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                                                                   EXHIBIT: 10.1

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                        PRINCIPAL SHAREHOLDERS AGREEMENT


                                  BY AND AMONG


                            AMERADA HESS CORPORATION,


                         AMERADA HESS (CAYMAN) LIMITED,


                              TRITON ENERGY LIMITED


                                       AND


       THE SHAREHOLDERS OF TRITON ENERGY LIMITED LISTED ON ANNEX A HERETO


                            Dated as of July 9, 2001



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                        PRINCIPAL SHAREHOLDERS AGREEMENT



         PRINCIPAL SHAREHOLDERS AGREEMENT (this "Agreement") dated as of July 9,
2001, by and among AMERADA HESS CORPORATION ("Parent"), a corporation organized
under the laws of Delaware, AMERADA HESS (CAYMAN) LIMITED ("Sub"), a company
limited by shares organized under the laws of the Cayman Islands and a wholly
owned subsidiary of Parent, each of the shareholders of the Company set forth on
Annex A hereto (each, a "Shareholder") and, solely for purposes of the last
sentence of Section 2.1, Section 5.3(b) and Article VIII, TRITON ENERGY LIMITED
(the "Company"), a company limited by shares organized under the laws of the
Cayman Islands.

                                   WITNESSETH:

         WHEREAS, Parent, Sub and the Company propose to enter into an
Acquisition Agreement, dated as of the date hereof (the "Acquisition
Agreement"), pursuant to which Sub is to make a tender offer to purchase,
subject to the terms and conditions of the Acquisition Agreement, any and all of
the Ordinary Shares (including the associated Rights) of the Company (the
"Offer");

         WHEREAS, as of the date hereof, each Shareholder or such Shareholder's
Affiliates "beneficially own" (as such term is defined in Rule 13d-3 promulgated
under the Exchange Act) and each Shareholder or such Shareholder's Affiliates
are entitled to dispose of (or to direct the disposition of) and to vote (or to
direct the voting of) the number of Ordinary Shares and/or Preferred Shares set
forth opposite such Shareholder's name on Annex A hereto, as such shares may be
adjusted by stock dividend, stock split, recapitalization, combination, merger,
amalgamation, scheme of arrangement, consolidation, reorganization or other
change in the capital structure of the Company affecting the Ordinary Shares or
Preferred Shares (such shares, together with any other shares the beneficial
ownership of which is acquired by such Shareholder or such Shareholder's
Affiliates during the period from and including the date hereof through and
including the date on which this Agreement is terminated in accordance with its
terms, are collectively referred to herein as such Shareholder's "Subject
Shares"); and

         WHEREAS, as a condition to the willingness of Parent and Sub to enter
into the Acquisition Agreement, and as an inducement and in consideration
therefor, Parent has required that each Shareholder agrees, and each Shareholder
has agreed, to enter into this Agreement;

         NOW, THEREFORE, in consideration of the foregoing and the mutual
premises, representations, warranties, covenants and agreements contained
herein, the parties hereto, intending to be legally bound, hereby agree as
follows:


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                                TABLE OF CONTENTS

<TABLE>
<CAPTION>
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<S>                        <C>                                                                                 <C>
ARTICLE I

DEFINITIONS...................................................................................................... 2
         Section 1.1       Definitions........................................................................... 2

ARTICLE II

TENDER OF SHARES................................................................................................. 2
         Section 2.1       Tender of Shares...................................................................... 2

ARTICLE III

VOTING AND PROXY................................................................................................. 3
         Section 3.1       Agreement to Vote the Subject Shares.................................................. 3
         Section 3.2       Grant of Proxy........................................................................ 3
         Section 3.3       Nature of Proxy....................................................................... 4

ARTICLE IV

PURCHASE AND SALE................................................................................................ 4
         Section 4.1       Purchase and Sale..................................................................... 4
         Section 4.2       Closing............................................................................... 4
         Section 4.3       Subsequent Offering Period............................................................ 5

ARTICLE V

COVENANTS........................................................................................................ 5
         Section 5.1       Generally............................................................................. 5
         Section 5.2       No Solicitation of Other Offers....................................................... 5
         Section 5.3       Investor Rights Agreement............................................................. 6
         Section 5.4       Conversion of Preferred Shares........................................................ 6
         Section 5.5       Compliance with Law; Acquisition Agreement............................................ 6
         Section 5.6       Extension of Initial Offering Period.................................................. 6

ARTICLE VI

REPRESENTATIONS AND WARRANTIES OF SHAREHOLDERS................................................................... 7
         Section 6.1       Due Organization, etc................................................................. 7
         Section 6.2       Ownership of Shares................................................................... 7
         Section 6.3       No Conflicts.......................................................................... 7
         Section 6.4       No Finder's Fees...................................................................... 7
</TABLE>


                                      (i)
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<TABLE>
<CAPTION>
                                                                                                               Page
                                                                                                               ----
<S>                        <C>                                                                                 <C>
         Section 6.5       No Encumbrances....................................................................... 8
         Section 6.6       Reliance by Parent.................................................................... 8
         Section 6.7       Investor Rights Agreement............................................................. 8

ARTICLE VII

REPRESENTATIONS AND WARRANTIES OF PARENT AND SUB................................................................. 8
         Section 7.1       Due Organization, etc................................................................. 8
         Section 7.2       No Conflicts.......................................................................... 9
         Section 7.3       Investment Intent..................................................................... 9
         Section 7.4       No Finder's Fees...................................................................... 9
         Section 7.5       Litigation............................................................................ 9
         Section 7.6       Ownership of Sub...................................................................... 9
         Section 7.7       Reliance by Shareholder............................................................... 9

ARTICLE VIII

REPRESENTATIONS AND WARRANTIES OF THE COMPANY................................................................... 10
         Section 8.1       No Adjustment........................................................................ 10
         Section 8.2       Investor Rights Agreement............................................................ 10

ARTICLE IX

MISCELLANEOUS................................................................................................... 10
         Section 9.1       Shareholder Capacity................................................................. 10
         Section 9.2       Publication.......................................................................... 10
         Section 9.3       Further Actions...................................................................... 10
         Section 9.4       Entire Agreement..................................................................... 10
         Section 9.5       Binding Effect; Benefit; Assignment.................................................. 11
         Section 9.6       Amendments, Waivers, etc............................................................. 11
         Section 9.7       Notices.............................................................................. 11
         Section 9.8       Specific Enforcement................................................................. 12
         Section 9.9       Remedies Cumulative.................................................................. 12
         Section 9.10      No Waiver............................................................................ 12
         Section 9.11      Applicable Law....................................................................... 12
         Section 9.12      Headings............................................................................. 13
         Section 9.13      Counterparts......................................................................... 13
         Section 9.14      Termination.......................................................................... 13
         Section 9.15      Affiliates........................................................................... 13
         Section 9.16      No Recourse.......................................................................... 13

ANNEX A......................................................................................................... 17

ANNEX B........................................................................................................  18
</TABLE>


                                      (ii)
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                                   ARTICLE I

                                   DEFINITIONS

         Section 1.1 Definitions. For purposes of this Agreement, capitalized
terms used and not defined herein shall have the respective meanings ascribed to
them in the Acquisition Agreement.

