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                                                                    EXHIBIT: 4.1




                       AMENDMENT NO. 4 TO RIGHTS AGREEMENT

         THIS AMENDMENT NO. 4, dated as of July 9, 2001 (this "Amendment"), is
between Triton Energy Limited, a company organized under the laws of the Cayman
Islands (the "Company"), and Mellon Investor Services LLC (as successor to
Chemical Bank), a national banking association (the "Rights Agent").

                                    RECITALS

         A. The Company and the Rights Agent are parties to a Rights Agreement
dated as of March 25, 1996, as amended (the "Rights Agreement").

         B. Pursuant to Section 27 of the Rights Agreement, the Company and the
Rights Agent desire to amend the Rights Agreement as set forth below.

         Accordingly, the Rights Agreement is hereby amended as follows:

1. AMENDMENT OF SECTION 1(a). Section 1(a) of the Rights Agreement is amended by
adding as the penultimate sentence to Section 1(a) the following:

         "Notwithstanding anything in this Agreement to the contrary, AHC and
         Hess Sub, together with the Affiliates and Associates of each of them,
         shall not be deemed to be an Acquiring Person for all purposes of this
         Agreement, provided that this sentence shall cease to apply if and when
         the Acquisition Agreement and the Principal Shareholders Agreement both
         terminate and neither AHC nor Hess Sub purchases any Ordinary Shares or
         8% Preference Shares pursuant thereto or, if AHC or Hess Sub has
         purchased any Ordinary Shares or 8% Preference Shares pursuant thereto
         then at such time after such purchase that AHC, Hess Sub, and their
         respective Affiliates and Associates, collectively, cease to be the
         Beneficial Owner of 10% or more of the number of outstanding Ordinary
         Shares (assuming for the purpose of this calculation the conversion or
         exchange of all outstanding securities of the Company convertible into
         or exchangeable for Ordinary Shares)."

2. AMENDMENT OF SECTION 1(o). Section 1(o) of the Rights Agreement is amended to
add the following sentence at the end thereof:

         "Notwithstanding anything in this Agreement to the contrary, a Share
         Acquisition Date shall not be deemed to have occurred as a result of
         (A) (i) the execution of the Acquisition Agreement, (ii) the execution
         of the Principal Shareholders Agreement or (iii) public announcement or
         the consummation (or the public announcement of such consummation) of
         the transactions contemplated by the Acquisition Agreement or the
         Principal Shareholders Agreement or (B) any other acquisition by AHC or
         Hess Sub, together with the Affiliates and Associates of each of them,
         of Beneficial Ownership of Ordinary Shares or 8% Preference Shares, or
         any public announcement thereof, after the purchase by AHC or Hess Sub
         of any Ordinary Shares or 8% Preference Shares pursuant to the
         Principal Shareholders Agreement or the Acquisition Agreement; provided
         that this sentence shall cease to apply to AHC and Hess Sub, together
         with the Affiliates and Associates of each of them, at such time that
         AHC and Hess Sub, together with the



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         Affiliates and Associates of each of them, cease to be the Beneficial
         Owner of an aggregate of 10% or more of the number of outstanding
         Ordinary Shares (assuming for the purpose of this calculation the
         conversion or exchange of all outstanding securities of the Company
         convertible into or exchangeable for Ordinary Shares)."

3. AMENDMENT OF SECTION 1. Section 1 of the Rights Agreement is amended to add
the following at the end thereof:

         "(q) "Acquisition Agreement" shall mean the Acquisition Agreement,
dated as of July 9, 2001, by and among AHC, Hess Sub and the Company.

         (r) "AHC" shall mean Amerada Hess Corporation, a Delaware corporation.

         (s) "Hess Sub" shall mean Amerada Hess (Cayman) Limited, a company
limited by shares under the laws of the Cayman Islands and a wholly-owned
subsidiary of AHC.

         (t) "Scheme of Arrangement" shall mean either (i) a compulsory
acquisition pursuant to Section 88 of the Companies Law (2001 Second Revision),
as amended, of the Cayman Islands or (ii) a scheme of arrangement in accordance
with Section 86 of the Companies Law (2001 Second Revision), as amended, of the
Cayman Islands, each as contemplated by the Acquisition Agreement.

         (u) "Principal Shareholders Agreement" shall mean the Principal
Shareholders Agreement, dated as of July 9, 2001, by and among AHC, Hess Sub,
the Company and the shareholders listed on Annex A thereto."

