
<PAGE>
 
                                                                    EXHIBIT 24.1

                               POWER OF ATTORNEY

      KNOW ALL MEN BY THESE PRESENTS, the undersigned, a Director of Halliburton
Company ("Company"), does hereby constitute and appoint Richard B. Cheney, Dale
P. Jones, David J. Lesar, Lester L. Coleman, Gary V. Morris and Susan S. Keith,
or any of them acting alone, his true and lawful attorneys and attorney, with
full power of substitution or resubstitution, to do any and all acts and things
and execute any and all instruments which said attorneys or attorney may deem
necessary or advisable to enable the Company to comply with the Securities Act
of 1933, as amended, the Trust Indenture Act of 1939, as amended, and other
federal or state securities laws, and any rules, regulations and requirements of
the Securities and Exchange Commission or state regulatory authorities in
respect thereof, in connection with the registration for offering under said
Securities Act of 1933, as amended, of a principal amount not to exceed
$600,000,000 of debentures or other evidences of indebtedness or such amount of
debentures or other evidences of indebtedness where the principal amount thereof
at maturity discounted to the date of issuance and sale will result in the
Company receiving net proceeds of $600,000,000 ("Debentures"), whether such
Debentures by their terms when issued contain provisions for convertibility into
the Company's Common Stock, subordination to existing or future indebtedness,
redemption or establishment of a sinking fund for retirement of the indebtedness
created thereby, or all, some or none of such provisions or features, of the
Company, or such lesser amount of Debentures, all upon such terms and in such
amounts as may be deemed appropriate by proper officers of the Company, and
subsequent offering for sale and sale thereof, including specifically, but
without limitation thereof, power and authority to sign my name as a Director of
the Company to a Registration Statement on the appropriate Form and on any other
applications and statements to be filed with the Securities and Exchange
Commission with respect to the offering or sale of Debentures or the Common
Stock of the Company into which such Debentures may be converted, if such filing
should be deemed appropriate by the proper officers of the Company, and all
amendments thereto, including without limitation post effective amendments
thereto, and to any instruments or documents filed as part of or in connection
therewith.

      IN TESTIMONY HEREOF, witness my hand this the 22nd day of July, 1997.



                                        /s/ Anne L. Armstrong
                                        ---------------------
                                        Anne L. Armstrong
<PAGE>
 
                                 POWER OF ATTORNEY

      KNOW ALL MEN BY THESE PRESENTS, the undersigned, a Director of Halliburton
Company ("Company"), does hereby constitute and appoint Dale P. Jones, David J.
Lesar, Lester L. Coleman, Gary V. Morris and Susan S. Keith, or any of them
acting alone, his true and lawful attorneys and attorney, with full power of
substitution or resubstitution, to do any and all acts and things and execute
any and all instruments which said attorneys or attorney may deem necessary or
advisable to enable the Company to comply with the Securities Act of 1933, as
amended, the Trust Indenture Act of 1939, as amended, and other federal or state
securities laws, and any rules, regulations and requirements of the Securities
and Exchange Commission or state regulatory authorities in respect thereof, in
connection with the registration for offering under said Securities Act of 1933,
as amended, of a principal amount not to exceed $600,000,000 of debentures or
other evidences of indebtedness or such amount of debentures or other evidences
of indebtedness where the principal amount thereof at maturity discounted to the
date of issuance and sale will result in the Company receiving net proceeds of
$600,000,000 ("Debentures"), whether such Debentures by their terms when issued
contain provisions for convertibility into the Company's Common Stock,
subordination to existing or future indebtedness, redemption or establishment of
a sinking fund for retirement of the indebtedness created thereby, or all, some
or none of such provisions or features, of the Company, or such lesser amount of
Debentures, all upon such terms and in such amounts as may be deemed appropriate
by proper officers of the Company, and subsequent offering for sale and sale
thereof, including specifically, but without limitation thereof, power and
authority to sign my name as a Director of the Company to a Registration
Statement on the appropriate Form and on any other applications and statements
to be filed with the Securities and Exchange Commission with respect to the
offering or sale of Debentures or the Common Stock of the Company into which
such Debentures may be converted, if such filing should be deemed appropriate by
the proper officers of the Company, and all amendments thereto, including
without limitation post effective amendments thereto, and to any instruments or
documents filed as part of or in connection therewith.

      IN TESTIMONY HEREOF, witness my hand this the 22nd day of July, 1997.



