EXHIBIT 24.1
 
                               POWER OF ATTORNEY

     The undersigned hereby constitutes and appoints Richard B. Cheney, David J.
Lesar, Lester L. Coleman, Robert M. Kennedy and Susan S. Keith, and each or any
of them, his or her true and lawful attorneys-in-fact and agents (with full
power to each of them to act alone), with full power of substitution and
resubstitution for him or her and in his or her name, place and stead in any and
all capacities, to sign the Registration Statement on Form S-4, or other
appropriate Form, relating to the merger of Landmark Graphics Corporation with
and into a wholly-owned subsidiary of Halliburton Company, and any and all
amendments (including post-effective amendments) or supplements to such
Registration Statement, and to file the same, with all exhibits thereto and all
documents in connection therewith, with the Securities and Exchange
Commission, granting unto said attorneys-in-fact and agents full power and
authority to do and perform each and every act and thing requisite and necessary
to be done (with full power to each of them to act alone), as fully and to all
intents and purposes as he or she might or could do in person, hereby ratifying
and confirming all that said attorneys-in-fact and agents or any of them, or
their substitutes, may lawfully do or cause to be done by virtue hereof.


Date: July l8, 1996            /s/ ANNE L. ARMSTRONG
                               -----------------------------------------------
                               Anne L. Armstrong
                               Title: Director

 
                               POWER OF ATTORNEY

     The undersigned hereby constitutes and appoints David J. Lesar, Lester L.
Coleman, Robert M. Kennedy and Susan S. Keith, and each or any of them, his or
her true and lawful attorneys-in-fact and agents (with full power to each of
them to act alone), with full power of substitution and resubstitution for him
or her and in his or her name, place and stead in any and all capacities, to
sign the Registration Statement on Form S-4, or other appropriate Form, relating
to the merger of Landmark Graphics Corporation with and into a wholly-owned
subsidiary of Halliburton Company, and any and all amendments (including post-
effective amendments) or supplements to such Registration Statement, and to file
the same, with all exhibits thereto and all documents in connection therewith,
with the Securities and Exchange Commission, granting unto said attorneys-in-
fact and agents full power and authority to do and perform each and every act
and thing requisite and necessary to be done (with full power to each of them to
act alone), as fully and to all intents and purposes as he or she might or could
do in person, hereby ratifying and confirming all that said attorneys-in-fact
and agents or any of them, or their substitutes, may lawfully do or cause to be
done by virtue hereof.

Date: July 18, 1996            /s/ RICHARD B. CHENEY
                               -----------------------------------------------
                               Richard B Cheney
                               Title: Chairman of the Board, President
                                      and Chief Executive Officer and Director

 
                               POWER OF ATTORNEY

     The undersigned hereby constitutes and appoints Richard B. Cheney, David J.
Lesar, Lester L. Coleman, Robert M. Kennedy and Susan S. Keith, and each or any
of them, his or her true and lawful attorneys-in-fact and agents (with full
power to each of them to act alone), with full power of substitution and
resubstitution for him or her and in his or her name, place and stead in any and
all capacities, to sign the Registration Statement on Form S-4, or other
appropriate Form, relating to the merger of Landmark Graphics Corporation with
and into a wholly-owned subsidiary of Halliburton Company, and any and all
amendments (including post-effective amendments) or supplements to such
Registration Statement, and to file the same, with all exhibits thereto and all
documents in connection therewith, with the Securities and Exchange Commission,
granting unto said attorneys-in-fact and agents full power and authority to do
and perform each and every act and thing requisite and necessary to be done
(with full power to each of them to act alone), as fully and to all intents and
purposes as he or she might or could do in person, hereby ratifying and
confirming all that said attorneys-in-fact and agents or any of them, or their
substitutes, may lawfully do or cause to be done by virtue hereof.

Date: July 18, 1996            /s/ LORD CLITHEROE
                               -----------------------------------------------
                               Lord Clitheroe
                               Title:  Director

 
                               POWER OF ATTORNEY

     The undersigned hereby constitutes and appoints Richard B. Cheney, David J.
Lesar, Lester L. Coleman, Robert M. Kennedy and Susan S. Keith, and each or any
of them, his or her true and lawful attorneys-in-fact and agents (with full
power to each of them to act alone), with full power of substitution and
resubstitution for him or her and in his or her name, place and stead in any and
all capacities, to sign the Registration Statement on Form S-4, or other
appropriate Form, relating to the merger of Landmark Graphics Corporation with
and into a wholly-owned subsidiary of Halliburton Company, and any and all
amendments (including post-effective amendments) or supplements to such
Registration Statement, and to file the same, with all exhibits thereto and all
documents in connection therewith, with the Securities and Exchange Commission,
granting unto said attorneys-in-fact and agents full power and authority to do
and perform each and every act and thing requisite and necessary to be done
(with full power to each of them to act alone), as fully and to all intents and
purposes as he or she might or could do in person, hereby ratifying and
confirming all that said attorneys-in-fact and agents or any of them, or their
substitutes, may lawfully do or cause to be done by virtue hereof.


