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                       [TRITON ENERGY LIMITED LETTERHEAD]

                                                                   July 17, 2001

Dear Triton Energy Limited Shareholder:

     I am pleased to report that on July 9, 2001, Triton Energy Limited entered
into an Acquisition Agreement with Amerada Hess Corporation and Amerada Hess
(Cayman) Limited pursuant to which Amerada Hess has agreed to acquire all of the
outstanding ordinary shares of Triton at a price of $45.00 per share, net to the
seller in cash, without interest. Under the terms of the proposed transaction,
Amerada Hess has commenced a tender offer for all such shares. The offer is
currently scheduled to expire at 12:00 midnight, New York City time, on Monday,
August 13, 2001, unless otherwise extended.

     Amerada Hess has also agreed with Hicks, Muse, Tate & Furst Incorporated to
acquire its approximately 38% ownership stake in Triton.

     If Amerada Hess acquires in the offer at least 90% of the ordinary shares,
Amerada Hess and Triton will take all necessary action to complete a compulsory
acquisition of all remaining ordinary shares under Cayman Islands law at the
same price as paid in the offer. If Amerada Hess does not acquire at least 90%
of the ordinary shares in the offer, then, upon the request of Amerada Hess,
Triton will pursue a scheme of arrangement under Cayman Islands law pursuant to
which, if approved by the shareholders, Amerada Hess would acquire the
outstanding ordinary shares and the outstanding 8% convertible preference shares
at a per share price of $45.00 in cash for each ordinary share and $180.00, plus
accumulated and unpaid dividends, in cash for each preference share.

     The transaction reflects the considerable progress Triton has made in
recent years and rewards our shareholders with premium value for their shares.
Triton today is a leading independent exploration and production company with
world-class assets around the globe, strong financial results and a solid
balance sheet. These achievements are a credit to our people, who have
consistently demonstrated the experience and commitment necessary to capitalize
on the potential of our assets.

     YOUR BOARD OF DIRECTORS HAS UNANIMOUSLY DETERMINED THAT THE AMERADA HESS
OFFER IS FAIR TO, AND IN THE BEST INTEREST OF, THE SHAREHOLDERS OF THE COMPANY
AND RECOMMENDS THAT SHAREHOLDERS ACCEPT THE OFFER AND TENDER THEIR SHARES IN THE
OFFER.

     Accompanying this letter is a copy of Triton's Solicitation/Recommendation
Statement on Schedule 14D-9 and Triton's Information Statement pursuant to
Section 14(f) of the Securities Exchange Act of 1934, as amended, each as filed
by Triton with the Securities and Exchange Commission.

     Also accompanying this letter is a copy of the Offer to Purchase and
related materials of Amerada Hess, including a Letter of Transmittal for use in
tendering your ordinary shares. These documents set forth the terms and
conditions of the offer and provide instructions for tendering your ordinary
shares.

     WE URGE YOU TO READ THE ENCLOSED MATERIALS CAREFULLY.

     The management and directors of Triton thank you for the support you have
given the company.

                                            Sincerely,

                                            TRITON ENERGY LIMITED

                                            James C. Musselman
                                            President, Chief Executive Officer
                                            and Director