
<PAGE>
 
                               POWER OF ATTORNEY
                                        
                                        
     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of
Halliburton Company, do 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, my true and lawful attorneys or attorney, 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 Halliburton Company 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 filing of the Registration Statement on Form S-8, or other appropriate form,
under said Securities Act of 1933, as amended, with respect to shares of the
Common Stock of Halliburton Company, par value $2.50 per share, to be sold and
offered for sale pursuant to the terms of option agreements assumed by
Halliburton Company in connection with the acquisition of NUMAR Corporation,
including, but not limited to, those option agreements entered into pursuant to
the NUMAR Corporation 1994 Stock Incentive Plan and the NUMAR Corporation 1995
Employee Stock Purchase Plan, both as amended, including specifically, but
without limitation thereof, power and authority to sign my name as Director of
Halliburton Company to any registration statements and applications and
statements to be filed with the Securities and Exchange Commission in respect of
said shares of Common Stock and all amendments thereto, including without
limitation post-effective amendments thereto, and to any instruments or
documents filed as a part of or in connection therewith; and I hereby ratify and
confirm all that said attorneys or attorney shall do or cause to be done by
virtue hereof.

     IN TESTIMONY HEREOF, witness my hand this the 29th day of September, 1997.

                                             /s/ Anne L. Armstrong
                                             ---------------------
                                             Anne L. Armstrong
<PAGE>
 
                               POWER OF ATTORNEY
                                        
                                        
     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of
Halliburton Company, do hereby constitute and appoint David J. Lesar, Lester L.
Coleman, Gary V. Morris and Susan S. Keith, or any of them acting alone, my true
and lawful attorneys or attorney, 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 Halliburton Company 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 filing of the
Registration Statement on Form S-8, or other appropriate form, under said
Securities Act of 1933, as amended, with respect to shares of the Common Stock
of Halliburton Company, par value $2.50 per share, to be sold and offered for
sale pursuant to the terms of option agreements assumed by Halliburton Company
in connection with the acquisition of NUMAR Corporation, including, but not
limited to, those option agreements entered into pursuant to the NUMAR
Corporation 1994 Stock Incentive Plan and the NUMAR Corporation 1995 Employee
Stock Purchase Plan, both as amended, including specifically, but without
limitation thereof, power and authority to sign my name as Director of
Halliburton Company to any registration statements and applications and
statements to be filed with the Securities and Exchange Commission in respect of
said shares of Common Stock and all amendments thereto, including without
limitation post-effective amendments thereto, and to any instruments or
documents filed as a part of or in connection therewith; and I hereby ratify and
confirm all that said attorneys or attorney shall do or cause to be done by
virtue hereof.

     IN TESTIMONY HEREOF, witness my hand this the 29th day of September, 1997.

                                             /s/ Richard B. Cheney
                                             ---------------------
                                             Richard B. Cheney
<PAGE>
 
                               POWER OF ATTORNEY
                                        
                                        
     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of
Halliburton Company, do 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, my true and lawful attorneys or attorney, 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 Halliburton Company 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 filing of the Registration Statement on Form S-8, or other appropriate form,
under said Securities Act of 1933, as amended, with respect to shares of the
Common Stock of Halliburton Company, par value $2.50 per share, to be sold and
offered for sale pursuant to the terms of option agreements assumed by
Halliburton Company in connection with the acquisition of NUMAR Corporation,
including, but not limited to, those option agreements entered into pursuant to
the NUMAR Corporation 1994 Stock Incentive Plan and the NUMAR Corporation 1995
Employee Stock Purchase Plan, both as amended, including specifically, but
without limitation thereof, power and authority to sign my name as Director of
Halliburton Company to any registration statements and applications and
statements to be filed with the Securities and Exchange Commission in respect of
said shares of Common Stock and all amendments thereto, including without
limitation post-effective amendments thereto, and to any instruments or
documents filed as a part of or in connection therewith; and I hereby ratify and
confirm all that said attorneys or attorney shall do or cause to be done by
virtue hereof.

     IN TESTIMONY HEREOF, witness my hand this the 29th day of September, 1997.