                                   ARTICLE II

                                TENDER OF SHARES

         Section 2.1 Tender of Shares. Each Shareholder hereby agrees to (A) in
the case of Ordinary Shares, tender validly (and not to withdraw unless
instructed by Purchaser), or to cause to be tendered validly (and not withdrawn
unless instructed by Purchaser), and (B) in the case of Preferred Shares, duly
surrender for conversion, conditional upon the Offer not being terminated, not
expiring and Sub accepting for payment Ordinary Shares in the Offer and with
appropriate instructions (which instructions shall be revoked only upon the
direction of Purchaser) that the Ordinary Shares issuable upon such conversion
are to be tendered pursuant to the Offer immediately prior to the expiration of
the initial offering period of the Offer (including any extensions thereof), in
each case pursuant to and in accordance with the terms of the Offer and Rule
14d-2 under the Exchange Act, all of such Shareholder's Subject Shares, in each
case not later than (i) the third (3rd) Business Day after commencement of the
Offer and (ii) in the case of any Subject Shares acquired after the date hereof,
whether upon the exercise of options, warrants or rights, the conversion or
exchange of convertible or exchangeable securities, or otherwise, the next
succeeding Business Day after acquisition thereof, and will cause such
Shareholder's Subject Shares to remain, in the case of Ordinary Shares, validly
tendered and not withdrawn and, in the case of Preferred Shares, surrendered for
conversion with appropriate tender instructions until the earlier of (x) the
Offer being terminated or expiring and Sub not accepting for payment all
Ordinary Shares validly tendered in the Offer and (y) Parent, in the case of
Ordinary Shares, instructing such Shareholder to withdraw such Shareholder's
Shares or, in the case of Preferred Shares, instructing such Shareholder to
revoke such Shareholder's tender and conversion instructions, in which case such
Shareholder shall immediately withdraw all Ordinary Shares and revoke tender and
conversion instructions with respect to Preferred Shares. Notwithstanding the
provisions of the preceding sentence, in the event that any Ordinary Shares are
for any reason withdrawn from the Offer or the tender and conversion
instructions relating to Preferred Shares are revoked, in either case other than
upon the instruction of Purchaser, such Ordinary Shares and Preferred Shares
shall remain subject to the terms of this Agreement so long as this Agreement
remains effective. The parties hereby acknowledge and agree that the obligation
of Sub to accept for payment and pay for the Ordinary Shares in the Offer,
including the Subject Shares, is subject to the conditions set forth in Annex A
to the Acquisition Agreement; provided, that the only conditions of Parent and
Sub to purchase Subject Shares pursuant to Section 4.1 of this Agreement are set
forth on Annex B hereto. The Company hereby acknowledges and agrees that the
surrender for conversion of Preferred Shares on a conditional basis shall not
constitute a conversion until the conditions relating thereto are satisfied or
waived and the Company hereby


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waives any and all notice or waiting period requirement with respect to a
conversion of such Preferred Shares.

                                  ARTICLE III

                                VOTING AND PROXY

         Section 3.1 Agreement to Vote the Subject Shares. Each Shareholder, in
its capacity as such, hereby agrees that during the period commencing on the
date hereof and continuing until the termination of this Agreement (such period,
the "Voting Period"), at any meeting (or any adjournment or postponement
thereof) of the holders of any class or classes of the share capital of the
Company, however called, or in connection with any written consent of the
holders of any class or classes of the share capital of the Company, such
Shareholder shall vote (or cause to be voted) the Subject Shares (x) in favor of
the approval of the terms of the Acquisition Agreement and each of the other
transactions contemplated by the Acquisition Agreement and this Agreement and
any actions required in furtherance thereof, (y) against any action, transaction
or agreement that would result in a breach in any respect of any covenant,
representation or warranty or any other obligation or agreement of the Company
or any of its Subsidiaries under the Acquisition Agreement or of such
Shareholder under this Agreement, and (z) except as otherwise agreed to in
writing in advance by Parent, against the following actions (other than the
transactions contemplated by the Acquisition Agreement): (i) any extraordinary
corporate transaction, such as an amalgamation, merger, scheme of arrangement,
consolidation or other business combination involving the Company or any of its
Subsidiaries and any Acquisition Proposal; (ii) a sale, lease or transfer of a
significant part of the assets of the Company or any of its Subsidiaries, or a
reorganization, recapitalization, dissolution or liquidation of the Company or
any of its Subsidiaries (each of the actions in (i) or (ii), a "Business
Combination"); (iii) (A) any change in the Persons who constitute the board of
directors of the Company; (B) any change in the present capitalization of the
Company or any amendment of the Company's Memorandum of Association or the
Company's Articles of Association; (C) any other material change in the
Company's corporate structure or business; or (D) any other action involving the
Company or any of its Subsidiaries that is intended, or could reasonably be
expected, to impede, interfere with, delay, postpone, or adversely affect the
transactions contemplated by this Agreement or the Acquisition Agreement. Each
Shareholder hereby agrees that such Shareholder shall not, and shall use
commercially reasonable efforts to cause its Affiliates not to, enter into any
agreement, letter of intent, agreement in principle or understanding with any
Person that violates or conflicts with or could reasonably be expected to
violate or conflict with the provisions and agreements contained in this
Agreement or the Acquisition Agreement.

