<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 (the "Company"), has made,
constituted and appointed and by these presents does hereby, make constitute and
appoint ROY A. GUTHRIE, KEITH W. HUGHES, FREDERIC C. LISKOW, CHESTER D.
LONGENECKER and JOHN F. STILLO, and each of them, his true and lawful attorneys,
for him and in the name, place and stead, and in his office and capacity as
aforesaid, to sign and file the Company's Annual Report on Form 10-K for the
fiscal year ended December 31, 1999, and any and all 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,
KEITH W. HUGHES, FREDERIC C. LISKOW, CHESTER D. LONGENECKER and JOHN F. STILLO,
and each of them, full power and authority to do and perform each and every act
and that 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 of all that said ROY A.
GUTHRIE, KEITH W. HUGHES, FREDERIC C. LISKOW, CHESTER D. LONGENECKER and JOHN F.
STILLO, or any of them, as said attorneys, may or shall lawfully do or cause to
be done by virtue hereof.

         IN WITNESS WHEREOF, each of the undersigned has subscribed his or her
name this 24th day of February, 2000.


<TABLE>
<S>                                                         <C>
Signature:        /s/  KEITH W. HUGHES                      Signature:     /s/  JUDY JOLLEY MOHRAZ
                  ---------------------------                              --------------------------
Name:             Keith W. Hughes                           Name:          Judy Jolley Mohraz
Title:            Chairman of the Board, Principal          Title:         Director
                  Executive Officer and Director

Signature:        /s/  J. CARTER BACOT                      Signature:     /s/  JOHN F. STILLO
                  ---------------------------                              --------------------------
Name:             J. Carter Bacot                           Name:          John F. Stillo
Title:            Director                                  Title:         Executive Vice President, Comptroller
                                                                           and Principal Accounting Officer

Signature:        /s/  ERIC S. DOBKIN                       Signature:     /s/  H. JAMES TOFFEY, JR.
                  ---------------------------                              --------------------------
Name:             Eric S. Dobkin                            Name:          H. James Toffey, Jr.
Title:            Director                                  Title:         Director

Signature:        /s/  ROY A. GUTHRIE                       Signature:     /s/  KENNETH WHIPPLE
                  ---------------------------                              --------------------------
Name:             Roy A. Guthrie                            Name:          Kenneth Whipple
Title:            Director, Senior Executive Vice           Title:         Director
                  President and Chief Financial Officer

Signature:        /s/  WILLIAM M. ISAAC
                  ---------------------------
Name:             William M.  Isaac
Title:            Director
</TABLE>