                                        /s/ Richard B. Cheney
                                        ---------------------
                                        Richard B. Cheney
<PAGE>
 
                                 POWER OF ATTORNEY

      KNOW ALL MEN BY THESE PRESENTS, the undersigned, a Director of Halliburton
Company ("Company"), does hereby constitute and appoint Richard B. Cheney, Dale
P. Jones, David J. Lesar, Lester L. Coleman, Gary V. Morris and Susan S. Keith,
or any of them acting alone, his true and lawful attorneys and attorney, with
full power of substitution or resubstitution, to do any and all acts and things
and execute any and all instruments which said attorneys or attorney may deem
necessary or advisable to enable the Company to comply with the Securities Act
of 1933, as amended, the Trust Indenture Act of 1939, as amended, and other
federal or state securities laws, and any rules, regulations and requirements of
the Securities and Exchange Commission or state regulatory authorities in
respect thereof, in connection with the registration for offering under said
Securities Act of 1933, as amended, of a principal amount not to exceed
$600,000,000 of debentures or other evidences of indebtedness or such amount of
debentures or other evidences of indebtedness where the principal amount thereof
at maturity discounted to the date of issuance and sale will result in the
Company receiving net proceeds of $600,000,000 ("Debentures"), whether such
Debentures by their terms when issued contain provisions for convertibility into
the Company's Common Stock, subordination to existing or future indebtedness,
redemption or establishment of a sinking fund for retirement of the indebtedness
created thereby, or all, some or none of such provisions or features, of the
Company, or such lesser amount of Debentures, all upon such terms and in such
amounts as may be deemed appropriate by proper officers of the Company, and
subsequent offering for sale and sale thereof, including specifically, but
without limitation thereof, power and authority to sign my name as a Director of
the Company to a Registration Statement on the appropriate Form and on any other
applications and statements to be filed with the Securities and Exchange
Commission with respect to the offering or sale of Debentures or the Common
Stock of the Company into which such Debentures may be converted, if such filing
should be deemed appropriate by the proper officers of the Company, and all
amendments thereto, including without limitation post effective amendments
thereto, and to any instruments or documents filed as part of or in connection
therewith.

      IN TESTIMONY HEREOF, witness my hand this the 21st day of July, 1997.



                                          /s/ Clitheroe
                                          -------------
                                          Lord Clitheroe
<PAGE>
 
                                 POWER OF ATTORNEY

      KNOW ALL MEN BY THESE PRESENTS, the undersigned, a Director of Halliburton
Company ("Company"), does hereby constitute and appoint Richard B. Cheney, Dale
P. Jones, David J. Lesar, Lester L. Coleman, Gary V. Morris and Susan S. Keith,
or any of them acting alone, his true and lawful attorneys and attorney, with
full power of substitution or resubstitution, to do any and all acts and things
and execute any and all instruments which said attorneys or attorney may deem
necessary or advisable to enable the Company to comply with the Securities Act
of 1933, as amended, the Trust Indenture Act of 1939, as amended, and other
federal or state securities laws, and any rules, regulations and requirements of
the Securities and Exchange Commission or state regulatory authorities in
respect thereof, in connection with the registration for offering under said
Securities Act of 1933, as amended, of a principal amount not to exceed
$600,000,000 of debentures or other evidences of indebtedness or such amount of
debentures or other evidences of indebtedness where the principal amount thereof
at maturity discounted to the date of issuance and sale will result in the
Company receiving net proceeds of $600,000,000 ("Debentures"), whether such
Debentures by their terms when issued contain provisions for convertibility into
the Company's Common Stock, subordination to existing or future indebtedness,
redemption or establishment of a sinking fund for retirement of the indebtedness
created thereby, or all, some or none of such provisions or features, of the
Company, or such lesser amount of Debentures, all upon such terms and in such
amounts as may be deemed appropriate by proper officers of the Company, and
subsequent offering for sale and sale thereof, including specifically, but
without limitation thereof, power and authority to sign my name as a Director of
the Company to a Registration Statement on the appropriate Form and on any other
applications and statements to be filed with the Securities and Exchange
Commission with respect to the offering or sale of Debentures or the Common
Stock of the Company into which such Debentures may be converted, if such filing
should be deemed appropriate by the proper officers of the Company, and all
amendments thereto, including without limitation post effective amendments
thereto, and to any instruments or documents filed as part of or in connection
therewith.

      IN TESTIMONY HEREOF, witness my hand this the 23rd day of July, 1997.



