<PAGE>   1
                                                                      Exhibit 24


                               POWER OF ATTORNEY

         KNOW ALL MEN BY THESE PRESENTS, that the undersigned, an officer
and/or a director of Associates First Capital Corporation, which corporation
proposes to file with the Securities and Exchange Commission, Washington, D.C.,
a Registration Statement pursuant to the provisions of the Securities Act of
1933, as amended, with respect to the issue and sale of certain securities of
the Company bearing such name or designation and having such terms and to be in
such form as may be selected by the responsible officers of the Company, has
made, constituted and appointed and by these presents, does hereby make,
constitute and appoint ROY A. GUTHRIE, JOHN F. STILLO, CHESTER D. LONGENECKER
and TIMOTHY M. HAYES, and each of them, his true and lawful attorneys, for him
and in his name, place and stead, and in his office and capacity as aforesaid,
to sign and file said Registration Statement and any and all amendments or
post-effective amendments thereto and any and all other documents to be signed
and filed with the Securities and Exchange Commission in connection therewith,
hereby granting to said ROY A. GUTHRIE, JOHN F. STILLO, CHESTER D. LONGENECKER
and TIMOTHY M. HAYES, and each of them, full power and authority to do and
perform each and every act and thing whatsoever requisite and necessary to be
done in the premises, as fully, to all intents and purposes, as he might or
could do if personally present, hereby ratifying and confirming in all respects
all that said ROY A. GUTHRIE, JOHN F. STILLO, CHESTER D. LONGENECKER and
TIMOTHY M. HAYES, or any of them, as said attorneys, may or shall lawfully do
or cause to be done by virtue hereof.

         IN WITNESS WHEREOF, the undersigned has set his hand this _27th_ day
of August, 1998.



                             SIGNATURE:    /s/ Harold D. Marshall
                                          -----------------------------------
                                          Harold D. Marshall
                             
                                OFFICE:   President, Chief Operating Officer 
                                          and Director





<PAGE>   2
                               POWER OF ATTORNEY

        KNOW ALL MEN BY THESE PRESENTS, that the undersigned, an officer and/or
a director of Associates First Capital Corporation, which corporation proposes
to file with the Securities and Exchange Commission, Washington, D.C., a
Registration Statement pursuant to the provisions of the Securities Act of
1933, as amended, with respect to the issue and sale of certain securities of
the Company  bearing such name or designation and having such terms and to be
in such form as may be selected by the responsible officers of the Company, has
made, constituted and appointed and by these presents, does hereby make,
constitute and appoint ROY A. GUTHRIE, JOHN F. STILLO, CHESTER D. LONGENECKER
and TIMOTHY M. HAYES, and each of them, his true and lawful attorneys, for him
and in his name, place and stead, and in his office and capacity as aforesaid,
to sign and file said Registration Statement and any and all amendments or
post-effective amendments thereto and any and all other documents to be signed
and filed with the Securities and Exchange Commission in connection therewith,
hereby granting to said ROY A. GUTHRIE, JOHN F. STILLO, CHESTER D. LONGENECKER
and TIMOTHY M. HAYES, and each of them, full power and authority to do and
perform each and every act and thing whatsoever requisite and necessary to be
done in the premises, as fully, to all intents and purposes, as he might or
could do if personally present, hereby ratifying and confirming in all respects
all that said ROY A. GUTHRIE, JOHN F. STILLO, CHESTER D. LONGENECKER and
TIMOTHY M. HAYES, or any of them, as said attorneys, may or shall lawfully do
or cause to be done by virtue hereof.

        IN WITNESS WHEREOF, the undersigned has set his hand this _27th_ day of
August, 1998.


                             SIGNATURE:   /s/ Keith W. Hughes
                                          -----------------------------------
                                          Keith W. Hughes
                             
                                OFFICE:   Chairman of the Board,
                                          Chief Executive Officer and Director
                             




<PAGE>   3
                               POWER OF ATTORNEY

         KNOW ALL MEN BY THESE PRESENTS, that the undersigned, an officer
and/or a director of Associates First Capital Corporation, which corporation
proposes to file with the Securities and Exchange Commission, Washington, D.C.,
a Registration Statement pursuant to the provisions of the Securities Act of
1933, as amended, with respect to the issue and sale of certain securities of
the Company bearing such name or designation and having such terms and to be
in such form as may be selected by the responsible officers of the Company, has
made, constituted and appointed and by these presents, does hereby make,
constitute and appoint ROY A. GUTHRIE, JOHN F. STILLO, CHESTER D. LONGENECKER
and TIMOTHY M. HAYES, and each of them, his true and lawful attorneys, for him
and in his name, place and stead, and in his office and capacity as aforesaid,
to sign and file said Registration Statement and any and all amendments or
post-effective amendments thereto and any and all other documents to be signed
and filed with the Securities and Exchange Commission in connection therewith,
hereby granting to said ROY A. GUTHRIE, JOHN F. STILLO, CHESTER D. LONGENECKER
and TIMOTHY M. HAYES, and each of them, full power and authority to do and
perform each and every act and thing whatsoever requisite and necessary to be
done in the premises, as fully, to all intents and purposes, as he might or
could do if personally present, hereby ratifying and confirming in all respects
all that said ROY A. GUTHRIE, JOHN F. STILLO, CHESTER D. LONGENECKER and
TIMOTHY M. HAYES, or any of them, as said attorneys, may or shall lawfully do
or cause to be done by virtue hereof.

