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                           OFFER TO PURCHASE FOR CASH
  ALL OF THE UNCONDITIONALLY ALLOTTED OR ISSUED AND FULLY PAID ORDINARY SHARES
       (INCLUDING THE ASSOCIATED SERIES A JUNIOR PARTICIPATING PREFERRED
                             SHARE PURCHASE RIGHTS)
                                       OF
                             TRITON ENERGY LIMITED
                                       AT
                         $45.00 NET PER ORDINARY SHARE
                                       BY

                         AMERADA HESS (CAYMAN) LIMITED
                          A WHOLLY OWNED SUBSIDIARY OF

                            AMERADA HESS CORPORATION

  THE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE AT 12:00 MIDNIGHT, NEW YORK CITY
        TIME, ON MONDAY, AUGUST 13, 2001, UNLESS THE OFFER IS EXTENDED.

                                                                   July 17, 2001

To Brokers, Dealers, Commercial Banks,
Trust Companies and Other Nominees:

     We have been appointed 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 act as Dealer Managers in connection with the Purchaser's offer
to purchase all of the existing unconditionally allotted or issued and fully
paid ordinary shares, par value $0.01 per share, of Triton Energy Limited (the
"Company"), a company limited by shares organized under the laws of the Cayman
Islands, 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 (the "Ordinary Shares") at a price of $45.00 per Ordinary
Share, net to the seller in cash, without interest thereon, on the terms and
subject to the conditions set forth in the Offer to Purchase, dated July 17,
2001 (the "Offer to Purchase"), and in the related Letter of Transmittal (which,
as they may be amended and supplemented from time to time, together constitute
the "Offer"), copies of which are enclosed herewith. Please furnish copies of
the enclosed materials to those of your clients for whose accounts you hold
Ordinary Shares in your name or in the name of your nominee.

     Enclosed herewith for your information and forwarding to your clients are
copies of the following documents:

          1. The Offer to Purchase, dated July 17, 2000.

          2. The Letter of Transmittal to tender Ordinary Shares for your use
     and for the information of your clients. Copies of the Letter of
     Transmittal may be used to tender Ordinary Shares.

          3. A letter to shareholders of the Company from James C. Musselman,
     President and Chief Executive Officer of the Company, together with a
     Solicitation/Recommendation Statement on Schedule 14D-9 filed with the
     Securities and Exchange Commission by the Company and mailed to
     shareholders of the Company.
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          4. The Notice of Guaranteed Delivery for Ordinary Shares to be used to
     accept the Offer if the procedures for tendering Ordinary Shares set forth
     in the Offer to Purchase cannot be completed prior to the Expiration Date
     (as defined in the Offer to Purchase).

          5. A printed form of letter which may be sent to your clients for
     whose accounts you hold Ordinary Shares registered in your name or in the
     name of your nominee, with space provided for obtaining such clients'
     instructions with regard to the Offer.

          6. Guidelines of the Internal Revenue Service for Certification of
     Taxpayer Identification Number on Substitute Form W-9.

     WE URGE YOU TO CONTACT YOUR CLIENTS AS PROMPTLY AS POSSIBLE. THE OFFER AND
WITHDRAWAL RIGHTS WILL EXPIRE AT 12:00 MIDNIGHT, NEW YORK CITY TIME, ON MONDAY,
AUGUST 13, 2001, UNLESS THE OFFER IS EXTENDED.

     Please note the following:

          1. The offer price is $45.00 per Ordinary Share, net to the seller in
     cash, without interest thereon, as set forth in the Introduction to the
     Offer to Purchase.

          2. The Offer is conditioned on, among other things, there being
     validly tendered and not properly withdrawn prior to the expiration of the
     Offer a number of Ordinary Shares, which represent at least 90% in value of
     the Ordinary Shares (the "Minimum Condition"). Amerada Hess or the
     Purchaser may, at any time, amend the Minimum Condition to equal the number
     of Ordinary Shares representing at least a majority of the total number of
     votes of the Ordinary Shares determined on a fully diluted basis. The Offer
     is also conditioned on the satisfaction of the HSR Condition (as defined in
     the Offer to Purchase) and the satisfaction of certain other terms and
     conditions. See the Introduction and Sections 14 -- "Conditions of the
     Offer" and 15 -- "Certain Legal Matters; Regulatory Approvals" of the Offer
     to Purchase.

          3. The Offer is being made for all of the unconditionally allotted or
     issued and fully paid Ordinary Shares.

          4. Holders of Ordinary Shares ("Holders") who tender Ordinary Shares
     pursuant to the Offer whose Ordinary Shares are registered in their own
     name and who tender directly to The Bank of New York, as Depositary (the
     "Depositary"), will not be obligated to pay brokerage fees or commissions
     or, except as set forth in Instruction 6 of the Letter of Transmittal,
     transfer taxes on the purchase of Ordinary Shares by the Purchaser pursuant
     to the Offer. However, federal income tax backup withholding at a rate of
     31% may be required, unless an exemption is available or unless the
     required tax identification information is provided. See the section
     entitled "Important Tax Information" in the Letter of Transmittal.

          5. The Offer and the withdrawal rights will expire at 12:00 midnight,
     New York City time, on Monday, August 13, 2001, unless the Offer is
     extended.