                                      /s/ Robert L. Crandall
                                      ----------------------
                                      Robert L. Crandall
<PAGE>
 
                                 POWER OF ATTORNEY

      KNOW ALL MEN BY THESE PRESENTS, the undersigned, a Director of Halliburton
Company ("Company"), does hereby constitute and appoint Richard B. Cheney, David
J. Lesar, Lester L. Coleman, Gary V. Morris and Susan S. Keith, or any of them
acting alone, his true and lawful attorneys and attorney, with full power of
substitution or resubstitution, to do any and all acts and things and execute
any and all instruments which said attorneys or attorney may deem necessary or
advisable to enable the Company to comply with the Securities Act of 1933, as
amended, the Trust Indenture Act of 1939, as amended, and other federal or state
securities laws, and any rules, regulations and requirements of the Securities
and Exchange Commission or state regulatory authorities in respect thereof, in
connection with the registration for offering under said Securities Act of 1933,
as amended, of a principal amount not to exceed $600,000,000 of debentures or
other evidences of indebtedness or such amount of debentures or other evidences
of indebtedness where the principal amount thereof at maturity discounted to the
date of issuance and sale will result in the Company receiving net proceeds of
$600,000,000 ("Debentures"), whether such Debentures by their terms when issued
contain provisions for convertibility into the Company's Common Stock,
subordination to existing or future indebtedness, redemption or establishment of
a sinking fund for retirement of the indebtedness created thereby, or all, some
or none of such provisions or features, of the Company, or such lesser amount of
Debentures, all upon such terms and in such amounts as may be deemed appropriate
by proper officers of the Company, and subsequent offering for sale and sale
thereof, including specifically, but without limitation thereof, power and
authority to sign my name as a Director of the Company to a Registration
Statement on the appropriate Form and on any other applications and statements
to be filed with the Securities and Exchange Commission with respect to the
offering or sale of Debentures or the Common Stock of the Company into which
such Debentures may be converted, if such filing should be deemed appropriate by
the proper officers of the Company, and all amendments thereto, including
without limitation post effective amendments thereto, and to any instruments or
documents filed as part of or in connection therewith.

      IN TESTIMONY HEREOF, witness my hand this the 22nd day of July, 1997.



                                         /s/ Dale P. Jones
                                         -----------------
                                         Dale P. Jones
<PAGE>
 
                                 POWER OF ATTORNEY

      KNOW ALL MEN BY THESE PRESENTS, the undersigned, a Director of Halliburton
Company ("Company"), does hereby constitute and appoint Richard B. Cheney, Dale
P. Jones, David J. Lesar, Lester L. Coleman, Gary V. Morris and Susan S. Keith,
or any of them acting alone, his true and lawful attorneys and attorney, with
full power of substitution or resubstitution, to do any and all acts and things
and execute any and all instruments which said attorneys or attorney may deem
necessary or advisable to enable the Company to comply with the Securities Act
of 1933, as amended, the Trust Indenture Act of 1939, as amended, and other
federal or state securities laws, and any rules, regulations and requirements of
the Securities and Exchange Commission or state regulatory authorities in
respect thereof, in connection with the registration for offering under said
Securities Act of 1933, as amended, of a principal amount not to exceed
$600,000,000 of debentures or other evidences of indebtedness or such amount of
debentures or other evidences of indebtedness where the principal amount thereof
at maturity discounted to the date of issuance and sale will result in the
Company receiving net proceeds of $600,000,000 ("Debentures"), whether such
Debentures by their terms when issued contain provisions for convertibility into
the Company's Common Stock, subordination to existing or future indebtedness,
redemption or establishment of a sinking fund for retirement of the indebtedness
created thereby, or all, some or none of such provisions or features, of the
Company, or such lesser amount of Debentures, all upon such terms and in such
amounts as may be deemed appropriate by proper officers of the Company, and
subsequent offering for sale and sale thereof, including specifically, but
without limitation thereof, power and authority to sign my name as a Director of
the Company to a Registration Statement on the appropriate Form and on any other
applications and statements to be filed with the Securities and Exchange
Commission with respect to the offering or sale of Debentures or the Common
Stock of the Company into which such Debentures may be converted, if such filing
should be deemed appropriate by the proper officers of the Company, and all
amendments thereto, including without limitation post effective amendments
thereto, and to any instruments or documents filed as part of or in connection
therewith.

      IN TESTIMONY HEREOF, witness my hand this the 23rd day of July, 1997.