         Section 3.2 Grant of Proxy. Each Shareholder hereby appoints Parent,
Sub and any designee of Parent or Sub, and each of them individually, such
Shareholder's proxy and attorney-in-fact, with full power of substitution and
resubstitution, to vote or act by written consent during the Voting Period with
respect to such Shareholder's Subject Shares in accordance with Section 3.1.
This proxy is given to secure the performance of the duties of each Shareholder
under this Agreement. Each Shareholder shall take such further action or execute
such other instruments as may be necessary to effectuate the intent of this
proxy.


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         Section 3.3 Nature of Proxy. The proxy and power of attorney granted
pursuant to Section 3.2 by each Shareholder shall be irrevocable during the term
of this Agreement, shall be deemed to be coupled with an interest sufficient in
law to support an irrevocable proxy and shall revoke all prior proxies granted
by such Shareholder. The power of attorney granted herein is a durable power of
attorney and shall survive the dissolution, bankruptcy, death or incapacity of
such Shareholder.

                                   ARTICLE IV

                               PURCHASE AND SALE

         Section 4.1 Purchase and Sale. Subject to the terms and conditions
herein set forth, if the initial offering period of the Offer (including any
extension thereof) has terminated or expired without the acceptance for purchase
of each Shareholder's Ordinary Shares tendered pursuant to Section 2.1 (the
"Purchase Date"), each Shareholder hereby severally agrees to sell, and Parent
hereby agrees to cause Sub, and Sub hereby agrees to purchase, all of each
Shareholder's Subject Shares. Sub shall have the right to purchase either the
Preferred Shares or to cause any Shareholder to convert such Preferred Shares
into Ordinary Shares and purchase such Ordinary Shares. The purchase price shall
be the greater of (a) in the case of Ordinary Shares, U.S. $45.00 per Ordinary
Share net to the Shareholder in cash and in the case of Preferred Shares,
$180.00 per Preferred Share, plus accumulated and unpaid dividends through the
date of purchase, net to the Shareholder in cash and (b) in the case of Ordinary
Shares, the highest price paid per Ordinary Share in the Offer and, in the case
of Preferred Shares, the as-converted equivalent amount per Preferred Share as
such highest price paid per Ordinary Share in the Offer, plus accumulated and
unpaid dividends through the date of purchase. The obligation of Sub to purchase
the Subject Shares is subject to the satisfaction or waiver of each of the
conditions set forth on Annex B.

         Section 4.2 Closing. Subject to Section 4.3, the Closing (the
"Closing") of the purchase of each Shareholder's Subject Shares referred to in
Section 4.1 shall take place on the third (3rd) Business Day after the Purchase
Date (the "Share Purchase Closing Date"); provided, that each of the conditions
set forth on Annex B shall have been satisfied or waived on such Share Purchase
Closing Date. If the conditions set forth on Annex B have not been satisfied or
waived on such Share Purchase Closing Date, the Share Purchase Closing Date
shall be the third (3rd) Business Day following the satisfaction or waiver of
such conditions. The Closing shall take place at the offices of White & Case
LLP, 1155 Avenue of the Americas, New York, New York. At the Closing, Parent or
Sub will deliver to each Shareholder, by wire transfer of immediately available
funds to the account designated by such Shareholder to Parent or Sub prior to
the Closing, the aggregate purchase price payable in respect of the Subject
Shares to be purchased from such Shareholder at the Closing and each Shareholder
will deliver to Parent or Sub such Subject Shares, free and clear of all Liens,
with the certificate or certificates evidencing such Subject Shares being duly
endorsed for transfer by such Shareholder and accompanied by all powers of
attorney and/or other instruments necessary to convey valid and unencumbered
title thereto to Sub. Each Shareholder will pay all United States federal, state
and local transfer taxes that may be payable in connection with the sale of the
Subject Shares to Sub.


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         Section 4.3 Subsequent Offering Period. Notwithstanding Section 4.2, in
the event that the Share Purchase Closing Date occurs during a subsequent
offering period being conducted pursuant to the Offer, upon the request of
Parent each Shareholder shall immediately tender such Shareholder's Ordinary
Shares (including Ordinary Shares issuable upon conversion of Preferred Shares)
into the Offer and, provided that the Shareholder's Ordinary Shares are accepted
and paid for in the subsequent offering period in accordance with applicable
law, the Closing pursuant to Section 4.2 shall not take place.

                                   ARTICLE V

                                    COVENANTS

         Section 5.1 Generally. Each Shareholder agrees that, except as
contemplated by the terms of this Agreement, such Shareholder shall not and
shall cause its Affiliates not to (i) sell, transfer, tender, pledge, encumber,
assign or otherwise dispose of, or enter into any contract, option or other
agreement with respect to, or consent to, the sale, transfer, tender, pledge,
encumbrance, assignment or other disposition of, any or all of such
Shareholder's Subject Shares; (ii) grant any proxies or powers of attorney in
respect of the Subject Shares, deposit any of such Shareholder's Subject Shares
into a voting trust or enter into a voting agreement with respect to any of such
Shareholder's Subject Shares; and (iii) such Shareholder shall not take any
action that would have the effect of preventing or disabling such Shareholder
from performing its obligations under this Agreement.

         Section 5.2 No Solicitation of Other Offers. Each Shareholder shall
(solely in his or its capacity as a Shareholder), and shall use its commercially
reasonable efforts to cause its Affiliates and each of its and their respective
officers, directors, employees, representatives, consultants, investment
bankers, attorneys, accountants and other agents immediately to, cease any
discussions or negotiations with any other Person or Persons that may be ongoing
with respect to any Acquisition Proposal. No Shareholder shall take, and shall
use its commercially reasonable efforts to cause its Affiliates and its and
their respective officers, directors, employees, representatives, consultants,
investment bankers, attorneys, accountants or other agents or Affiliates not to
take, any action (i) to encourage, solicit, initiate or facilitate, directly or
indirectly, the making or submission of any Acquisition Proposal (including,
without limitation, by taking any action that would make the Rights Agreement
inapplicable to an Acquisition Proposal), (ii) to enter into any agreement,
arrangement or understanding with respect to any Acquisition Proposal, or to
agree to approve or endorse any Acquisition Proposal or enter into any
agreement, arrangement or understanding that would require the Company to
abandon, terminate or fail to consummate the Amalgamation or any other
transaction contemplated by this Agreement, (iii) to initiate or participate in
any way in any discussions or negotiations with, or furnish or disclose any
information to, any Person (other than Parent or Sub) in connection with any
Acquisition Proposal, (iv) to facilitate or further in any other manner any
inquiries or the making or submission of any proposal that constitutes, or may
reasonably be expected to lead to, any Acquisition Proposal, or (v) to grant any
waiver or release under any standstill, confidentiality or similar agreement
entered into by the Company or any of its Affiliates or representatives. Each
Shareholder shall use its commercially reasonable efforts to enforce, to the
fullest extent permitted under applicable law, the provisions of any standstill,
confidentiality or similar agreement entered


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into by such Shareholder or any of its Affiliates or representatives including,
but not limited to, where necessary obtaining injunctions to prevent any
breaches of such agreements and to enforce specifically the terms and provisions
thereof in any court having jurisdiction.