          6. The Board of Directors of the Company has unanimously (i)
     determined that the Acquisition Agreement (as defined in the Offer to
     Purchase), the Principal Shareholders Agreement (as defined in the Offer to
     Purchase) and the transactions contemplated thereby, including the Offer,
     the Scheme of Arrangement (as defined in the Offer to Purchase) and the
     Compulsory Acquisition (as defined in the Offer to Purchase) are fair to
     and in the best interests of the Company and the holders of Ordinary Shares
     and Preferred Shares(as defined in the Offer to Purchase) (other than, in
     the case of transactions contemplated by the Principal Shareholders
     Agreement, the Principal Shareholders (as defined in the Offer to
     Purchase)), (ii) approved the execution, delivery and performance by the
     Company of the Acquisition Agreement and the Principal Shareholders
     Agreement and the transactions contemplated thereby, including the Offer,
     the Scheme of Arrangement and the Compulsory Acquisition, and (iii)
     resolved to recommend that the Holders accept the Offer and tender their
     Ordinary Shares (including the Rights) pursuant to the Offer and that the
     holders of Ordinary Shares and Preferred Shares approve the Scheme of
     Arrangement, if such approval is sought.
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          7. Notwithstanding any other provision of the Offer, payment for
     Ordinary Shares accepted for payment pursuant to the Offer will be made
     only after timely receipt by the Depositary of (i) Certificates or, if such
     Ordinary Shares are held in book-entry form, timely confirmation of a
     book-entry transfer (a "Book-Entry Confirmation") of such Ordinary Shares
     into the Depositary's account at The Depository Trust Company, and if
     certificates evidencing the associated Rights have been issued, such
     certificates or a Book-Entry Confirmation, if available, with respect to
     such certificates (unless the Purchaser elects, in its sole discretion, to
     make payment for the Ordinary Shares pending receipt of such certificates
     or a Book-Entry Confirmation, if available, with respect to such
     certificates), (ii) a properly completed and duly executed Letter of
     Transmittal or a copy thereof with any required signature guarantees (or,
     in the case of a book-entry transfer, an Agent's Message (as defined in the
     Offer to Purchase)) and (iii) any other documents required by the Letter of
     Transmittal. Accordingly, tendering Holders may be paid at different times
     depending upon when Certificates for Ordinary Shares (or certificates for
     Rights) or Book-Entry Confirmations with respect to Ordinary Shares (or
     Rights, if applicable) are actually received by the Depositary. UNDER NO
     CIRCUMSTANCES WILL INTEREST BE PAID ON THE PURCHASE PRICE OF THE ORDINARY
     SHARES TO BE PAID BY THE PURCHASER, REGARDLESS OF ANY EXTENSION OF THE
     OFFER OR ANY DELAY IN MAKING SUCH PAYMENT.

     In order to take advantage of the Offer, Certificates, as well as a Letter
of Transmittal (or copy thereof), properly completed and duly executed with any
required signature guarantees (or, in the case of a book-entry delivery, an
Agent's Message), and all other documents required by the Letter of Transmittal
must be received by the Depositary, all in accordance with the instructions set
forth in the Letter of Transmittal and the Offer to Purchase.

     Any Holder who desires to tender Ordinary Shares and whose Certificate(s)
evidencing such Ordinary Shares are not immediately available, or who cannot
comply with the procedures for book-entry transfer described in the Offer to
Purchase on a timely basis, may tender such Ordinary Shares by following the
procedures for guaranteed delivery set forth in Section 3 -- "Procedures for
Tendering Ordinary Shares" of the Offer to Purchase.

     Neither Amerada Hess nor the Purchaser will pay any fees or commissions to
any broker, dealer or other person for soliciting tenders of Ordinary Shares
pursuant to the Offer (other than the Dealer Managers, the Depositary and the
Information Agent as described in the Offer to Purchase). The Purchaser will,
however, upon request, reimburse you for customary mailing and handling expenses
incurred by you in forwarding any of the enclosed materials to your clients. The
Purchaser will pay or cause to be paid any transfer taxes with respect to the
transfer and sale of purchased Ordinary Shares to it or its order pursuant to
the Offer, except as otherwise provided in Instruction 6 of the Letter of
Transmittal.

     Questions and requests for assistance may be directed to the Information
Agent or the Dealer Managers at their respective addresses and telephone numbers
as set forth below. Additional copies of this Offer to Purchase, the Letter of
Transmittal, or other related tender offer materials may be obtained from the
Information Agent or from brokers, dealers, commercial banks or trust companies.

                    The Information Agent for the Offer is:

                             D.F. KING & CO., INC.
                                77 Water Street
                            New York, New York 10005
             Banks and Brokerage Firms, Please Call: (212) 269-5550
                    All others, Please Call: (800) 758-5880

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                     The Dealer Managers for the Offer are:

                              GOLDMAN, SACHS & CO.
                                85 Broad Street
                            New York, New York 10004
                          Call Collect: (212) 902-1000
                           Toll Free: (800) 323-5678

     Requests for copies of the enclosed materials may also be directed to the
Dealer Managers or to the Information Agent at the above addresses and telephone
numbers.

                                          Very truly yours,

                                          GOLDMAN, SACHS & CO.

     NOTHING CONTAINED HEREIN OR IN THE ENCLOSED DOCUMENTS SHALL CONSTITUTE YOU
OR ANY OTHER PERSON THE AGENT OF THE PURCHASER, AMERADA HESS, THE COMPANY, THE
DEALER MANAGERS, THE DEPOSITARY, THE INFORMATION AGENT OR ANY AFFILIATE OF ANY
OF THEM, OR AUTHORIZE YOU OR ANY OTHER PERSON TO MAKE ANY STATEMENT OR USE ANY
DOCUMENT ON BEHALF OF ANY OF THEM IN CONNECTION WITH THE OFFER OTHER THAN THE
ENCLOSED DOCUMENTS AND THE STATEMENTS CONTAINED THEREIN.

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