<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., and KATHY L. COX, 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, 1998 (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 21st day of January, 1999.


                                       /s/ H. Jesse Arnelle   
                                       ------------------------------------
                                       H. JESSE ARNELLE



<PAGE>   2


                                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, JR., and KATHY L. COX, 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, 1998 (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 21st day of January, 1999.


                                       /s/ Lynne V. Cheney   
                                       ------------------------------------
                                       LYNNE V. CHENEY



<PAGE>   3


                                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., and KATHY L. COX, 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, 1998 (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 21st day of January, 1999.


                                       /s/ Preston M. Geren III
                                       ------------------------------------
                                       PRESTON M. GEREN III



<PAGE>   4


                                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., and KATHY L. COX, 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, 1998 (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 21st day of January, 1999.


                                       /s/ Lawrence M. Jones   
                                       ------------------------------------
                                       LAWRENCE M. JONES



<PAGE>   5


                                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., and KATHY L. COX, 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, 1998 (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 21st day of January, 1999.


                                       /s/ Drew Lewis   
                                       ------------------------------------
                                       DREW LEWIS



<PAGE>   6


                                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, JR., and KATHY L. COX, 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, 1998 (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 21st day of January, 1999.


                                       /s/ Claudine B. Malone     
                                       ------------------------------------
                                       CLAUDINE B. MALONE



<PAGE>   7


                                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., and
KATHY L. COX, 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, 1998 (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 21st day of January, 1999.


                                       /s/ John W. Poduska, Sr., Ph.D.   
                                       ------------------------------------
                                       JOHN W. PODUSKA, SR., PH.D.



<PAGE>   8


                                POWER OF ATTORNEY

                       UNION PACIFIC RESOURCES GROUP INC.

     KNOW ALL MEN BY THESE PRESENTS, that MICHAEL E. ROSSI, a Director of Union
Pacific Resources Group Inc., a Utah Corporation (the "Corporation"), hereby
appoints JACK L. MESSMAN, JOSEPH A. LASALA, JR., and KATHY L. COX, 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, 1998 (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 21st day of January, 1999.


                                       /s/ Michael E. Rossi   
                                       ------------------------------------
                                       MICHAEL E. ROSSI



<PAGE>   9


                                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., and KATHY L. COX, 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, 1998 (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 21st day of January, 1999.


                                       /s/ Samuel K. Skinner   
                                       ------------------------------------
                                       SAMUEL K. SKINNER



<PAGE>   10


                                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., and KATHY L. COX, 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, 1998 (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 21st day of January, 1999.


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