         IN WITNESS WHEREOF, the undersigned has set his hand this _27th day of
August, 1998.


                             SIGNATURE:   /s/ Roy A. Guthrie
                                          ------------------------------------
                                          Roy A. Guthrie
                             
                                OFFICE:   Senior Executive Vice President,
                                          Chief Financial Officer and Director
                             




<PAGE>   4
                               POWER OF ATTORNEY

        KNOW ALL MEN BY THESE PRESENTS, that the undersigned, an officer and/or
a director of Associates First Capital Corporation, which corporation proposes
to file with the Securities and Exchange Commission, Washington, D.C., a
Registration Statement pursuant to the provisions of the Securities Act of
1933, as amended, with respect to the issue and sale of certain securities of
the Company bearing such name or designation and having such terms and to be
in such form as may be selected by the responsible officers of the Company, has
made, constituted and appointed and by these presents, does hereby make,
constitute and appoint ROY A. GUTHRIE, JOHN F. STILLO, CHESTER D. LONGENECKER
and TIMOTHY M. HAYES, and each of them, his true and lawful attorneys, for him
and in his name, place and stead, and in his office and capacity as aforesaid,
to sign and file said Registration Statement and any and all amendments or
post-effective amendments thereto and any and all other documents to be signed
and filed with the Securities and Exchange Commission in connection therewith,
hereby granting to said ROY A. GUTHRIE, JOHN F. STILLO, CHESTER D. LONGENECKER
and TIMOTHY M. HAYES, and each of them, full power and authority to do and
perform each and every act and thing whatsoever requisite and necessary to be
done in the premises, as fully, to all intents and purposes, as he might or
could do if personally present, hereby ratifying and confirming in all respects
all that said ROY A. GUTHRIE, JOHN F. STILLO, CHESTER D. LONGENECKER and
TIMOTHY M. HAYES, or any of them, as said attorneys, may or shall lawfully do
or cause to be done by virtue hereof.

        IN WITNESS WHEREOF, the undersigned has set his hand this _27th_ day of
August, 1998.


                             SIGNATURE:   /s/ John F. Stillo
                                          -------------------------------------
                                          John F. Stillo
                             
                                OFFICE:   Senior Vice President, Comptroller, 
                                          and Principal Accounting Officer
                             




<PAGE>   5
                               POWER OF ATTORNEY

         KNOW ALL MEN BY THESE PRESENTS, that the undersigned, an officer
and/or a director of Associates First Capital Corporation, which corporation
proposes to file with the Securities and Exchange Commission, Washington, D.C.,
a Registration Statement pursuant to the provisions of the Securities Act of
1933, as amended, with respect to the issue and sale of certain securities of
the Company bearing such name or designation and having such terms and to be
in such form as may be selected by the responsible officers of the Company, has
made, constituted and appointed and by these presents, does hereby make,
constitute and appoint ROY A. GUTHRIE, JOHN F. STILLO, CHESTER D. LONGENECKER
and TIMOTHY M. HAYES, and each of them, his true and lawful attorneys, for him
and in his name, place and stead, and in his office and capacity as aforesaid,
to sign and file said Registration Statement and any and all amendments or
post-effective amendments thereto and any and all other documents to be signed
and filed with the Securities and Exchange Commission in connection therewith,
hereby granting to said ROY A. GUTHRIE, JOHN F. STILLO, CHESTER D. LONGENECKER
and TIMOTHY M. HAYES, and each of them, full power and authority to do and
perform each and every act and thing whatsoever requisite and necessary to be
done in the premises, as fully, to all intents and purposes, as he might or
could do if personally present, hereby ratifying and confirming in all respects
all that said ROY A. GUTHRIE, JOHN F. STILLO, CHESTER D. LONGENECKER and
TIMOTHY M. HAYES, or any of them, as said attorneys, may or shall lawfully do
or cause to be done by virtue hereof.

         IN WITNESS WHEREOF, the undersigned has set his hand this 27th__ day
of August, 1998.