         Section 5.3 Investor Rights Agreement. (a) HM4 Triton L.P. ("HM4
Triton"), a Cayman Islands exempted limited partnership and a Shareholder,
hereby gives its consent for purposes of Article IV of the Investor Rights
Agreement, to the consummation of the transactions contemplated by this
Agreement and the Acquisition Agreement and the taking of any actions by the
Company and its Subsidiaries in furtherance thereof. HM4 Triton agrees that it
shall not take any action, grant any consent, or otherwise exercise any of such
Shareholder's rights (including by way of failing or declining to grant any
approval or consent) under the Investor Rights Agreement (including Section 4.3
or otherwise) without the prior written consent of Parent. Without limiting the
foregoing, HM4 Triton agrees that it shall not amend, or agree to amend, any
provision of the Investors Rights Agreement without the prior written consent of
Parent.

         (b) The Company hereby waives any right of first offer, right to
purchase Shares, right to notice or other right it may be provided in Section
3.3 of the Investor Rights Agreement that may be triggered as a consequence of
this Agreement or the Acquisition Agreement or the consummation of the
transactions contemplated hereby or thereby. The Company agrees that it shall
not amend, or agree to amend, any provision of the Investor Rights Agreement
without the prior written consent of Parent.

         Section 5.4 Conversion of Preferred Shares. Each Shareholder agrees not
to convert, and to cause its Affiliates not to convert, any Preferred Shares,
conditionally or otherwise, other than as required by Section 2.1, Section 4.1
or Section 4.3 of this Agreement or with the prior written consent of Parent.
Each Shareholder hereby agrees to convert immediately any or all of the
Preferred Shares beneficially owned by such Shareholder upon the request of
Parent; provided, that all of the conditions in Annex B to this Agreement have
been satisfied or waived and Purchaser or Sub purchases such Ordinary Shares
within three (3) Business days thereafter.

         Section 5.5 Compliance with Law; Acquisition Agreement. Each
Shareholder agrees and Parent and Sub agree to comply with all applicable law,
including without limitation, the Exchange Act in connection with the
transactions contemplated by this Agreement. The Shareholders and Parent and Sub
agree to prepare and promptly (but in no event later than ten (10) Business Days
following the date of this Agreement) file all necessary applications under HSR
Act with respect to the purchase of the Subject Shares pursuant to this
Agreement. Each of Parent and Sub agree to materially perform all of their
respective agreements and materially satisfy all of their respective obligations
under the Acquisition Agreement.

         Section 5.6 Extension of Initial Offering Period. Parent and Sub agree
not to extend the initial offering period of the Offer beyond the date which is
sixty (60) days after the date of commencement (within the meaning of Rule 14d-2
under the Exchange Act) of the Offer without the prior consent of HM4 Triton.


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                                   ARTICLE VI

                 REPRESENTATIONS AND WARRANTIES OF SHAREHOLDERS

         Each Shareholder hereby represents and warrants to Parent and Sub as
follows:

         Section 6.1 Due Organization, etc. Such Shareholder (if it is a company
or partnership) is duly organized and validly existing under the laws of the
jurisdiction of its incorporation or organization. Such Shareholder (i) if it is
a company or partnership, has all necessary power and authority and/or (ii) if
it is an individual, has the capacity, in each case to execute and deliver this
Agreement and to consummate the transactions contemplated hereby. The execution
and delivery of this Agreement and the consummation of the transactions
contemplated hereby by such Shareholder (if it is a company or partnership) have
been duly authorized by all necessary action on the part of such Shareholder.

         Section 6.2 Ownership of Shares. Such Shareholder or its Affiliate
legally or beneficially owns the number of Ordinary Shares and/or Preferred
Shares set forth opposite such Shareholder's name on Annex A hereto. The number
of Ordinary Shares and/or Preferred Shares set forth opposite such Shareholder's
name on Annex A hereto are all of the Ordinary Shares and/or Preferred Shares
legally or beneficially owned by such Shareholder. Such Shareholder has sole
voting power and sole power of disposition, in each case with respect to all of
the Shares set forth opposite such Shareholder's name on Annex A hereto, with no
limitations, qualifications or restrictions on such rights, subject only to
applicable securities laws and the terms of this Agreement.

         Section 6.3 No Conflicts. (i) Except for compliance with Antitrust
Laws, no filing with any Governmental Entity, no Permit and no authorization,
consent or approval of any other Person is necessary for the execution of this
Agreement by such Shareholder and the consummation by such Shareholder of the
transactions contemplated hereby and (ii) none of the execution and delivery of
this Agreement by such Shareholder, the consummation by such Shareholder of the
transactions contemplated hereby or compliance by such Shareholder with any of
the provisions hereof shall (A) conflict with or result in any breach of any
applicable organizational documents applicable to such Shareholder, (B) result
in, or give rise to, a violation or breach of, or constitute (with or without
notice or lapse of time or both) a default under any of the terms, conditions or
provisions of any material note, bond, mortgage, indenture, license, contract,
commitment, arrangement, understanding, agreement or other instrument or
obligation of any kind to which such Shareholder is a party or by which such
Shareholder or any of such Shareholder's Subject Shares, properties or assets
may be bound, or (C) assuming compliance with Antitrust Laws, violate any order,
writ, injunction, decree, judgment, order, statute, rule or regulation
applicable to such Shareholder or any of such Shareholder's properties or
assets, which could reasonably be expected to adversely affect such
Shareholder's ability to perform its obligations under this Agreement.