                                             /s/ Clitheroe
                                             -------------
                                             Lord Clitheroe
<PAGE>
 
                               POWER OF ATTORNEY
                                        
                                        
     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of
Halliburton Company, do 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, my true and lawful attorneys or attorney, 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 Halliburton Company 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 filing of the Registration Statement on Form S-8, or other appropriate form,
under said Securities Act of 1933, as amended, with respect to shares of the
Common Stock of Halliburton Company, par value $2.50 per share, to be sold and
offered for sale pursuant to the terms of option agreements assumed by
Halliburton Company in connection with the acquisition of NUMAR Corporation,
including, but not limited to, those option agreements entered into pursuant to
the NUMAR Corporation 1994 Stock Incentive Plan and the NUMAR Corporation 1995
Employee Stock Purchase Plan, both as amended, including specifically, but
without limitation thereof, power and authority to sign my name as Director of
Halliburton Company to any registration statements and applications and
statements to be filed with the Securities and Exchange Commission in respect of
said shares of Common Stock and all amendments thereto, including without
limitation post-effective amendments thereto, and to any instruments or
documents filed as a part of or in connection therewith; and I hereby ratify and
confirm all that said attorneys or attorney shall do or cause to be done by
virtue hereof.

     IN TESTIMONY HEREOF, witness my hand this the 26th day of September, 1997.

                                             /s/ Robert L. Crandall
                                             ----------------------
                                             Robert L. Crandall
<PAGE>
 
                               POWER OF ATTORNEY
                                        
                                        
     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of
Halliburton Company, do 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, my true and lawful attorneys or attorney, 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 Halliburton Company 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 filing of the Registration Statement on Form S-8, or other appropriate form,
under said Securities Act of 1933, as amended, with respect to shares of the
Common Stock of Halliburton Company, par value $2.50 per share, to be sold and
offered for sale pursuant to the terms of option agreements assumed by
Halliburton Company in connection with the acquisition of NUMAR Corporation,
including, but not limited to, those option agreements entered into pursuant to
the NUMAR Corporation 1994 Stock Incentive Plan and the NUMAR Corporation 1995
Employee Stock Purchase Plan, both as amended, including specifically, but
without limitation thereof, power and authority to sign my name as Director of
Halliburton Company to any registration statements and applications and
statements to be filed with the Securities and Exchange Commission in respect of
said shares of Common Stock and all amendments thereto, including without
limitation post-effective amendments thereto, and to any instruments or
documents filed as a part of or in connection therewith; and I hereby ratify and
confirm all that said attorneys or attorney shall do or cause to be done by
virtue hereof.

     IN TESTIMONY HEREOF, witness my hand this the 26th day of September, 1997.

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

                                        
     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of
Halliburton Company, do 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, my true and lawful attorneys or attorney, 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 Halliburton Company 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 filing of the Registration Statement on Form S-8, or other appropriate form,
under said Securities Act of 1933, as amended, with respect to shares of the
Common Stock of Halliburton Company, par value $2.50 per share, to be sold and
offered for sale pursuant to the terms of option agreements assumed by
Halliburton Company in connection with the acquisition of NUMAR Corporation,
including, but not limited to, those option agreements entered into pursuant to
the NUMAR Corporation 1994 Stock Incentive Plan and the NUMAR Corporation 1995
Employee Stock Purchase Plan, both as amended, including specifically, but
without limitation thereof, power and authority to sign my name as Director of
Halliburton Company to any registration statements and applications and
statements to be filed with the Securities and Exchange Commission in respect of
said shares of Common Stock and all amendments thereto, including without
limitation post-effective amendments thereto, and to any instruments or
documents filed as a part of or in connection therewith; and I hereby ratify and
confirm all that said attorneys or attorney shall do or cause to be done by
virtue hereof.

     IN TESTIMONY HEREOF, witness my hand this the 26th day of September, 1997.

                                             /s/ Dale P. Jones
                                             -----------------
                                             Dale P. Jones
<PAGE>
 
                               POWER OF ATTORNEY
                                        
                                        
     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of
Halliburton Company, do 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, my true and lawful attorneys or attorney, 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 Halliburton Company 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 filing of the Registration Statement on Form S-8, or other appropriate form,
under said Securities Act of 1933, as amended, with respect to shares of the
Common Stock of Halliburton Company, par value $2.50 per share, to be sold and
offered for sale pursuant to the terms of option agreements assumed by
Halliburton Company in connection with the acquisition of NUMAR Corporation,
including, but not limited to, those option agreements entered into pursuant to
the NUMAR Corporation 1994 Stock Incentive Plan and the NUMAR Corporation 1995
Employee Stock Purchase Plan, both as amended, including specifically, but
without limitation thereof, power and authority to sign my name as Director of
Halliburton Company to any registration statements and applications and
statements to be filed with the Securities and Exchange Commission in respect of
said shares of Common Stock and all amendments thereto, including without
limitation post-effective amendments thereto, and to any instruments or
documents filed as a part of or in connection therewith; and I hereby ratify and
confirm all that said attorneys or attorney shall do or cause to be done by
virtue hereof.