                             SIGNATURE:   /s/ J. Carter Bacot
                                          -------------------------------------
                                          J. Carter Bacot
                             
                                OFFICE:   Director
                             




<PAGE>   6
                               POWER OF ATTORNEY

         KNOW ALL MEN BY THESE PRESENTS, that the undersigned, an officer
and/or a director of Associates First Capital Corporation, which corporation
proposes to file with the Securities and Exchange Commission, Washington, D.C.,
a Registration Statement pursuant to the provisions of the Securities Act of
1933, as amended, with respect to the issue and sale of certain securities of
the Company bearing such name or designation and having such terms and to be
in such form as may be selected by the responsible officers of the Company, has
made, constituted and appointed and by these presents, does hereby make,
constitute and appoint ROY A. GUTHRIE, JOHN F. STILLO, CHESTER D. LONGENECKER
and TIMOTHY M. HAYES, and each of them, his true and lawful attorneys, for him
and in his name, place and stead, and in his office and capacity as aforesaid,
to sign and file said Registration Statement and any and all amendments or
post-effective amendments thereto and any and all other documents to be signed
and filed with the Securities and Exchange Commission in connection therewith,
hereby granting to said ROY A. GUTHRIE, JOHN F. STILLO, CHESTER D. LONGENECKER
and TIMOTHY M. HAYES, and each of them, full power and authority to do and
perform each and every act and thing whatsoever requisite and necessary to be
done in the premises, as fully, to all intents and purposes, as he might or
could do if personally present, hereby ratifying and confirming in all respects
all that said ROY A. GUTHRIE, JOHN F. STILLO, CHESTER D. LONGENECKER and
TIMOTHY M. HAYES, or any of them, as said attorneys, may or shall lawfully do
or cause to be done by virtue hereof.

         IN WITNESS WHEREOF, the undersigned has set his hand this _27th_ day
of August, 1998.


                             SIGNATURE:   /s/ Eric S. Dobkin
                                          -------------------------------------
                                          Eric S. Dobkin
                             
                                OFFICE:   Director
                             




<PAGE>   7
                               POWER OF ATTORNEY

         KNOW ALL MEN BY THESE PRESENTS, that the undersigned, an officer
and/or a director of Associates First Capital Corporation, which corporation
proposes to file with the Securities and Exchange Commission, Washington, D.C.,
a Registration Statement pursuant to the provisions of the Securities Act of
1933, as amended, with respect to the issue and sale of certain securities of
the Company bearing such name or designation and having such terms and to be
in such form as may be selected by the responsible officers of the Company, has
made, constituted and appointed and by these presents, does hereby make,
constitute and appoint ROY A. GUTHRIE, JOHN F. STILLO, CHESTER D. LONGENECKER
and TIMOTHY M. HAYES, and each of them, his true and lawful attorneys, for him
and in his name, place and stead, and in his office and capacity as aforesaid,
to sign and file said Registration Statement and any and all amendments or
post-effective amendments thereto and any and all other documents to be signed
and filed with the Securities and Exchange Commission in connection therewith,
hereby granting to said ROY A. GUTHRIE, JOHN F. STILLO, CHESTER D. LONGENECKER
and TIMOTHY M. HAYES, and each of them, full power and authority to do and
perform each and every act and thing whatsoever requisite and necessary to be
done in the premises, as fully, to all intents and purposes, as he might or
could do if personally present, hereby ratifying and confirming in all respects
all that said ROY A. GUTHRIE, JOHN F. STILLO, CHESTER D. LONGENECKER and
TIMOTHY M. HAYES, or any of them, as said attorneys, may or shall lawfully do
or cause to be done by virtue hereof.

         IN WITNESS WHEREOF, the undersigned has set his hand this _27th_ day
of August, 1998.


                             SIGNATURE:   /s/ H. James Toffey, Jr.
                                          -------------------------------------
                                          H. James Toffey, Jr.
                             
                                OFFICE:   Director
                             




<PAGE>   8
                               POWER OF ATTORNEY

         KNOW ALL MEN BY THESE PRESENTS, that the undersigned, an officer
and/or a director of Associates First Capital Corporation, which corporation
proposes to file with the Securities and Exchange Commission, Washington, D.C.,
a Registration Statement pursuant to the provisions of the Securities Act of
1933, as amended, with respect to the issue and sale of certain securities of
the Company bearing such name or designation and having such terms and to be
in such form as may be selected by the responsible officers of the Company, has
made, constituted and appointed and by these presents, does hereby make,
constitute and appoint ROY A. GUTHRIE, JOHN F. STILLO, CHESTER D. LONGENECKER
and TIMOTHY M. HAYES, and each of them, his true and lawful attorneys, for him
and in his name, place and stead, and in his office and capacity as aforesaid,
to sign and file said Registration Statement and any and all amendments or
post-effective amendments thereto and any and all other documents to be signed
and filed with the Securities and Exchange Commission in connection therewith,
hereby granting to said ROY A. GUTHRIE, JOHN F. STILLO, CHESTER D. LONGENECKER
and TIMOTHY M. HAYES, and each of them, full power and authority to do and
perform each and every act and thing whatsoever requisite and necessary to be
done in the premises, as fully, to all intents and purposes, as he might or
could do if personally present, hereby ratifying and confirming in all respects
all that said ROY A. GUTHRIE, JOHN F. STILLO, CHESTER D. LONGENECKER and
TIMOTHY M. HAYES, or any of them, as said attorneys, may or shall lawfully do
or cause to be done by virtue hereof.

         IN WITNESS WHEREOF, the undersigned has set his hand this _27th_ day
of August, 1998.


                             SIGNATURE:   /s/ William M. Isaac
                                          -------------------------------------
                                          William M. Isaac
                             
                                OFFICE:   Director