         Section 6.4 No Finder's Fees. Except as disclosed pursuant to the
Acquisition Agreement, no broker, investment banker, financial advisor or other
Person is entitled to any broker's, finder's, financial advisor's or other
similar fee or commission in connection with the


                                      -7-
<PAGE>   11


transactions contemplated hereby based upon arrangements made by or on behalf of
such Shareholder.

         Section 6.5 No Encumbrances. Such Shareholder's Subject Shares and the
certificates representing such Shareholder's Subject Shares are now, and at all
times during the term hereof will be, held by such Shareholder, or by a nominee
or custodian for the benefit of such Shareholder, free and clear of all Liens
except for any such encumbrances or proxies arising hereunder. The transfer by
such Shareholder of such Shareholder's Subject Shares to Sub shall pass to and
unconditionally vest in Sub good and valid title to all of such Shareholder's
Shares, free and clear of all claims, Liens, restrictions, limitations and
encumbrances whatsoever, other than any such encumbrances created by Sub.

         Section 6.6 Reliance by Parent. Such Shareholder understands and
acknowledges that Parent is entering into, and causing Sub to enter into, the
Acquisition Agreement in reliance upon the execution and delivery of this
Agreement by such Shareholder.

         Section 6.7 Investor Rights Agreement. The Investor Rights Agreement
has been duly executed and delivered by HM4 Triton and constitutes a valid and
binding obligation of HM4 Triton enforceable against HM4 Triton in accordance
with its terms, except to the extent that its enforceability may be subject to
applicable bankruptcy, insolvency, reorganization, moratorium or other similar
laws affecting the enforcement of creditors' rights generally and by general
equitable principles. Upon the purchase by Parent or Sub of the Preferred Shares
beneficially owned by HM4 Triton, Parent and Sub shall constitute "the
Purchaser" as such term is defined in the Investor Rights Agreement and shall be
entitled to all of the benefits of "the Purchaser" thereunder.

                                  ARTICLE VII

                REPRESENTATIONS AND WARRANTIES OF PARENT AND SUB

         Parent and Sub hereby jointly and severally represent and warrant to
each Shareholder as follows:

         Section 7.1 Due Organization, etc. Each of Parent and Sub is a company
duly organized and validly existing under the laws of the jurisdiction of its
incorporation or organization. Each of Parent and Sub has all necessary power
and authority to execute and deliver this Agreement and to consummate the
transactions contemplated hereby. The execution and delivery of this Agreement
and the consummation of the transactions contemplated hereby by Parent and Sub
have been duly authorized by all necessary action on the part of Parent and Sub
and, assuming its due authorization, execution and delivery by each Shareholder
constitutes a valid and binding obligation of each of Parent and Sub,
enforceable against each of Parent and Sub in accordance with its terms, except
to the extent that its enforceability may be subject to applicable bankruptcy,
insolvency, reorganization, moratorium and similar laws affecting the
enforcement of creditors' rights generally and by general equitable principles.


                                      -8-
<PAGE>   12


         Section 7.2 No Conflicts. (i) Except for compliance with Antitrust Laws
and federal securities laws, no filing with any Governmental Entity, no Permit
and no authorization, consent or approval of any other Person is necessary for
the execution of this Agreement by Parent or Sub and the consummation by Parent
and Sub of the transactions contemplated hereby and (ii) none of the execution
and delivery of this Agreement by Parent or Sub, the consummation by Parent or
Sub of the transactions contemplated hereby shall (A) conflict with or result in
any breach of the organizational documents of Parent or Sub, (B) result in a
violation or breach of, or constitute (with or without notice or lapse of time
or both) a default (or give rise to any third party right of termination,
cancellation, material modification or acceleration) under any of the terms,
conditions or provisions of any material note, bond, mortgage, indenture,
license, contract, commitment, arrangement, understanding, agreement or other
instrument or obligation of any kind to which Parent or Sub is a party or by
which Parent or Sub or any of their respective properties or assets may be
bound, or (C) assuming compliance with Antitrust Laws, violate any order, writ,
injunction, decree, judgment, order, statute, rule or regulation applicable to
Parent or Sub or any of their respective properties or assets which could
reasonably be expected to adversely affect Parent's or Sub's ability to perform
its obligations under this Agreement.

         Section 7.3 Investment Intent. The purchase of the Subject Shares from
such Shareholder pursuant to this Agreement is for the account of Parent or Sub
for the purpose of investment and not with a view to or for sale in connection
with any distribution thereof in violation of any applicable provisions of the
Securities Act.

         Section 7.4 No Finder's Fees. Except for Goldman Sachs & Co., Inc.
(whose fees and expenses as financial advisor to Parent and Sub shall be paid by
Parent or Sub), no broker, investment banker, financial advisor or other Person
is entitled to any broker's, finder's, financial advisor's or other similar fee
or commission in connection with the transactions contemplated hereby based upon
arrangements made by or on behalf of Parent or Sub.

         Section 7.5 Litigation. As of the date of this Agreement, there is no
suit, action, proceeding or indemnification claim pending or, to the knowledge
of Parent, threatened against or affecting Parent or any of its Subsidiaries
that individually or in the aggregate reasonably could be expected to (i) impair
the ability of Parent or Sub to perform its obligations under this Agreement in
any material respect or (ii) delay in any material respect or prevent the
consummation of any of the transactions contemplated by this Agreement, nor is
there any judgment, decree, injunction, rule or order of any Governmental Entity
or arbitrator outstanding against Parent or any of its Subsidiaries having, or
which reasonably could be expected to have, any effect referred to in clause (i)
or (ii) above.

         Section 7.6 Ownership of Sub. Parent owns, directly or indirectly, all
of the issued and outstanding share capital of Sub, and there are no outstanding
options, warrants or other securities convertible into, or rights to acquire,
any share capital of Sub.

         Section 7.7 Reliance by Shareholder. Parent and Sub understand and
acknowledge that each Shareholder is entering into this Agreement in reliance
upon the execution and delivery of the Acquisition Agreement by Parent and Sub.


                                      -9-
<PAGE>   13


                                  ARTICLE VIII

                  REPRESENTATIONS AND WARRANTIES OF THE COMPANY

         The Company hereby represents and warrants to each Shareholder and each
of Parent and Sub as follows:

         Section 8.1 No Adjustment. There has been no adjustment to the
conversion price of the Preferred Shares pursuant to Section 5(c) of the Share
Designation resolutions of the Board of Directors of the Company relating to the
Preferred Shares.