Date:  July 18, 1996           /s/ ROBERT L. CRANDALL
                               -----------------------------------------------
                               Robert L. Crandall
                               Title:  Director

 
                               POWER OF ATTORNEY

     The undersigned hereby constitutes and appoints Richard B. Cheney, David J.
Lesar, Lester L. Coleman, Robert M. Kennedy and Susan S. Keith, and each or any
of them, his or her true and lawful attorneys-in-fact and agents (with full
power to each of them to act alone), with full power of substitution and
resubstitution for him or her and in his or her name, place and stead in any and
all capacities, to sign the Registration Statement on Form S-4, or other
appropriate Form, relating to the merger of Landmark Graphics Corporation with
and into a wholly-owned subsidiary of Halliburton Company, and any and all
amendments (including post-effective amendments) or supplements to such
Registration Statement, and to file the same, with all exhibits thereto and all
documents in connection therewith, with the Securities and Exchange Commission,
granting unto said attorneys-in-fact and agents full power and authority to do
and perform each and every act and thing requisite and necessary to be done
(with full power to each of them to act alone), as fully and to all intents and
purposes as he or she might or could do in person, hereby ratifying and
confirming all that said attorneys-in-fact and agents or any of them, or their
substitutes, may lawfully do or cause to be done by virtue hereof.


Date:  July 18, 1996           /s/ W.R. HOWELL
                               -----------------------------------------------
                               W.R. Howell
                               Title:  Director

 
                               POWER OF ATTORNEY

     The undersigned hereby constitutes and appoints Richard B. Cheney, David J.
Lesar, Lester L. Coleman, Robert M. Kennedy and Susan S. Keith, and each or any
of them, his or her true and lawful attorneys-in-fact and agents (with full
power to each of them to act alone), with full power of substitution and
resubstitution for him or her and in his or her name, place and stead in any and
all capacities, to sign the Registration Statement on Form S-4, or other
appropriate Form, relating to the merger of Landmark Graphics Corporation with
and into a wholly-owned subsidiary of Halliburton Company, and any and all
amendments (including post-effective amendments) or supplements to such
Registration Statement, and to file the same, with all exhibits thereto and all
documents in connection therewith, with the Securities and Exchange Commission,
granting unto said attorneys-in-fact and agents full power and authority to do
and perform each and every act and thing requisite and necessary to be done
(with full power to each of them to act alone), as fully and to all intents and
purposes as he or she might or could do in person, hereby ratifying and
confirming all that said attorneys-in-fact and agents or any of them, or their
substitutes, may lawfully do or cause to be done by virtue hereof.


Date:  July 18, 1996           /s/ DALE P. JONES
                               -----------------------------------------------
                               Dale P. Jones
                               Title:  Director

 
                               POWER OF ATTORNEY

     The undersigned hereby constitutes and appoints Richard B. Cheney, David J.
Lesar, Lester L. Coleman, Robert M. Kennedy and Susan S. Keith, and each or any
of them, his or her true and lawful attorneys-in-fact and agents (with full
power to each of them to act alone), with full power of substitution and
resubstitution for him or her and in his or her name, place and stead in any and
all capacities, to sign the Registration Statement on Form S-4, or other
appropriate Form, relating to the merger of Landmark Graphics Corporation with
and into a wholly-owned subsidiary of Halliburton Company, and any and all
amendments (including post-effective amendments) or supplements to such
Registration Statement, and to file the same, with all exhibits thereto and all
documents in connection therewith, with the Securities and Exchange Commission,
granting unto said attorneys-in-fact and agents full power and authority to do
and perform each and every act and thing requisite and necessary to be done
(with full power to each of them to act alone), as fully and to all intents and
purposes as he or she might or could do in person, hereby ratifying and
confirming all that said attorneys-in-fact and agents or any of them, or their
substitutes, may lawfully do or cause to be done by virtue hereof.

