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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
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                      (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 P. 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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*    Set forth the amount on which the filing fee is calculated and state how it
     was determined.

/ /  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:
          Form or Registration No.:
          Filing Party:
          Date Filed:

/X/  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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