         Section 8.2 Investor Rights Agreement. The Investor Rights Agreement
has been duly executed and delivered by the Company and constitutes a valid and
binding obligation of the Company enforceable against the Company in accordance
with its terms, except to the extent that its enforceability may be subject to
applicable bankruptcy, insolvency, reorganization, moratorium or other similar
laws affecting the enforcement of creditors' rights generally and by general
equitable principles. Upon the purchase by Parent or Sub of the Preferred Shares
beneficially owned by HM4 Triton, Parent and Sub shall constitute "the
Purchaser" as such term is defined in the Investor Rights Agreement and shall be
entitled to all of the benefits of "the Purchaser" thereunder.

                                   ARTICLE IX

                                  MISCELLANEOUS

         Section 9.1 Shareholder Capacity. No Shareholder executing this
Agreement who is or becomes during the term hereof a director or officer of the
Company makes any agreement or understanding herein in his, her or its capacity
as such director or officer. Each Shareholder executes this Agreement solely in
his or her capacity as the record holder or beneficial owner of such
Shareholder's Subject Shares and nothing herein shall limit or affect any
actions taken by a Shareholder or any officer, director, partner or Affiliate of
such Shareholder in his, her or its capacity as an officer or director of the
Company.

         Section 9.2 Publication. Each Shareholder hereby permits Parent and Sub
to publish and disclose in the Offer Documents and, if approval of the
shareholders of the Company is required under applicable law, in the Proxy
Statement (including all documents and schedules filed with the Commission) its
identity and ownership of Ordinary Shares and/or Preferred Shares and the nature
of its commitments, arrangements, and understandings pursuant to this Agreement.

         Section 9.3 Further Actions. Each of the parties hereto agrees that it
will use its commercially reasonable efforts to do all things necessary to
convey the Subject Shares pursuant to, and in accordance with, this Agreement.

         Section 9.4 Entire Agreement. This Agreement contains the entire
understanding of the parties hereto with respect to the subject matter contained
herein and supersedes all prior agreements and understandings, oral and written,
with respect thereto.


                                      -10-
<PAGE>   14


         Section 9.5 Binding Effect; Benefit; Assignment. This Agreement shall
inure to the benefit of and be binding upon the parties hereto and their
permitted assigns. Neither this Agreement nor any of the rights, interests or
obligations hereunder shall be assigned by any of the parties hereto, except by
will or by the laws of descent and distribution, without the prior written
consent of each of the other parties, except that each of Parent and Sub may
assign and transfer its rights and obligations hereunder to any direct or
indirect wholly owned Subsidiary of Parent; provided, however, that such
Subsidiary is directly or indirectly wholly owned by Parent on the Share
Purchase Closing Date. Nothing in this Agreement, expressed or implied, is
intended to confer on any Person, other than the parties hereto, any rights or
remedies.

         Section 9.6 Amendments, Waivers, etc. This Agreement may not be
amended, changed, supplemented, waived or otherwise modified or terminated,
except upon the execution and delivery of a written agreement executed by all of
the relevant parties hereto.

         Section 9.7 Notices. All notices, requests, demands, waivers and other
communications required or permitted to be given under this Agreement shall be
in writing and shall be deemed to have been duly given if delivered in person or
mailed, certified or registered mail with postage prepaid, or sent by facsimile
(upon confirmation of receipt), as follows:

         (i)      If to any Shareholder, to such Shareholder at the address set
                  forth immediately beneath such Shareholder's name on Annex A:

                  with a copy (which shall not constitute notice) to:

                  Weil, Gotshal & Manges LLP
                  100 Crescent Court, Suite 1300
                  Dallas, TX  75201
                  Attention:  Glenn D. West
                  Fax:  214-746-7777


         (ii)     If to Parent or Sub, to it at:

                  Amerada Hess Corporation
                  1185 Avenue of the Americas
                  New York, NY  10036
                  Attention:  J. Barclay Collins, II
                  Fax:  212-536-8390


                                      -11-
<PAGE>   15


                  with a copy (which shall not constitute notice) to:

                  White & Case LLP
                  1155 Avenue of the Americas
                  New York, New York  10036
                  Attention:   Timothy B. Goodell, Esq.
                               Gregory P. Pryor, Esq.
                  Fax:  212-354-8113

or to such other Person or address as any party shall specify by notice in
writing to each of the other parties. All such notices, requests, demands,
waivers and communications shall be deemed to have been received on the date of
delivery, except for a notice of a change of address, which shall be effective
only upon receipt thereof.

         Section 9.8 Specific Enforcement. The parties agree that irreparable
damage would occur in the event that any of the provisions of this Agreement
were not performed in accordance with their specific terms or were otherwise
breached. Accordingly, the parties shall be entitled to an injunction or
injunctions to prevent breaches of this Agreement and to enforce specifically
the terms and provisions of this Agreement, this being in addition to any other
remedy to which they are entitled at law or in equity.

         Section 9.9 Remedies Cumulative. All rights, powers and remedies
provided under this Agreement or otherwise available in respect hereof at law or
in equity shall be cumulative and not alternative, and the exercise of any
thereof by any party shall not preclude the simultaneous or later exercise of
any other such right, power or remedy by such party.

         Section 9.10 No Waiver. The failure of any party hereto to exercise any
right, power or remedy provided under this Agreement or otherwise available in
respect hereof at law or in equity, or to insist upon compliance by any other
party hereto with its obligations hereunder, and any custom or practice of the
parties at variance with the terms hereof shall not constitute a waiver by such
party of its right to exercise any such or other right, power or remedy or to
demand such compliance.