Date: July 23, 1996            /s/ DELANO E. LEWIS
                               -----------------------------------------------
                               Delano E. Lewis
                               Title: Director

 
                               POWER OF ATTORNEY

     The undersigned hereby constitutes and appoints Richard B. Cheney, David J.
Lesar, Lester L. Coleman, Robert M. Kennedy and Susan S. Keith, and each or any
of them, his or her true and lawful attorneys-in-fact and agents (with full
power to each of them to act alone), with full power of substitution and
resubstitution for him or her and in his or her name, place and stead in any and
all capacities, to sign the Registration Statement on Form S-4, or other
appropriate Form, relating to the merger of Landmark Graphics Corporation with
and into a wholly-owned subsidiary of Halliburton Company, and any and all
amendments (including post-effective amendments) or supplements to such
Registration Statement, and to file the same, with all exhibits thereto and all
documents in connection therewith, with the Securities and Exchange Commission,
granting unto said attorneys-in-fact and agents full power and authority to do
and perform each and every act and thing requisite and necessary to be done
(with full power to each of them to act alone), as fully and to all intents and
purposes as he or she might or could do in person, hereby ratifying and
confirming all that said attorneys-in-fact and agents or any of them, or their
substitutes, may lawfully do or cause to be done by virtue hereof.


Date:  July 19, 1996           /s/ C.J. SILAS
                               -----------------------------------------------
                               C.J. Silas
                               Title: Director

 
                               POWER OF ATTORNEY

     The undersigned hereby constitutes and appoints Richard B. Cheney, David J.
Lesar, Lester L. Coleman, Robert M. Kennedy and Susan S. Keith, and each or any
of them, his or her true and lawful attorneys-in-fact and agents (with full
power to each of them to act alone), with full power of substitution and
resubstitution for him or her and in his or her name, place and stead in any and
all capacities, to sign the Registration Statement on Form S-4, or other
appropriate Form, relating to the merger of Landmark Graphics Corporation with
and into a wholly-owned subsidiary of Halliburton Company, and any and all
amendments (including post-effective amendments) or supplements to such
Registration Statement, and to file the same, with all exhibits thereto and all
documents in connection therewith, with the Securities and Exchange Commission,
granting unto said attorneys-in-fact and agents full power and authority to do
and perform each and every act and thing requisite and necessary to be done
(with full power to each of them to act alone), as fully and to all intents and
purposes as he or she might or could do in person, hereby ratifying and
confirming all that said attorneys-in-fact and agents or any of them, or their
substitutes, may lawfully do or cause to be done by virtue hereof.


Date:  July 18, 1996           /s/ ROGER T. STAUBACH
                               -----------------------------------------------
                               Roger T. Staubach
                               Title:  Director

 
                               POWER OF ATTORNEY

     The undersigned hereby constitutes and appoints Richard B. Cheney, David J.
Lesar, Lester L. Coleman, Robert M. Kennedy and Susan S. Keith, and each or any
of them, his or her true and lawful attorneys-in-fact and agents (with full
power to each of them to act alone), with full power of substitution and
resubstitution for him or her and in his or her name, place and stead in any and
all capacities, to sign the Registration Statement on Form S-4, or other
appropriate Form, relating to the merger of Landmark Graphics Corporation with
and into a wholly-owned subsidiary of Halliburton Company, and any and all
amendments (including post-effective amendments) or supplements to such
Registration Statement, and to file the same, with all exhibits thereto and all
documents in connection therewith, with the Securities and Exchange Commission,
granting unto said attorneys-in-fact and agents full power and authority to do
and perform each and every act and thing requisite and necessary to be done
(with full power to each of them to act alone), as fully and to all intents and
purposes as he or she might or could do in person, hereby ratifying and
confirming all that said attorneys-in-fact and agents or any of them, or their
substitutes, may lawfully do or cause to be done by virtue hereof.


Date:  July 18, l996           /s/ RICHARD J. STEGEMEIER
                               -----------------------------------------------
                               Richard J. Stegemeier
                               Title: Director

 
                               POWER OF ATTORNEY

     The undersigned hereby constitutes and appoints Richard B. Cheney, David J.
Lesar, Lester L. Coleman, Robert M. Kennedy and Susan S. Keith, and each or any
of them, his or her true and lawful attorneys-in-fact and agents (with full
power to each of them to act alone), with full power of substitution and
resubstitution for him or her and in his or her name, place and stead in any and
all capacities, to sign the Registration Statement on Form S-4, or other
appropriate Form, relating to the merger of Landmark Graphics Corporation with
and into a wholly-owned subsidiary of Halliburton Company, and any and all
amendments (including post-effective amendments) or supplements to such
Registration Statement, and to file the same, with all exhibits thereto and all
documents in connection therewith , with the Securities and Exchange Commission,
granting unto said attorneys-in-fact and agents full power and authority to do
and perform each and every act and thing requisite and necessary to be done
(with full power to each of them to act alone), as fully and to all intents and
purposes as he or she might or could do in person, hereby ratifying and
confirming all that said attorneys-in-fact and agents or any of them, or their
substitutes, may lawfully do or cause to be done by virtue hereof.


Date: July 18, 1996            /s/ E.L. WILLIAMSON
                               -----------------------------------------------
                               E. L. Williamson
                               Title: Director