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THIS DOCUMENT IS IMPORTANT AND REQUIRES YOUR IMMEDIATE ATTENTION. IF YOU ARE IN
ANY DOUBT AS TO THE ACTION TO BE TAKEN, YOU SHOULD SEEK YOUR OWN FINANCIAL
ADVICE IMMEDIATELY FROM YOUR OWN APPROPRIATELY AUTHORIZED INDEPENDENT FINANCIAL
ADVISOR. IF YOU HAVE SOLD OR TRANSFERRED ALL OF YOUR REGISTERED HOLDINGS OF
ORDINARY SHARES (AS DEFINED BELOW), PLEASE FORWARD THIS DOCUMENT AND ALL
ACCOMPANYING DOCUMENTS TO THE STOCKBROKER, BANK OR OTHER AGENT THROUGH WHOM THE
SALE OR TRANSFER WAS EFFECTED, FOR TRANSMISSION TO THE PURCHASER OR TRANSFEREE.

                         NOTICE OF GUARANTEED DELIVERY
                   (NOT TO BE USED FOR SIGNATURE GUARANTEES)
                                   TO TENDER
                 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
                       PURSUANT TO THE OFFER TO PURCHASE
                              DATED JULY 17, 2001
                                       BY

                         AMERADA HESS (CAYMAN) LIMITED
                          A WHOLLY OWNED SUBSIDIARY OF

                            AMERADA HESS CORPORATION

     As set forth under Section 3 -- "Procedures for Tendering Ordinary Shares"
in the Offer to Purchase, dated July 17, 2001, and any supplements or amendments
thereto (the "Offer to Purchase"), this form (or a copy hereof) must be used to
accept the Offer (as defined in the Offer to Purchase) if (i) certificates (the
"Certificates") representing Ordinary Shares of Triton Energy Limited (as
defined in the Offer to Purchase), par value $0.01 per share, together with the
associated Series A junior participating preferred share purchase rights (the
"Rights"), are not immediately available (including because certificates for
Rights have not yet been distributed by the Rights Agent (as defined in the
Offer to Purchase)), (ii) time will not permit all required documents to reach
The Bank of New York (the "Depositary") prior to the Expiration Date (as defined
in Section 1 -- "Terms of the Offer" of the Offer to Purchase) or (iii) the
procedure for book-entry transfer cannot be completed on a timely basis. This
Notice of Guaranteed Delivery may be delivered by hand to the Depositary, or
transmitted by facsimile transmission, or by mail to the Depositary and must
include a guarantee by an Eligible Institution (as defined in Section 3 --
"Procedures for Tendering Ordinary Shares") in the form set forth herein. See
the guaranteed delivery procedures described in the Offer to Purchase under
Section 3 -- "Procedures for Tendering Ordinary Shares."

                        The Depositary for the Offer is:
                              THE BANK OF NEW YORK



            By Mail:                      By Facsimile:              By Hand/Overnight Courier:
                                                            
      THE BANK OF NEW YORK                (for Eligible                 THE BANK OF NEW YORK
  TENDER & EXCHANGE DEPARTMENT          Institutions only)          TENDER & EXCHANGE DEPARTMENT
         P.O. Box 11248                   (212) 815-6213                 101 Barclay Street
     Church Street Station                                           Receive and Deliver Window
   Receive and Deliver Window    For Confirmation Only Telephone:     New York, New York 10286
 New York, New York 10286-1248
                                          (212) 815-6156


     DELIVERY OF THIS NOTICE OF GUARANTEED DELIVERY TO AN ADDRESS OTHER THAN AS
SET FORTH ABOVE OR TRANSMISSION OF INSTRUCTION VIA FACSIMILE TRANSMISSION OTHER
THAN AS SET FORTH ABOVE WILL NOT CONSTITUTE A VALID DELIVERY.

