<PAGE>   1
                                                                      EXHIBIT 24

                               POWER OF ATTORNEY

                       UNION PACIFIC RESOURCES GROUP INC.

         KNOW ALL MEN BY THESE PRESENTS, that H. JESSE ARNELLE, a Director of
Union Pacific Resources Group Inc., a Utah Corporation (the "Corporation"),
hereby appoints JACK L. MESSMAN, JOSEPH A. LASALA, JR., MARK S. KNOUSE and MARK
L.  JONES, and each of them acting individually, his true and lawful attorney,
each with power to act without the other and full power of substitution, to
execute, deliver and file, for and on his behalf, and in his name and in his
capacity as Director, an Annual Report on Form 10-K for the year ended December
31, 1996 (or other appropriate form) for filing with the Securities and
Exchange Commission and any other documents in support thereof or supplemental
or amendatory thereto, hereby granting to such attorneys and each of them full
power and authority to do and perform each and every act and thing whatsoever
as such attorney or attorneys may deem necessary or advisable to carry out
fully the intent of the foregoing as the undersigned might or could do
personally or in his capacity as Director, hereby ratifying and confirming all
acts and things which such attorney or attorneys may do or cause to be done by
virtue of this power of attorney.

         IN WITNESS WHEREOF, the undersigned has executed this power of
attorney as of this  5th day of February, 1997.




                                         /s/ H. Jesse Arnelle
                                        ----------------------------------------
                                        H. JESSE ARNELLE
<PAGE>   2
                                                                      EXHIBIT 24

                               POWER OF ATTORNEY

                       UNION PACIFIC RESOURCES GROUP INC.

         KNOW ALL MEN BY THESE PRESENTS, that LYNNE V. CHENEY, a Director of
Union Pacific Resources Group Inc., a Utah Corporation (the "Corporation"),
hereby appoints JACK L. MESSMAN, JOSEPH A. LASALA, MARK S. KNOUSE and MARK L.
JONES, and each of them acting individually, her true and lawful attorney, each
with power to act without the other and full power of substitution, to execute,
deliver and file, for and on her behalf, and in her name and in her capacity as
Director, an Annual Report on Form 10-K for the year ended December 31, 1996
(or other appropriate form) for filing with the Securities and Exchange
Commission and any other documents in support thereof or supplemental or
amendatory thereto, hereby granting to such attorneys and each of them full
power and authority to do and perform each and every act and thing whatsoever
as such attorney or attorneys may deem necessary or advisable to carry out
fully the intent of the foregoing as the undersigned might or could do
personally or in her capacity as Director, hereby ratifying and confirming all
acts and things which such attorney or attorneys may do or cause to be done by
virtue of this power of attorney.

         IN WITNESS WHEREOF, the undersigned has executed this power of
attorney as of this  5th day of February, 1997.




                                         /s/ Lynne V. Cheney
                                        ----------------------------------------
                                        LYNNE V. CHENEY
<PAGE>   3
                                                                      EXHIBIT 24

                               POWER OF ATTORNEY

                       UNION PACIFIC RESOURCES GROUP INC.

         KNOW ALL MEN BY THESE PRESENTS, that PRESTON M. GEREN III, a Director
of Union Pacific Resources Group Inc., a Utah Corporation (the "Corporation"),
hereby appoints JACK L. MESSMAN, JOSEPH A. LASALA, JR., MARK S. KNOUSE and MARK
L.  JONES, and each of them acting individually, his true and lawful attorney,
each with power to act without the other and full power of substitution, to
execute, deliver and file, for and on his behalf, and in his name and in his
capacity as Director, an Annual Report on Form 10-K for the year ended December
31, 1996 (or other appropriate form) for filing with the Securities and
Exchange Commission and any other documents in support thereof or supplemental
or amendatory thereto, hereby granting to such attorneys and each of them full
power and authority to do and perform each and every act and thing whatsoever
as such attorney or attorneys may deem necessary or advisable to carry out
fully the intent of the foregoing as the undersigned might or could do
personally or in his capacity as Director, hereby ratifying and confirming all
acts and things which such attorney or attorneys may do or cause to be done by
virtue of this power of attorney.

         IN WITNESS WHEREOF, the undersigned has executed this power of
attorney as of this  5th day of February, 1997.




