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                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
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                                  SCHEDULE TO

                             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)

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                          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
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                                 $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.

[ ] 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.

[ ] 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.

     [ ] 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 Tender Offer Statement on Schedule TO ("Schedule TO") relates to the
offer by Amerada Hess (Cayman) Limited (the "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,
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 hereto as Exhibit (a)(1), and
in the related Letter of Transmittal, a copy of which is attached hereto as
Exhibit (a)(2) (which, as they may be amended and supplemented from time to
time, together constitute the "Offer"). This Schedule TO is being filed on
behalf of the Purchaser and Amerada Hess.

     The information in the Offer to Purchase, including all schedules and
annexes thereto, is incorporated herein by reference in response to all the
items of this Schedule TO, except as otherwise set forth below.

ITEM 10.  FINANCIAL STATEMENTS.

     (a) Financial information. Not applicable.

     (b) Pro forma information. Not applicable.

ITEM 11.  ADDITIONAL INFORMATION.

     (b) Other material information.  The information set forth in the Letter of
Transmittal attached hereto as Exhibit (a)(2) is incorporated herein by
reference.

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ITEM 12. EXHIBITS.



EXHIBIT NO.                                DESCRIPTION
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Exhibit (a)(1)     Offer to Purchase.
Exhibit (a)(2)     Letter of Transmittal.
Exhibit (a)(3)     Notice of Guaranteed Delivery.
Exhibit (a)(4)     Guidelines for Certification of Taxpayer Identification
                   Number on 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.(1)
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").(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").(3)
Exhibit (d)(1)     Acquisition Agreement dated as of July 9, 2001 by and among
                   Amerada Hess Corporation, Amerada Hess (Cayman) Limited and
                   Triton Energy Limited.
Exhibit (d)(2)     Principal Shareholders Agreement dated as of July 9, 2001 by
                   and 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.
Exhibit (d)(4)     Amendment No. 1 to Acquisition Agreement, dated as of July
                   17, 2001, by and among Amerada Hess Corporation, Amerada
                   Hess (Cayman) Limited and Triton Energy Limited.


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

(2) Incorporated by reference to Exhibit 4(4) to the Form 10-K filed by Amerada
    Hess Corporation on March 15, 2001, Commission File No. 333-50358.

(3) Incorporated by reference to Exhibit 4(5) to the Form 10-K filed by Amerada
    Hess Corporation on March 15, 2001, Commission File No. 333-50358.

ITEM 13.  INFORMATION REQUIRED BY SCHEDULE 13E-3.

     Not applicable.

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                                   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 17, 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: Director

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                                 EXHIBIT INDEX



EXHIBIT NO.                                DESCRIPTION
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Exhibit (a)(1)     Offer to Purchase.
Exhibit (a)(2)     Letter of Transmittal.
Exhibit (a)(3)     Notice of Guaranteed Delivery.
Exhibit (a)(4)     Guidelines for Certification of Taxpayer Identification
                   Number on 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.(1)
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").(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").(3)
Exhibit (d)(1)     Acquisition Agreement dated as of July 9, 2001 by and among
                   Amerada Hess Corporation, Amerada Hess (Cayman) Limited and
                   Triton Energy Limited.
Exhibit (d)(2)     Principal Shareholders Agreement dated as of July 9, 2001 by
                   and 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.
Exhibit (d)(4)     Amendment No. 1 to Acquisition Agreement, dated as of July
                   17, 2001, by and among Amerada Hess Corporation, Amerada
                   Hess (Cayman) Limited and Triton Energy Limited.


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

(2) Incorporated by reference to Exhibit 4(4) to the Form 10-K filed by Amerada
    Hess Corporation on March 15, 2001, Commission File No. 333-50358.

(3) Incorporated by reference to Exhibit 4(5) to the Form 10-K filed by Amerada
    Hess Corporation on March 15, 2001, Commission File No. 333-50358.

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