                                         /s/ W. R. Howell
                                         ----------------
                                         W. R. Howell
<PAGE>
 
                                 POWER OF ATTORNEY

      KNOW ALL MEN BY THESE PRESENTS, the undersigned, a Director of Halliburton
Company ("Company"), does hereby constitute and appoint Richard B. Cheney, Dale
P. Jones, David J. Lesar, Lester L. Coleman, Gary V. Morris and Susan S. Keith,
or any of them acting alone, his true and lawful attorneys and attorney, with
full power of substitution or resubstitution, to do any and all acts and things
and execute any and all instruments which said attorneys or attorney may deem
necessary or advisable to enable the Company to comply with the Securities Act
of 1933, as amended, the Trust Indenture Act of 1939, as amended, and other
federal or state securities laws, and any rules, regulations and requirements of
the Securities and Exchange Commission or state regulatory authorities in
respect thereof, in connection with the registration for offering under said
Securities Act of 1933, as amended, of a principal amount not to exceed
$600,000,000 of debentures or other evidences of indebtedness or such amount of
debentures or other evidences of indebtedness where the principal amount thereof
at maturity discounted to the date of issuance and sale will result in the
Company receiving net proceeds of $600,000,000 ("Debentures"), whether such
Debentures by their terms when issued contain provisions for convertibility into
the Company's Common Stock, subordination to existing or future indebtedness,
redemption or establishment of a sinking fund for retirement of the indebtedness
created thereby, or all, some or none of such provisions or features, of the
Company, or such lesser amount of Debentures, all upon such terms and in such
amounts as may be deemed appropriate by proper officers of the Company, and
subsequent offering for sale and sale thereof, including specifically, but
without limitation thereof, power and authority to sign my name as a Director of
the Company to a Registration Statement on the appropriate Form and on any other
applications and statements to be filed with the Securities and Exchange
Commission with respect to the offering or sale of Debentures or the Common
Stock of the Company into which such Debentures may be converted, if such filing
should be deemed appropriate by the proper officers of the Company, and all
amendments thereto, including without limitation post effective amendments
thereto, and to any instruments or documents filed as part of or in connection
therewith.

      IN TESTIMONY HEREOF, witness my hand this the 22nd day of July, 1997.



                                 /s/ Delano E. Lewis
                                 -------------------
                                 Delano E. Lewis
<PAGE>
 
                                 POWER OF ATTORNEY

      KNOW ALL MEN BY THESE PRESENTS, the undersigned, a Director of Halliburton
Company ("Company"), does hereby constitute and appoint Richard B. Cheney, Dale
P. Jones, David J. Lesar, Lester L. Coleman, Gary V. Morris and Susan S. Keith,
or any of them acting alone, his true and lawful attorneys and attorney, with
full power of substitution or resubstitution, to do any and all acts and things
and execute any and all instruments which said attorneys or attorney may deem
necessary or advisable to enable the Company to comply with the Securities Act
of 1933, as amended, the Trust Indenture Act of 1939, as amended, and other
federal or state securities laws, and any rules, regulations and requirements of
the Securities and Exchange Commission or state regulatory authorities in
respect thereof, in connection with the registration for offering under said
Securities Act of 1933, as amended, of a principal amount not to exceed
$600,000,000 of debentures or other evidences of indebtedness or such amount of
debentures or other evidences of indebtedness where the principal amount thereof
at maturity discounted to the date of issuance and sale will result in the
Company receiving net proceeds of $600,000,000 ("Debentures"), whether such
Debentures by their terms when issued contain provisions for convertibility into
the Company's Common Stock, subordination to existing or future indebtedness,
redemption or establishment of a sinking fund for retirement of the indebtedness
created thereby, or all, some or none of such provisions or features, of the
Company, or such lesser amount of Debentures, all upon such terms and in such
amounts as may be deemed appropriate by proper officers of the Company, and
subsequent offering for sale and sale thereof, including specifically, but
without limitation thereof, power and authority to sign my name as a Director of
the Company to a Registration Statement on the appropriate Form and on any other
applications and statements to be filed with the Securities and Exchange
Commission with respect to the offering or sale of Debentures or the Common
Stock of the Company into which such Debentures may be converted, if such filing
should be deemed appropriate by the proper officers of the Company, and all
amendments thereto, including without limitation post effective amendments
thereto, and to any instruments or documents filed as part of or in connection
therewith.

      IN TESTIMONY HEREOF, witness my hand this the 23rd day of July, 1997.