     IN TESTIMONY HEREOF, witness my hand this the 29th day of September, 1997.

                                             /s/ Delano E. Lewis
                                             -------------------
                                             Delano E. Lewis
<PAGE>
 
                               POWER OF ATTORNEY
                                        
                                        
     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of
Halliburton Company, do 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, my true and lawful attorneys or attorney, 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 Halliburton Company 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 filing of the Registration Statement on Form S-8, or other appropriate form,
under said Securities Act of 1933, as amended, with respect to shares of the
Common Stock of Halliburton Company, par value $2.50 per share, to be sold and
offered for sale pursuant to the terms of option agreements assumed by
Halliburton Company in connection with the acquisition of NUMAR Corporation,
including, but not limited to, those option agreements entered into pursuant to
the NUMAR Corporation 1994 Stock Incentive Plan and the NUMAR Corporation 1995
Employee Stock Purchase Plan, both as amended, including specifically, but
without limitation thereof, power and authority to sign my name as Director of
Halliburton Company to any registration statements and applications and
statements to be filed with the Securities and Exchange Commission in respect of
said shares of Common Stock and all amendments thereto, including without
limitation post-effective amendments thereto, and to any instruments or
documents filed as a part of or in connection therewith; and I hereby ratify and
confirm all that said attorneys or attorney shall do or cause to be done by
virtue hereof.

     IN TESTIMONY HEREOF, witness my hand this the 29th day of September, 1997.

                                             /s/ C. J. Silas
                                             ---------------
                                             C. J. Silas
<PAGE>
 
                               POWER OF ATTORNEY
                                        
                                        
     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of
Halliburton Company, do 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, my true and lawful attorneys or attorney, 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 Halliburton Company 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 filing of the Registration Statement on Form S-8, or other appropriate form,
under said Securities Act of 1933, as amended, with respect to shares of the
Common Stock of Halliburton Company, par value $2.50 per share, to be sold and
offered for sale pursuant to the terms of option agreements assumed by
Halliburton Company in connection with the acquisition of NUMAR Corporation,
including, but not limited to, those option agreements entered into pursuant to
the NUMAR Corporation 1994 Stock Incentive Plan and the NUMAR Corporation 1995
Employee Stock Purchase Plan, both as amended, including specifically, but
without limitation thereof, power and authority to sign my name as Director of
Halliburton Company to any registration statements and applications and
statements to be filed with the Securities and Exchange Commission in respect of
said shares of Common Stock and all amendments thereto, including without
limitation post-effective amendments thereto, and to any instruments or
documents filed as a part of or in connection therewith; and I hereby ratify and
confirm all that said attorneys or attorney shall do or cause to be done by
virtue hereof.

     IN TESTIMONY HEREOF, witness my hand this the 29th day of September, 1997.

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

                                        
     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of
Halliburton Company, do 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, my true and lawful attorneys or attorney, 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 Halliburton Company 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 filing of the Registration Statement on Form S-8, or other appropriate form,
under said Securities Act of 1933, as amended, with respect to shares of the
Common Stock of Halliburton Company, par value $2.50 per share, to be sold and
offered for sale pursuant to the terms of option agreements assumed by
Halliburton Company in connection with the acquisition of NUMAR Corporation,
including, but not limited to, those option agreements entered into pursuant to
the NUMAR Corporation 1994 Stock Incentive Plan and the NUMAR Corporation 1995
Employee Stock Purchase Plan, both as amended, including specifically, but
without limitation thereof, power and authority to sign my name as Director of
Halliburton Company to any registration statements and applications and
statements to be filed with the Securities and Exchange Commission in respect of
said shares of Common Stock and all amendments thereto, including without
limitation post-effective amendments thereto, and to any instruments or
documents filed as a part of or in connection therewith; and I hereby ratify and
confirm all that said attorneys or attorney shall do or cause to be done by
virtue hereof.

     IN TESTIMONY HEREOF, witness my hand this the 25th day of September, 1997.

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