                                         /s/ Preston M. Geren III
                                        ----------------------------------------
                                        PRESTON M. GEREN III
<PAGE>   4
                                                                      EXHIBIT 24

                               POWER OF ATTORNEY

                       UNION PACIFIC RESOURCES GROUP INC.

         KNOW ALL MEN BY THESE PRESENTS, that LAWRENCE M. JONES, a Director of
Union Pacific Resources Group Inc., a Utah Corporation (the "Corporation"),
hereby appoints JACK L. MESSMAN, JOSEPH A. LASALA, JR., MARK S. KNOUSE and MARK
L.  JONES, and each of them acting individually, his true and lawful attorney,
each with power to act without the other and full power of substitution, to
execute, deliver and file, for and on his behalf, and in his name and in his
capacity as Director, an Annual Report on Form 10-K for the year ended December
31, 1996 (or other appropriate form) for filing with the Securities and
Exchange Commission and any other documents in support thereof or supplemental
or amendatory thereto, hereby granting to such attorneys and each of them full
power and authority to do and perform each and every act and thing whatsoever
as such attorney or attorneys may deem necessary or advisable to carry out
fully the intent of the foregoing as the undersigned might or could do
personally or in his capacity as Director, hereby ratifying and confirming all
acts and things which such attorney or attorneys may do or cause to be done by
virtue of this power of attorney.

         IN WITNESS WHEREOF, the undersigned has executed this power of
attorney as of this  5th day of February, 1997.




                                         /s/ Lawrence M. Jones
                                        ----------------------------------------
                                        LAWRENCE M. JONES
<PAGE>   5
                                                                      EXHIBIT 24

                               POWER OF ATTORNEY

                       UNION PACIFIC RESOURCES GROUP INC.

         KNOW ALL MEN BY THESE PRESENTS, that DREW LEWIS, a Director of Union
Pacific Resources Group Inc., a Utah Corporation (the "Corporation"), hereby
appoints JACK L. MESSMAN, JOSEPH A. LASALA, JR., MARK S. KNOUSE and MARK L.
JONES, and each of them acting individually, his true and lawful attorney, each
with power to act without the other and full power of substitution, to execute,
deliver and file, for and on his behalf, and in his name and in his capacity as
Director, an Annual Report on Form 10-K for the year ended December 31, 1996
(or other appropriate form) for filing with the Securities and Exchange
Commission and any other documents in support thereof or supplemental or
amendatory thereto, hereby granting to such attorneys and each of them full
power and authority to do and perform each and every act and thing whatsoever
as such attorney or attorneys may deem necessary or advisable to carry out
fully the intent of the foregoing as the undersigned might or could do
personally or in his capacity as Director, hereby ratifying and confirming all
acts and things which such attorney or attorneys may do or cause to be done by
virtue of this power of attorney.

         IN WITNESS WHEREOF, the undersigned has executed this power of
attorney as of this  5th day of February, 1997.




                                         /s/ Drew Lewis
                                        ----------------------------------------
                                        DREW LEWIS
<PAGE>   6
                                                                      EXHIBIT 24

                               POWER OF ATTORNEY

                       UNION PACIFIC RESOURCES GROUP INC.

         KNOW ALL MEN BY THESE PRESENTS, that CLAUDINE B. MALONE, a Director of
Union Pacific Resources Group Inc., a Utah Corporation (the "Corporation"),
hereby appoints JACK L. MESSMAN, JOSEPH A. LASALA, MARK S. KNOUSE and MARK L.
JONES, and each of them acting individually, her true and lawful attorney, each
with power to act without the other and full power of substitution, to execute,
deliver and file, for and on her behalf, and in her name and in her capacity as
Director, an Annual Report on Form 10-K for the year ended December 31, 1996
(or other appropriate form) for filing with the Securities and Exchange
Commission and any other documents in support thereof or supplemental or
amendatory thereto, hereby granting to such attorneys and each of them full
power and authority to do and perform each and every act and thing whatsoever
as such attorney or attorneys may deem necessary or advisable to carry out
fully the intent of the foregoing as the undersigned might or could do
personally or in her capacity as Director, hereby ratifying and confirming all
acts and things which such attorney or attorneys may do or cause to be done by
virtue of this power of attorney.

         IN WITNESS WHEREOF, the undersigned has executed this power of
attorney as of this  5th day of February, 1997.




                                         /s/ Claudine B. Malone
                                        ----------------------------------------
                                        CLAUDINE B. MALONE
<PAGE>   7
                                                                      EXHIBIT 24


                               POWER OF ATTORNEY

                       UNION PACIFIC RESOURCES GROUP INC.