     This Notice of Guaranteed Delivery is not to be used to guarantee a
signature. If a signature on a Letter of Transmittal is required to be
guaranteed by an Eligible Institution (as defined in Section 3 -- "Procedures
for Tendering Ordinary Shares" of the Offer to Purchase) under the instructions
thereto, such signature guarantee must appear in the applicable space provided
in the signature box on the Letter of Transmittal.
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LADIES AND GENTLEMEN:

     THE UNDERSIGNED HEREBY TENDERS TO AMERADA HESS (CAYMAN) LIMITED, A COMPANY
LIMITED BY SHARES ORGANIZED UNDER THE LAWS OF THE CAYMAN ISLANDS AND A WHOLLY
OWNED SUBSIDIARY OF AMERADA HESS CORPORATION, A DELAWARE CORPORATION, ON THE
TERMS AND SUBJECT TO THE CONDITIONS SET FORTH IN THE OFFER TO PURCHASE AND THE
RELATED LETTER OF TRANSMITTAL, RECEIPT OF EACH OF WHICH IS HEREBY ACKNOWLEDGED,
THE NUMBER OF ORDINARY SHARES INDICATED BELOW PURSUANT TO THE GUARANTEED
DELIVERY PROCEDURES DESCRIBED IN THE OFFER TO PURCHASE UNDER SECTION 3 --
"PROCEDURES FOR TENDERING ORDINARY SHARES."

     NO AUTHORITY HEREIN CONFERRED OR AGREED TO BE CONFERRED SHALL BE AFFECTED
BY, AND ALL SUCH AUTHORITY SHALL SURVIVE, THE DEATH OR INCAPACITY OF THE
UNDERSIGNED. ALL OBLIGATIONS OF THE UNDERSIGNED HEREUNDER SHALL BE BINDING UPON
THE HEIRS, EXECUTORS, ADMINISTRATORS, LEGAL REPRESENTATIVES, SUCCESSORS AND
ASSIGNS OF THE UNDERSIGNED.

NAME OF RECORD HOLDER(S):
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ADDRESS(ES):
- --------------------------------------------------------------------------------
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AREA CODE(S) AND TEL. NO(S).:
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SIGNATURE(S):
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DATE:
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NUMBER OF ORDINARY SHARES:
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CERTIFICATE NUMBER(S) IF AVAILABLE:
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IF ORDINARY SHARES WILL BE TENDERED BY BOOK-ENTRY TRANSFER CHECK BOX:

[ ] The Depository Trust Company
   Account Number:
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THE GUARANTEE BELOW MUST BE COMPLETED

                                   GUARANTEE

                    (NOT TO BE USED FOR SIGNATURE GUARANTEE)

     The undersigned, an Eligible Institution (as defined in Section
3 -- "Procedures for Tendering Ordinary Shares" of the Offer to Purchase),
hereby guarantees that the undersigned will deliver to the Depositary, at one of
its addresses set forth above, either the Certificates representing the Ordinary
Shares, together with the associated Series A junior participating preferred
share purchase rights, tendered hereby, in proper form for transfer, or Book-
Entry Confirmation (as defined in the Offer to Purchase), together with a
properly completed and duly executed Letter of Transmittal, including any
required signature guarantees, or, in the case of book-entry delivery of
Ordinary Shares, an Agent's Message (as defined in the Offer to Purchase), and
any other documents required by the Letter of Transmittal, all within three New
York Stock Exchange trading days (as defined in Section 3 -- "Procedures for
Tendering Ordinary Shares" of the Offer to Purchase) after the date hereof.

                                 NAME OF FIRM:

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 Address:
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                                                                      (ZIP CODE)

 Area Code and Tel. No.:
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                             AUTHORIZED SIGNATURE:

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 Name:
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                                 (PLEASE PRINT)

 Title:
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 Date:
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NOTE:  DO NOT SEND CERTIFICATES WITH THIS NOTICE OF GUARANTEED DELIVERY;
       CERTIFICATES SHOULD BE SENT WITH YOUR LETTER OF TRANSMITTAL.

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