         Section 9.11 Applicable Law. THIS AGREEMENT AND THE LEGAL RELATIONS
BETWEEN THE PARTIES HERETO SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH
THE LAWS OF THE STATE OF DELAWARE, WITHOUT REGARD TO THE CONFLICT OF LAWS RULES
THEREOF. THE COMPETENT STATE OR FEDERAL COURTS LOCATED WITHIN THE STATE OF
DELAWARE WILL HAVE JURISDICTION OVER ANY AND ALL DISPUTES BETWEEN THE PARTIES
HERETO, WHETHER IN LAW OR EQUITY, ARISING OUT OF OR RELATING TO THIS AGREEMENT
AND THE AGREEMENTS, INSTRUMENTS AND DOCUMENTS CONTEMPLATED HEREBY, AND THE
PARTIES CONSENT TO AND AGREE TO SUBMIT TO THE JURISDICTION OF SUCH COURTS. EACH
OF THE PARTIES HEREBY WAIVES AND AGREES NOT TO ASSERT IN ANY SUCH DISPUTE, TO
THE FULLEST EXTENT PERMITTED BY APPLICABLE LAW, ANY CLAIM THAT (I) SUCH PARTY IS
NOT PERSONALLY SUBJECT TO THE JURISDICTION OF SUCH COURTS, (II) SUCH PARTY


                                      -12-
<PAGE>   16


AND SUCH PARTY'S PROPERTY IS IMMUNE FROM ANY LEGAL PROCESS ISSUED BY SUCH COURTS
OR (III) ANY LITIGATION OR OTHER PROCEEDING COMMENCED IN SUCH COURTS IS BROUGHT
IN AN INCONVENIENT FORUM. THE PARTIES HEREBY AGREE THAT DELIVERY OR SENDING OF
PROCESS OR OTHER PAPERS IN CONNECTION WITH ANY SUCH ACTION OR PROCEEDING IN THE
MANNER PROVIDED IN SECTION 9.7, OR IN SUCH OTHER MANNER AS MAY BE PERMITTED BY
LAW, SHALL BE VALID AND SUFFICIENT SERVICE THEREOF AND HEREBY WAIVE ANY
OBJECTIONS TO SERVICE ACCOMPLISHED IN THE MANNER HEREIN PROVIDED. EACH OF THE
PARTIES TO THIS AGREEMENT HEREBY IRREVOCABLY WAIVES ALL RIGHT TO A TRIAL BY JURY
IN ANY ACTION, PROCEEDING OR COUNTERCLAIM ARISING OUT OF OR RELATING TO THIS
AGREEMENT OR THE TRANSACTIONS CONTEMPLATED HEREBY.

         Section 9.12 Headings. The descriptive headings of this Agreement are
inserted for convenience only, do not constitute a part of this Agreement and
shall not affect in any way the meaning or interpretation of this Agreement.

         Section 9.13 Counterparts. This Agreement may be executed in several
counterparts, each of which shall be deemed to be an original, and all of which
together shall be deemed to be one and the same instrument.

         Section 9.14 Termination. This Agreement shall terminate, and none of
Parent, Sub or any Shareholder shall have any rights or obligations hereunder
and this Agreement shall become null and void and have no effect upon the
earliest to occur of (a) the mutual consent of Parent, Sub and HM4 Triton and
(b) by any of Parent, Sub or HM4 Triton if the Subject Shares have not been
acquired by Sub on or prior to December 31, 2001; or (c) by HM4 Triton if Sub is
in material breach of its obligations under Section 4.2; provided, that no party
that is in material breach of this Agreement may terminate this Agreement;
provided, further, that termination of this Agreement shall not prevent any
party hereunder from seeking any remedies (at law or in equity) against any
other party hereto for such party's breach of any of the terms of this
Agreement. Notwithstanding the foregoing, Sections 9.4, 9.5, 9.7, 9.9, 9.11 and
this Section 9.14 shall survive the termination of this Agreement.

         Section 9.15 Affiliates. As used in this Agreement, an "Affiliate" of
any Person shall mean any Person directly or indirectly controlling, controlled
by, or under common control with, such Person; provided, however, that for the
purposes of this Agreement, the Company shall not be deemed to be an "Affiliate"
of any Shareholder.

         Section 9.16 No Recourse. The partners, members, officers, directors,
shareholders and Affiliates of a Shareholder shall not have any personal
liability or obligation to any Person arising under this Agreement in such
capacities. Each Shareholder's liability under this Agreement shall be several
and not joint and in all events shall be limited with respect to each
Shareholder to the amount of cash consideration actually received by such
Shareholder in the Offer or pursuant to this Agreement in respect of such
Shareholder's Ordinary Shares and Preferred Shares set forth on Annex A.

                                     * * *


                                      -13-
<PAGE>   17


         IN WITNESS WHEREOF, Parent, Sub and each Shareholder have caused this
Agreement to be duly executed as of the day and year first above written.

AMERADA HESS CORPORATION


By: /s/ JOHN B. HESS
   --------------------------------------------
   Name:  John B. Hess
   Title:  Chairman of the Board and Chief Executive Officer


AMERADA HESS (CAYMAN) LIMITED


By: /s/ J. BARCLAY COLLINS
   --------------------------------------------
   Name:  J. Barclay Collins
   Title:  Director


TRITON ENERGY LIMITED


By: /s/ A. E. TURNER, III
   --------------------------------------------
   Name:  A. E. Turner, III
   Title:  Senior Vice President


HM4 Triton, L.P.

       By:    HM4/GP Partners Cayman, L.P., its general partner

              By:    HM GP Partners IV Cayman, L.P., its general partner

                     By:   HM Fund IV Cayman, LLC, its general partner


                           By: /s/ THOMAS O. HICKS
                               --------------------------------------------
                               Name:
                               Title:

/s/ THOMAS O. HICKS
------------------------------------
Thomas O. Hicks


                                      -14-
<PAGE>   18


TOH Investors, L.P.

       By:    TOH Management Company, LLC, its general partner


              By:  /s/ THOMAS O. HICKS
                  ---------------------------------------------
                  Name:  Thomas O. Hicks
                  Title:

TOH, Jr. Ventures, Ltd.