         KNOW ALL MEN BY THESE PRESENTS, that JOHN W. PODUSKA, SR., PH.D., a
Director of Union Pacific Resources Group Inc., a Utah Corporation (the
"Corporation"), hereby appoints JACK L. MESSMAN, JOSEPH A. LASALA, JR., MARK S.
KNOUSE and MARK L. JONES, and each of them acting individually, his true and
lawful attorney, each with power to act without the other and full power of
substitution, to execute, deliver and file, for and on his behalf, and in his
name and in his capacity as Director, an Annual Report on Form 10-K for the
year ended December 31, 1996 (or other appropriate form) for filing with the
Securities and Exchange Commission and any other documents in support thereof
or supplemental or amendatory thereto, hereby granting to such attorneys and
each of them full power and authority to do and perform each and every act and
thing whatsoever as such attorney or attorneys may deem necessary or advisable
to carry out fully the intent of the foregoing as the undersigned might or
could do personally or in his capacity as Director, hereby ratifying and
confirming all acts and things which such attorney or attorneys may do or cause
to be done by virtue of this power of attorney.

         IN WITNESS WHEREOF, the undersigned has executed this power of
attorney as of this  5th day of February, 1997.



                                         /s/ John W. Poduska, Sr., Ph.D.
                                        ----------------------------------------
                                        JOHN W. PODUSKA, SR., PH.D.
<PAGE>   8
                                                                      EXHIBIT 24

                               POWER OF ATTORNEY

                       UNION PACIFIC RESOURCES GROUP INC.

         KNOW ALL MEN BY THESE PRESENTS, that SAMUEL K. SKINNER, a Director of
Union Pacific Resources Group Inc., a Utah Corporation (the "Corporation"),
hereby appoints JACK L. MESSMAN, JOSEPH A. LASALA, JR., MARK S. KNOUSE and MARK
L.  JONES, and each of them acting individually, his true and lawful attorney,
each with power to act without the other and full power of substitution, to
execute, deliver and file, for and on his behalf, and in his name and in his
capacity as Director, an Annual Report on Form 10-K for the year ended December
31, 1996 (or other appropriate form) for filing with the Securities and
Exchange Commission and any other documents in support thereof or supplemental
or amendatory thereto, hereby granting to such attorneys and each of them full
power and authority to do and perform each and every act and thing whatsoever
as such attorney or attorneys may deem necessary or advisable to carry out
fully the intent of the foregoing as the undersigned might or could do
personally or in his capacity as Director, hereby ratifying and confirming all
acts and things which such attorney or attorneys may do or cause to be done by
virtue of this power of attorney.

         IN WITNESS WHEREOF, the undersigned has executed this power of
attorney as of this  5th day of February, 1997.




                                         /s/ Samuel K. Skinner
                                        ----------------------------------------
                                        SAMUEL K. SKINNER
<PAGE>   9
                                                                      EXHIBIT 24

                               POWER OF ATTORNEY

                       UNION PACIFIC RESOURCES GROUP INC.

         KNOW ALL MEN BY THESE PRESENTS, that JAMES R. THOMPSON, a Director of
Union Pacific Resources Group Inc., a Utah Corporation (the "Corporation"),
hereby appoints JACK L. MESSMAN, JOSEPH A. LASALA, JR., MARK S. KNOUSE and MARK
L.  JONES, and each of them acting individually, his true and lawful attorney,
each with power to act without the other and full power of substitution, to
execute, deliver and file, for and on his behalf, and in his name and in his
capacity as Director, an Annual Report on Form 10-K for the year ended December
31, 1996 (or other appropriate form) for filing with the Securities and
Exchange Commission and any other documents in support thereof or supplemental
or amendatory thereto, hereby granting to such attorneys and each of them full
power and authority to do and perform each and every act and thing whatsoever
as such attorney or attorneys may deem necessary or advisable to carry out
fully the intent of the foregoing as the undersigned might or could do
personally or in his capacity as Director, hereby ratifying and confirming all
acts and things which such attorney or attorneys may do or cause to be done by
virtue of this power of attorney.

         IN WITNESS WHEREOF, the undersigned has executed this power of
attorney as of this  5th day of February, 1997.




                                         /s/ James R. Thompson
                                        ----------------------------------------
                                        JAMES R. THOMPSON