Exhibit 24.1

                                POWER OF ATTORNEY


     Each person whose signature appears below authorizes Thomas G. Finck,
Peter Rugg and Robert B. Holland, III, or any of them, to execute in the name
of each such person who is then an officer or director of Triton Energy Limited
or Triton Energy Corporation (each a "Registrant") and to file a Registration
Statement on Form S-3 relating to debt securities of Triton Energy Limited and
Triton Energy Corporation and equity securities of Triton Energy Limited,
including debt securities constituting joint and several debt obligations of
the Registrants and guarantees by a Registrant of the debt securities of the
other Registrant, and Preference Shares, Ordinary Shares, and Warrants to
Purchase preference shares, ordinary shares and debt securities, and any
amendments thereto (and any additional Registration Statement related thereto
permitted by Rule 462(b) promulgated under the Securities Act of 1933 (and all
further amendments including post-effective amendments thereto)) in each case
necessary or advisable to enable the Registrant to comply with the Securities
Act of 1933, as amended, and any rules, regulations and requirements of the
Securities and Exchange Commission, in respect thereof, in connection with the
registration of the securities which are the subject of such Registration
Statements, which amendments may make such changes in such Registration
Statements as such attorney may deem appropriate.

                                   SIGNATURES

     Pursuant to the requirements of the Securities Act of 1933, as amended,
this Power of Attorney has been signed by the following persons in the
capacities and on the dates indicated.

         Signature                        Title              Date


/s/Thomas G. Finck           President, Chief Executive      May 7, 1996
- -----------------------      Officer, Director (Principal
Thomas G. Finck              Executive Officer)

/s/Peter Rugg                Senior Vice President and       May 7, 1996
- -----------------------      Chief Financial Officer
Peter Rugg                   (Principal Financial and
                             Accounting Officer)

/s/Ernest E. Cook            Director                        May 7, 1996
- -----------------------
Ernest E. Cook


/s/Sheldon R. Erikson        Director                        May 7, 1996
- -----------------------
Sheldon R. Erikson

/s/Ray H. Eubank             Director                        May 7, 1996
- -----------------------
Ray H. Eubank

/s/Jesse E. Hendricks        Director                        May 7, 1996
- -----------------------
Jesse E. Hendricks

/s/Fitzgerald S. Hudson      Director                        May 7, 1996
- -----------------------
Fitzgerald S. Hudson

                             Director                        May 7, 1996
                       
John R. Huff

/s/John P. Lewis             Director                        May 7, 1996
- -----------------------
John P. Lewis


/s/Michael E. McMahon        Director                        May 7, 1996
- -----------------------
Michael E. McMahon

/s/Wellslake D. Morse, Jr.   Director                        May 7, 1996
- --------------------------
Wellslake D. Morse, Jr.

/s/Edwin D. Williamson       Director                        May 7, 1996
- -----------------------
Edwin D. Williamson