       By:    TOH Management Company, LLC, its general partner


              By:  /s/ THOMAS O. HICKS
                  ---------------------------------------------
                  Name:  Thomas O. Hicks
                  Title:

Catherine Forgrave Hicks 1993 Trust


By:  /s/ THOMAS O. HICKS
   --------------------------------------------
      Thomas O. Hicks,
      Trustee

John Alexander Hicks 1984 Trust


By:  /s/ THOMAS O. HICKS
   --------------------------------------------
      Thomas O. Hicks,
      Trustee

Mack Hardin Hicks 1984 Trust


By:  /s/ THOMAS O. HICKS
   --------------------------------------------
      Thomas O. Hicks,
      Trustee

Robert Bradley Hicks 1984 Trust


By:  /s/ THOMAS O. HICKS
   --------------------------------------------
      Thomas O. Hicks,
      Trustee


                                      -15-
<PAGE>   19


William Cree Hicks 1992 Trust


By:   /s/ THOMAS O. HICKS
   --------------------------------------------
      Thomas O. Hicks,
      Trustee



                                      -16-
<PAGE>   20


                                     ANNEX A

        LIST OF SHAREHOLDERS AND OWNERSHIP OF ORDINARY SHARES, $0.01 PAR
         VALUE AND 8% CONVERTIBLE PREFERENCE SHARES, $0.01 PAR VALUE OF
                              TRITON ENERGY LIMITED


<TABLE>
<CAPTION>
                                                                                                                      8%
                                                                                                ORDINARY          PREFERENCE
               SHAREHOLDER                                     ADDRESS                           SHARES             SHARES
------------------------------------------- ----------------------------------------------- ----------------- --------------------
<S>                                         <C>                                             <C>               <C>
HM4 Triton, L.P.                            c/o Hicks, Muse, Tate & Furst Incorporated         1,434,252           5,030,835
                                            200 Crescent Court
                                            Suite 1600
                                            Dallas, TX 75201

Thomas O. Hicks                             c/o Hicks, Muse, Tate & Furst Incorporated          295,515             14,507
                                            200 Crescent Court
                                            Suite 1600
                                            Dallas, TX 75201

TOH Investors, L.P.                         c/o Hicks, Muse, Tate & Furst Incorporated           3,007              10,548
                                            200 Crescent Court
                                            Suite 1600
                                            Dallas, TX 75201

TOH, Jr. Ventures, Ltd.                     c/o Hicks, Muse, Tate & Furst Incorporated            434                 470
                                            200 Crescent Court
                                            Suite 1600
                                            Dallas, TX 75201

Catherine Forgrave Hicks 1993 Trust         c/o Hicks, Muse, Tate & Furst Incorporated            133                 465
                                            200 Crescent Court
                                            Suite 1600
                                            Dallas, TX 75201

John Alexander Hicks 1984 Trust             c/o Hicks, Muse, Tate & Furst Incorporated            133                 465
                                            200 Crescent Court
                                            Suite 1600
                                            Dallas, TX 75201

Mack Hardin Hicks 1984 Trust                c/o Hicks, Muse, Tate & Furst Incorporated            133                 465
                                            200 Crescent Court
                                            Suite 1600
                                            Dallas, TX 75201

Robert Bradley Hicks 1984 Trust             c/o Hicks, Muse, Tate & Furst Incorporated            133                 465
                                            200 Crescent Court
                                            Suite 1600
                                            Dallas, TX 75201

William Cree Hicks 1992 Trust               c/o Hicks, Muse, Tate & Furst Incorporated            133                 465
                                            200 Crescent Court
                                            Suite 1600
                                            Dallas, TX 75201
</TABLE>


                                      -17-
<PAGE>   21

                                     ANNEX B

         Sub shall not be required to purchase any Subject Shares if (i) the
Subject Shares shall have been purchased pursuant to the Offer, (ii) any
applicable waiting period (and any extension thereof) under the Antitrust Laws
shall not have expired or been terminated, or (iii) if, at any time on or after
the date of this Agreement and at or before the time of payment for any Subject
Shares, any of the following shall exist:

         (a) there shall be threatened, instituted or pending any action or
 proceeding by any Governmental Entity, (i) challenging or seeking to, or which
 could reasonably be expected to, make illegal, impede, delay or otherwise
 directly or indirectly restrain, prohibit or make materially more costly the
 transactions contemplated by this Agreement, (ii) seeking to prohibit or
 materially limit the ownership or operation by Parent or Sub of all or any
 material portion of the business or assets of the Company and its Subsidiaries
 taken as a whole or to compel Parent or Sub to dispose of or hold separately
 all or any material portion of the business or assets of Parent and its
 Subsidiaries taken as a whole or the Company and its Subsidiaries taken as a
 whole, or seeking to impose any limitation on the ability of Parent or Sub to
 conduct its business or own such assets, (iii) seeking to impose limitations on
 the ability of Parent or Sub effectively to exercise full rights of ownership
 of the Subject Shares, including, without limitation, the right to vote any
 Subject Shares acquired or owned by Sub or Parent on all matters properly
 presented to the Company's shareholders (other than voting restrictions under
 applicable law in effect on the date of this Agreement), (iv) seeking to
 require divestiture by Parent or Sub of any Subject Shares, or (v) otherwise
 directly or indirectly relating to the transactions contemplated by this
 Agreement and which could reasonably be expected to have a Material Adverse
 Effect on the Company and its Subsidiaries taken as a whole or on Parent and
 its Subsidiaries taken as a whole;

         (b) there shall be any action taken, or any statute, rule, regulation,
 legislation, interpretation, judgment, order or injunction proposed, enacted,
 enforced, promulgated, amended or issued after the date of this Agreement and
 applicable to or deemed applicable to (i) Parent, Sub, the Company or any
 Subsidiary of the Company or (ii) the transactions contemplated by this
 Agreement by any Governmental Entity other than the routine application of the
 waiting period provisions of the HSR Act to the transactions contemplated by
 this Agreement, that could reasonably be expected to result directly or
 indirectly in any of the consequences referred to in paragraph (a) above;

         (c) except for inaccuracies in any representations or warranties of the
 Shareholders that result from actions or inactions required by this Agreement,
 any representation or warranty of the Shareholders and the Company contained in
 this Agreement shall not be materially true and correct as of the Closing; or

         (d) any Shareholder or the Company shall have failed to perform in any
 material respect any obligation or to comply in any material respect with any
 agreement or covenant under this Agreement.

         The foregoing conditions are for the sole benefit of Parent and Sub and
may be asserted by Parent or Sub, or may be waived by Parent or Sub, in whole or
in part, at any time and from time


                                      -18-
<PAGE>   22


to time in their respective sole discretion. The failure by Parent or Sub at any
time to exercise any of the foregoing rights shall not be deemed a waiver of any
such right and each such right shall be deemed an ongoing right which may be
asserted at any time and from time to time.





                                      -19-