                                     /s/ C. J. Silas
                                     ---------------
                                     C. J. Silas
<PAGE>
 
                                 POWER OF ATTORNEY

      KNOW ALL MEN BY THESE PRESENTS, the undersigned, a Director of Halliburton
Company ("Company"), does hereby constitute and appoint Richard B. Cheney, Dale
P. Jones, David J. Lesar, Lester L. Coleman, Gary V. Morris and Susan S. Keith,
or any of them acting alone, his true and lawful attorneys and attorney, with
full power of substitution or resubstitution, to do any and all acts and things
and execute any and all instruments which said attorneys or attorney may deem
necessary or advisable to enable the Company to comply with the Securities Act
of 1933, as amended, the Trust Indenture Act of 1939, as amended, and other
federal or state securities laws, and any rules, regulations and requirements of
the Securities and Exchange Commission or state regulatory authorities in
respect thereof, in connection with the registration for offering under said
Securities Act of 1933, as amended, of a principal amount not to exceed
$600,000,000 of debentures or other evidences of indebtedness or such amount of
debentures or other evidences of indebtedness where the principal amount thereof
at maturity discounted to the date of issuance and sale will result in the
Company receiving net proceeds of $600,000,000 ("Debentures"), whether such
Debentures by their terms when issued contain provisions for convertibility into
the Company's Common Stock, subordination to existing or future indebtedness,
redemption or establishment of a sinking fund for retirement of the indebtedness
created thereby, or all, some or none of such provisions or features, of the
Company, or such lesser amount of Debentures, all upon such terms and in such
amounts as may be deemed appropriate by proper officers of the Company, and
subsequent offering for sale and sale thereof, including specifically, but
without limitation thereof, power and authority to sign my name as a Director of
the Company to a Registration Statement on the appropriate Form and on any other
applications and statements to be filed with the Securities and Exchange
Commission with respect to the offering or sale of Debentures or the Common
Stock of the Company into which such Debentures may be converted, if such filing
should be deemed appropriate by the proper officers of the Company, and all
amendments thereto, including without limitation post effective amendments
thereto, and to any instruments or documents filed as part of or in connection
therewith.

      IN TESTIMONY HEREOF, witness my hand this the 22nd day of July, 1997.



                                 /s/ Roger T. Staubach
                                 ---------------------
                                 Roger T. Staubach
<PAGE>
 
                                 POWER OF ATTORNEY

      KNOW ALL MEN BY THESE PRESENTS, the undersigned, a Director of Halliburton
Company ("Company"), does hereby constitute and appoint Richard B. Cheney, Dale
P. Jones, David J. Lesar, Lester L. Coleman, Gary V. Morris and Susan S. Keith,
or any of them acting alone, his true and lawful attorneys and attorney, with
full power of substitution or resubstitution, to do any and all acts and things
and execute any and all instruments which said attorneys or attorney may deem
necessary or advisable to enable the Company to comply with the Securities Act
of 1933, as amended, the Trust Indenture Act of 1939, as amended, and other
federal or state securities laws, and any rules, regulations and requirements of
the Securities and Exchange Commission or state regulatory authorities in
respect thereof, in connection with the registration for offering under said
Securities Act of 1933, as amended, of a principal amount not to exceed
$600,000,000 of debentures or other evidences of indebtedness or such amount of
debentures or other evidences of indebtedness where the principal amount thereof
at maturity discounted to the date of issuance and sale will result in the
Company receiving net proceeds of $600,000,000 ("Debentures"), whether such
Debentures by their terms when issued contain provisions for convertibility into
the Company's Common Stock, subordination to existing or future indebtedness,
redemption or establishment of a sinking fund for retirement of the indebtedness
created thereby, or all, some or none of such provisions or features, of the
Company, or such lesser amount of Debentures, all upon such terms and in such
amounts as may be deemed appropriate by proper officers of the Company, and
subsequent offering for sale and sale thereof, including specifically, but
without limitation thereof, power and authority to sign my name as a Director of
the Company to a Registration Statement on the appropriate Form and on any other
applications and statements to be filed with the Securities and Exchange
Commission with respect to the offering or sale of Debentures or the Common
Stock of the Company into which such Debentures may be converted, if such filing
should be deemed appropriate by the proper officers of the Company, and all
amendments thereto, including without limitation post effective amendments
thereto, and to any instruments or documents filed as part of or in connection
therewith.

      IN TESTIMONY HEREOF, witness my hand this the 21st day of July, 1997.



                                   /s/ R. J. Stegemeier
                                   --------------------
                                   Richard J. Stegemeier
