
<PAGE>
 
                                 Exhibit 24

                              POWER OF ATTORNEY

     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of 
Halliburton Company, do hereby constitute and appoint Thomas H. Cruikshank, 
Dale P. Jones 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 
registration under said Securities Act of 1933, as amended, of 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 the 1993 Stock and Long-Term 
Incentive Plan of Halliburton Company, as amended and as the same may be from 
time to time amended, including specifically, but without limitation thereof, 
power and authority to sign by 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 2nd day of December, 1993.

                                
                                         /s/ Anne L. Armstrong
                                         -------------------------
                                         Anne L. Armstrong
<PAGE>
 
                                 Exhibit 24

                              POWER OF ATTORNEY

     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of 
Halliburton Company, do hereby constitute and appoint Thomas H. Cruikshank, 
Dale P. Jones 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 
registration under said Securities Act of 1933, as amended, of 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 the 1993 Stock and Long-Term 
Incentive Plan of Halliburton Company, as amended and as the same may be from 
time to time amended, including specifically, but without limitation thereof, 
power and authority to sign by 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 2nd day of December, 1993.

                                
                                         /s/ Robert W. Campbell 
                                         -------------------------
                                         Robert W. Campbell




<PAGE>
 
                                 Exhibit 24

                              POWER OF ATTORNEY

     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of 
Halliburton Company, do hereby constitute and appoint Thomas H. Cruikshank, 
Dale P. Jones 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 
registration under said Securities Act of 1933, as amended, of 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 the 1993 Stock and Long-Term 
Incentive Plan of Halliburton Company, as amended and as the same may be from 
time to time amended, including specifically, but without limitation thereof, 
power and authority to sign by 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 2nd day of December, 1993.

                                
                                         /s/ Lord Clitheroe
                                         -------------------------
                                         Lord Clitheroe

<PAGE>
 
                                 Exhibit 24

                              POWER OF ATTORNEY

     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of 
Halliburton Company, do hereby constitute and appoint Thomas H. Cruikshank, 
Dale P. Jones 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 
registration under said Securities Act of 1933, as amended, of 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 the 1993 Stock and Long-Term 
Incentive Plan of Halliburton Company, as amended and as the same may be from 
time to time amended, including specifically, but without limitation thereof, 
power and authority to sign by 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 2nd day of December, 1993.

                                
                                         /s/Robert L. Crandall
                                         -------------------------
                                         Robert L. Crandall

<PAGE>
 
                                 Exhibit 24

                              POWER OF ATTORNEY

     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of 
Halliburton Company, do hereby constitute and appoint Thomas H. Cruikshank, 
Dale P. Jones 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 
registration under said Securities Act of 1933, as amended, of 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 the 1993 Stock and Long-Term 
Incentive Plan of Halliburton Company, as amended and as the same may be from 
time to time amended, including specifically, but without limitation thereof, 
power and authority to sign by 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 7 day of December, 1993.

                                
                                         /s/ W. R. Howell
                                         -------------------------
                                         W. R. Howell

<PAGE>
 
                                 Exhibit 24

                              POWER OF ATTORNEY

     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of 
Halliburton Company, do hereby constitute and appoint Thomas H. Cruikshank, 
Dale P. Jones 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 
registration under said Securities Act of 1933, as amended, of 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 the 1993 Stock and Long-Term 
Incentive Plan of Halliburton Company, as amended and as the same may be from 
time to time amended, including specifically, but without limitation thereof, 
power and authority to sign by 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 2nd day of December, 1993.

                                
                                         /s/ Dale P. Jones
                                         -------------------------
                                         Dale P. Jones

<PAGE>
 
                                 Exhibit 24

                              POWER OF ATTORNEY

     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of 
Halliburton Company, do hereby constitute and appoint Thomas H. Cruikshank, 
Dale P. Jones 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 
registration under said Securities Act of 1933, as amended, of 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 the 1993 Stock and Long-Term 
Incentive Plan of Halliburton Company, as amended and as the same may be from 
time to time amended, including specifically, but without limitation thereof, 
power and authority to sign by 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 2nd day of December, 1993.

                                
                                         /s/ C. J. Silas
                                         -------------------------
                                         C. J. Silas

<PAGE>
 
                                 Exhibit 24

                              POWER OF ATTORNEY

     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of 
Halliburton Company, do hereby constitute and appoint Thomas H. Cruikshank, 
Dale P. Jones 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 
registration under said Securities Act of 1933, as amended, of 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 the 1993 Stock and Long-Term 
Incentive Plan of Halliburton Company, as amended and as the same may be from 
time to time amended, including specifically, but without limitation thereof, 
power and authority to sign by 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 3rd day of December, 1993.

                                
                                         /s/ Roger T. Staubach
                                         -------------------------
                                         Roger T. Staubach

<PAGE>
 
                                 Exhibit 24

                              POWER OF ATTORNEY

     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of 
Halliburton Company, do hereby constitute and appoint Thomas H. Cruikshank, 
Dale P. Jones 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 
registration under said Securities Act of 1933, as amended, of 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 the 1993 Stock and Long-Term 
Incentive Plan of Halliburton Company, as amended and as the same may be from 
time to time amended, including specifically, but without limitation thereof, 
power and authority to sign by 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 17th day of May, 1994.

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

<PAGE>
 
                                 Exhibit 24

                              POWER OF ATTORNEY

     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of 
Halliburton Company, do hereby constitute and appoint Thomas H. Cruikshank, 
Dale P. Jones 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 
registration under said Securities Act of 1933, as amended, of 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 the 1993 Stock and Long-Term 
Incentive Plan of Halliburton Company, as amended and as the same may be from 
time to time amended, including specifically, but without limitation thereof, 
power and authority to sign by 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 2nd day of December, 1993.

                                
                                         /s/ E. L. Williamson
                                         -------------------------
                                         E. L. Williamson

