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                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
                            -------------------------
                                   SCHEDULE TO
                                (Amendment No. 2)
                             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. 2 to Tender Offer  Statement on Schedule TO ("Amendment
No. 2") amends and  supplements  the Tender Offer Statement on Schedule TO filed
with the Securities and Exchange Commission on July 17, 2001 ("Schedule TO"), as
amended by Amendment No. 1 filed July 30, 2001, 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. 2 is being
filed on behalf of Purchaser and Amerada Hess.

Item 7.  Source and Amount of Funds or Other Consideration

     The  following  text  is  added  after  the  fourth  paragraph  of  Section
9--"Source and Amount of Funds" on page 28 of the Offer to Purchase:

     "On July 30, 2001,  Amerada Hess entered into a definitive Credit Agreement
     with Citibank  relating to the Revolving  Facility  (the  "Citibank  Credit
     Agreement").  Pursuant to the Citibank Credit  Agreement,  borrowings under
     the Revolving  Facility will bear interest at a rate per annum equal to (at
     Amerada Hess'  election) (i) the  administrative  agent's base rate or (ii)
     the London  Interbank  Offered  Rate (LIBOR) plus a margin of 42.5 to 115.0
     basis points on Eurodollar borrowings.  There is also a facility fee on the
     Revolving  Facility  at a rate of 7.5 to 35.0 basis  points per annum and a
     utilization  fee of 5.0 to 25.0 basis  points on the facility to the extent
     more than  one-third  utilized.  The margins and such fees will be based on
     Amerada  Hess' public debt ratings  (rather  than Amerada  Hess'  long-term
     senior  unsecured  non-credit-enhanced  debt ratings as contemplated in the
     commitment letter).  Borrowings under the Revolving Facility may be made on
     the first  date that  certain  conditions  precedent  have been  satisfied,
     including  that the  Purchaser  shall have  accepted for payment at least a
     majority  of the  outstanding  Ordinary  Shares on a fully  diluted  basis.
     Amerada Hess has agreed to pay certain  expenses of, and provide  customary
     indemnities for,  Citibank.  The Citibank Credit Agreement  incorporates by
     reference all of the terms and conditions of Credit  Facility A (as defined
     below) (including conditions, representations and warranties, covenants and
     events  of  default)  not  otherwise   addressed  in  the  Citibank  Credit
     Agreement. The foregoing summary of the Revolving Facility and the Citibank
     Credit  Agreement  is qualified in its entirety by reference to the text of
     the Citibank Credit Agreement, a copy of which has been filed as an exhibit
     to the Schedule TO relating to the Offer which the Purchaser has filed with
     the  Commission.  The Citibank  Credit  Agreement  may be inspected at, and
     copies may be obtained from, the same places and in the manner set forth in
     Section 7--"Certain Information Concerning the Company.""

Item 11.  Additional Information



     Section 15--"Certain Legal Matters;  Regulatory Approval" on pages 57-59 of
the  Offer to  Purchase  is hereby  amended  and  supplemented  to  include  the
following  text  after the third  paragraph  under  the  subsection  "Regulatory
Approvals" on page 59 of the Offer to Purchase:

     "On July 27, 2001, the Purchaser  received notice from the FTC of the early
     termination  of the  waiting  period  under  the HSR Act,  relating  to the
     proposed acquisition of the Company."

Item 12.  Exhibits.

Exhibit No.       Description

Exhibit (a)(1)    Offer to Purchase.(1)

Exhibit (a)(2)    Letter of Transmittal.(1)

Exhibit (a)(3)    Notice of Guaranteed Delivery.(1)

Exhibit (a)(4)    Guidelines for Substitute Form W-9.(1)

Exhibit (a)(5)    Form  of  letter  to brokers, dealers, commercial banks, trust
                  companies and other nominees.(1)

Exhibit (a)(6)    Form of letter to  be used  by  brokers,  dealers, commercial
                  banks,   trust  companies  and   other   nominees   to  their
                  clients.(1)

Exhibit (a)(7)    Press  Release  issued  by  the  Purchaser dated July 10, 2001
                  announcing the tender offer.(2)

Exhibit (a)(8)    Summary  newspaper  advertisement,  dated  July 17, 2001, pub-
                  lished in The Wall Street Journal.(1)

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").(3)


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

(1)  Previously  filed.

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

(3)  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.


                                      -2-




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").(4)

Exhibit (b)(3)    Credit  Agreement  dated as of July 30, 2001  between  Amerada
                  Hess Corporation and Citibank, N.A. (5)

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

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.(1)

Exhibit (d)(3)    Confidentiality  Agreement  dated as of June 4,  2001  between
                  Amerada Hess Corporation and Triton Energy Limited.(1)


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

(4)  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.

(5)  Filed herewith.



                                      -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: August 3, 2001
                                    AMERADA HESS CORPORATION


                                     By: /s/ J. Barclay Collins II
                                        ----------------------------------------
                                        Name:  J. Barclay Collins II
                                        Title: Executive Vice President and
                                                 General Counsel

                                    AMERADA HESS (CAYMAN) LIMITED


                                     By: /s/ J. Barclay Collins II
                                        ---------------------------------------
                                        Name:  J. Barclay Collins II
                                        Title: Executive Vice President and
                                                 General Counsel





Exhibit No.       Description

Exhibit (a)(1)    Offer to Purchase.(1)

Exhibit (a)(2)    Letter of Transmittal.(1)

Exhibit (a)(3)    Notice of Guaranteed Delivery.(1)

Exhibit (a)(4)    Guidelines for Substitute Form W-9.(1)

Exhibit(a)(5)     Form of letter to brokers,  dealers,  commercial banks,  trust
                  companies and other nominees.(1)

Exhibit (a)(6)    Form of  letter  to be used by  brokers,  dealers,  commercial
                  banks, trust companies and other nominees to their clients.(1)

Exhibit (a)(7)    Press  Release  issued by the  Purchaser  dated July 10,  2001
                  announcing the tender offer.(2)

Exhibit (a)(8)    Summary   newspaper   advertisement,   dated  July  17,  2001,
                  published in The Wall Street Journal.(1)

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").(3)

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").(4)


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

(1)  Previously filed.

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

(3)  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.

(4)  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.






Exhibit (b)(3)    Credit  Agreement  dated as of July 30, 2001  between  Amerada
                  Hess Corporation and Citibank, N.A.(6)

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

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.(1)

Exhibit (d)(3)    Confidentiality  Agreement  dated as of June 4,  2001  between
                  Amerada Hess Corporation and Triton Energy Limited.(1)

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

(6)  Filed herewith.