4. AMENDMENT OF SECTION 2. The first sentence of Section 2 of the Rights
Agreement is amended to delete the following words:

         "and the holders of the Rights (who, in accordance with Section 3
         hereof, shall prior to the Distribution Date also be the holders of the
         Ordinary Shares)"

5. AMENDMENT OF SECTION 3(a). Section 3(a) of the Rights Agreement is amended to
add the following sentence at the end thereof:

         "Notwithstanding anything in this Agreement to the contrary, a
         Distribution Date shall not be deemed to have occurred as a result of
         (A) (i) the execution of the Acquisition Agreement, (ii) the execution
         of the Principal Shareholders Agreement or (iii) public announcement or
         the consummation (or the public announcement of such consummation) of
         the transactions contemplated by the Acquisition Agreement or the
         Principal Shareholders Agreement or (B) any other acquisition by AHC or
         Hess Sub, together with the Affiliates and Associates of each of them,
         of Beneficial Ownership of Ordinary Shares or 8% Preference Shares, or
         any public announcement thereof, after the purchase by AHC or Hess Sub
         of any Ordinary Shares or 8% Preference Shares pursuant to the
         Principal Shareholders Agreement or the Acquisition Agreement; provided
         that this sentence shall cease to apply to AHC and Hess Sub, together
         with the Affiliates and Associates of each of them, at such time that
         AHC and Hess Sub, together with the Affiliates and Associates of each
         of them, cease to be the Beneficial Owner of an



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         aggregate of 10% or more of the number of outstanding Ordinary Shares
         (assuming for the purpose of this calculation the conversion or
         exchange of all outstanding securities of the Company convertible into
         or exchangeable for Ordinary Shares)."

6. AMENDMENT OF SECTION 20(c). Section 20(c) of the Rights Agreement is amended
to add the following words to the end of such section:

         "Anything to the contrary notwithstanding, in no event shall the Rights
Agent be liable for special, punitive, indirect, consequential or incidental
loss or damage of any kind whatsoever (including but not limited to lost
profits), even if the Rights Agent has been advised of the likelihood of such
loss or damage."

7. ADDITION OF SECTION 34. The parties hereto hereby amend the Rights Agreement
by adding the following Section 34 to the Rights Agreement:

         "Section 34. Additional Agreements. (a) Simultaneously with the
effective time of the Scheme of Arrangement, (i) this Agreement will be
terminated and be without any further force or effect, (ii) none of the parties
to this Agreement will have any rights, obligations or liabilities hereunder,
and (iii) the holders of the Rights will not be entitled to any benefits, rights
or other interests under this Agreement, including without limitation the right
to purchase or otherwise acquire Preference Shares or any other securities of
the Company.

         (b) Notwithstanding anything in this Agreement to the contrary, this
Agreement, and the rights conveyed hereby, shall be inapplicable to (i) the
transactions contemplated by the Acquisition Agreement and the Principal
Shareholders Agreement or any announcement thereof and (ii) any acquisition by
AHC or Hess Sub, together with the Affiliates and Associates of each of them of
Beneficial Ownership of Ordinary Shares or 8% Preference Shares, or any public
announcement thereof after the purchase by AHC or Hess Sub of any Ordinary
Shares or 8% Preference Shares pursuant to the Principal Shareholders Agreement
or the Acquisition Agreement for so long as AHC and Hess Sub, together with the
Affiliates and Associates of each of them, Beneficially Owns an aggregate of at
least 10% of the number of outstanding Ordinary Shares (assuming for the purpose
of this calculation, the conversion or exchange of all outstanding securities of
the Company convertible into or exchangeable for Ordinary Shares)."



8. EFFECTIVENESS. This Amendment shall be deemed effective as of the date and
year first above written. Except as amended hereby, the Rights Agreement shall
remain in full force and effect and shall be otherwise unaffected hereby.

9. MISCELLANEOUS. This Amendment shall be deemed to be a contract made under the
laws of the Cayman Islands and for all purposes shall be governed by and
construed in accordance with the laws of such Country applicable to contracts to
be made and performed entirely within such Country except that the rights,
duties and obligations of the Rights Agent shall be governed by and construed in
accordance with the Laws of the State of New York, U.S.A. This Amendment may be
executed in any number of counterparts, each of such counterparts shall for all
purposes be deemed to be an original, and all such counterparts shall together
constitute but one and the same instrument. If any term, provision, covenant or
restriction of this Amendment



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is held by a court of competent jurisdiction or other authority to be invalid,
illegal, or unenforceable, the remainder of the terms, provisions, covenants and
restrictions of this Amendment shall remain in full force and effect and shall
in no way be affected or impaired or invalidated.







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         EXECUTED as of the date and year set forth above.

ATTEST:                                    TRITON ENERGY LIMITED



 /s/ THOMAS J. MURPHY                      By: /s/ A. E. TURNER, III
----------------------------                  ----------------------------------
Name: Thomas J. Murphy                     Name:  A. E. Turner, III
Title: Secretary                           Title:  Senior Vice President

ATTEST:                                    MELLON INVESTOR SERVICES LLC



 /s/ MARGARET W. GRUBB                     By: /s/ JANIS E. MASON
----------------------------                  ----------------------------------
Name:  Margaret W. Grubb                   Name:  Janis E. Mason
Title:  Assistant Vice President           Title:  Relationship Manager