following acceptance for
     payment of Ordinary Shares,  the Purchaser  understands that all conditions
     to the Offer,  other than those  dependent  upon the  receipt of  necessary
     governmental regulatory approvals, must be satisfied or waived prior to the
     Expiration Date."

Item 12.  Exhibits.

Exhibit No.         Description
-----------         -----------

Exhibit (a)(1)      Offer to Purchase

Exhibit (a)(2)      Letter of Transmittal

Exhibit (a)(3)      Notice of Guaranteed Delivery

Exhibit (a)(4)      Guidelines for Substitute Form W-9

Exhibit (a)(5)      Form of letter to brokers, dealers,  commercial banks, trust
                    companies and other nominees.

Exhibit (a)(6)      Form of letter to be used by brokers, dealers, commercial
                    banks, trust companies and other nominees to their
                    clients.

Exhibit  (a)(7)     Press Release  issued by the  Purchaser  dated July 10, 2001
                    announcing the tender offer.

Exhibit (a)(8)      Summary  newspaper  advertisement,   dated  July  17,  2001,
                    published in The Wall Street Journal.

Exhibit (b)(1)      Third  Amended and  Restated  Credit  Agreement  dated as of
                    January 23, 2001 among Amerada Hess Corporation, the lenders
                    party  thereto and Goldman  Sachs  Credit  Partners  L.P. as
                    joint book runner,  joint lead arranger and sole syndication
                    agent, Chase Securities, Inc. as joint book runner and joint
                    lead  arranger  and  The  Chase  Manhattan  Bank,  N.A.,  as
                    administrative agent ("Facility A").

Exhibit (b)(2)      Third  Amended and  Restated  Credit  Agreement  dated as of
                    January 23, 2001 among Amerada Hess Corporation, the Lenders
                    Party  thereto and Goldman  Sachs  Credit  Partners  L.P. as
                    joint book runner,  joint lead arranger and sole syndication
                    agent, Chase Securities, Inc. as joint book runner and joint
                    lead  arranger  and  The  Chase  Manhattan  Bank,  N.A.,  as
                    administrative agent ("Facility B").

Exhibit (d)(1)      Acquisition Agreement dated as of July 9, 2001 among Amerada
                    Hess  Corporation,  Amerada Hess (Cayman) Limited and Triton
                    Energy Limited.

                                      -2-

Exhibit (d)(2)      Principal  Shareholders  Agreement  dated as of July 9, 2001
                    among  Amerada  Hess  Corporation,   Amerada  Hess  (Cayman)
                    Limited,  Triton Energy  Limited,  HM4 Triton,  L.P. and the
                    other  shareholders of Triton Energy Limited listed on Annex
                    A thereto.

Exhibit (d)(3)      Confidentiality  Agreement  dated as of June 4, 2001 between
                    Amerada Hess Corporation and Triton Energy Limited.

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

 Previously filed.

 Incorporated  by  reference to Exhibit 99.1 to the Form 8-K/A filed on July
     10, 2001 by Amerada Hess Corporation.

 Incorporated by reference to Exhibit 4(4) to the Form 10-K filed by Amerada
     Hess Corporation on March 28, 2001, Commission File No. 333-50358.

 Incorporated by reference to Exhibit 4(5) to the Form 10-K filed by Amerada
     Hess Corporation on March 28, 2001, Commission File No. 333-50358.

                                      -3-



                                    SIGNATURE

     After due inquiry  and to the best of my  knowledge  and belief,  I certify
that the information set forth in this statement is true, complete and correct.

Dated: July 30, 2001
                                      AMERADA HESS CORPORATION


                                      By: /s/ John Y. Schreyer
                                         ------------------------------
                                          Name:   John Y. Schreyer
                                          Title:  Executive Vice President and
                                                    Chief Financial Officer


                                      AMERADA HESS (CAYMAN) LIMITED


                                      By:  /s/ John Y. Schreyer
                                         ------------------------------
                                          Name:   John Y. Schreyer
                                          Title:  Director



Exhibit No.         Description
-----------         -----------

Exhibit (a)(1)      Offer to Purchase

Exhibit (a)(2)      Letter of Transmittal

Exhibit (a)(3)      Notice of Guaranteed Delivery

Exhibit (a)(4)      Guidelines for Substitute Form W-9

Exhibit (a)(5)      Form of letter to brokers, dealers,  commercial banks, trust
                    companies and other nominees.

Exhibit (a)(6)      Form of letter to be used by  brokers,  dealers,  commercial
                    banks,   trust   companies  and  other   nominees  to  their
                    clients.

Exhibit (a)(7)      Press Release  issued by the  Purchaser  dated July 10, 2001
                    announcing the tender offer.

Exhibit (a)(8)      Summary  newspaper  advertisement,   dated  July  17,  2001,
                    published in The Wall Street Journal.

Exhibit (b)(1)      Third  Amended and  Restated  Credit  Agreement  dated as of
                    January 23, 2001 among Amerada Hess Corporation, the lenders
                    party  thereto and Goldman  Sachs  Credit  Partners  L.P. as
                    joint book runner,  joint lead arranger and sole syndication
                    agent, Chase Securities, Inc. as joint book runner and joint
                    lead  arranger  and  The  Chase  Manhattan  Bank,  N.A.,  as
                    administrative agent ("Facility A").

Exhibit (b)(2)      Third  Amended and  Restated  Credit  Agreement  dated as of
                    January 23, 2001 among Amerada Hess Corporation, the Lenders
                    Party  thereto and Goldman  Sachs  Credit  Partners  L.P. as
                    joint book runner,  joint lead arranger and sole syndication
                    agent, Chase Securities, Inc. as joint book runner and joint
                    lead  arranger  and  The  Chase  Manhattan  Bank,  N.A.,  as
                    administrative agent ("Facility B").

Exhibit (d)(1)      Acquisition Agreement dated as of July 9, 2001 among Amerada
                    Hess  Corporation,  Amerada Hess (Cayman) Limited and Triton
                    Energy Limited.


Exhibit (d)(2)      Principal  Shareholders  Agreement  dated as of July 9, 2001
                    among  Amerada  Hess  Corporation,   Amerada  Hess  (Cayman)
                    Limited,  Triton Energy  Limited,  HM4 Triton,  L.P. and the
                    other  shareholders of Triton Energy Limited listed on Annex
                    A thereto.

Exhibit (d)(3)      Confidentiality  Agreement  dated as of June 4, 2001 between
                    Amerada Hess Corporation and Triton Energy Limited.

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

 Previously filed.

 Incorporated  by  reference to Exhibit 99.1 to the Form 8-K/A filed on July
     10, 2001 by Amerada Hess Corporation.

 Incorporated by reference to Exhibit 4(4) to the Form 10-K filed by Amerada
     Hess Corporation on March 28, 2001, Commission File No. 333-50358.

 Incorporated by reference to Exhibit 4(5) to the Form 10-K filed by Amerada
     Hess Corporation on March 28, 2001, Commission File No. 333-50358.