<PAGE>   1
                                                                   EXHIBIT 25.1

      -------------------------------------------------------------------

                       SECURITIES AND EXCHANGE COMMISSION
                            Washington, D. C. 20549
                           -------------------------

                                    FORM T-1

                            STATEMENT OF ELIGIBILITY
                    UNDER THE TRUST INDENTURE ACT OF 1939 OF
                   A CORPORATION DESIGNATED TO ACT AS TRUSTEE

                  -------------------------------------------
              CHECK IF AN APPLICATION TO DETERMINE ELIGIBILITY OF
                A TRUSTEE PURSUANT TO SECTION 305(b)(2) ________

                    ----------------------------------------

                            THE CHASE MANHATTAN BANK
              (Exact name of trustee as specified in its charter)


NEW YORK                                                    13-4994650
(State of incorporation                               (I.R.S. employer
if not a national bank)                            identification No.)

270 PARK AVENUE
NEW YORK, NEW YORK                                               10017
(Address of principal executive offices)                    (Zip Code)

                               William H. McDavid
                                General Counsel
                                270 Park Avenue
                            New York, New York 10017
                              Tel: (212) 270-2611
           (Name, address and telephone number of agent for service)

                  --------------------------------------------
                      ASSOCIATES FIRST CAPITAL CORPORATION
              (Exact name of obligor as specified in its charter)


DELAWARE                                                  06-0876639
(State or other jurisdiction of                     (I.R.S. employer
incorporation or organization)                   identification No.)

250 EAST CARPENTER FREEWAY
IRVING, TEXAS                                             75062-2729
(Address of principal executive offices)                  (Zip Code)

                                      -----
                             SENIOR DEBT SECURITIES
                      (Title of the indenture securities)



<PAGE>   2




                                    GENERAL

Item 1.  General Information.

         Furnish the following information as to the trustee:

         (a) Name and address of each examining or supervising authority to
which it is subject.

             New York State Banking Department, State House, Albany, New York
             12110.

             Board of Governors of the Federal Reserve System, Washington, D.C.,
             20551

             Federal Reserve Bank of New York, District No. 2, 33 Liberty
             Street, New York, N.Y.

             Federal Deposit Insurance Corporation, Washington, D.C., 20429.


         (b) Whether it is authorized to exercise corporate trust powers.

             Yes.


Item 2.  Affiliations with the Obligor.

             If the obligor is an affiliate of the trustee, describe each such
             affiliation.

             None.


                                      -2-





<PAGE>   3






Item 16. List of Exhibits

         List below all exhibits filed as a part of this Statement of
Eligibility.

         1. A copy of the Articles of Association of the Trustee as now in
effect, including the Organization Certificate and the Certificates of Amendment
dated February 17, 1969, August 31, 1977, December 31, 1980, September 9, 1982,
February 28, 1985, December 2, 1991 and July 10, 1996 (see Exhibit 1 to Form T-1
filed in connection with Registration Statement No. 333-06249, which is
incorporated by reference).

         2. A copy of the Certificate of Authority of the Trustee to Commence
Business (see Exhibit 2 to Form T-1 filed in connection with Registration
Statement No. 33-50010, which is incorporated by reference. On July 14, 1996, in
connection with the merger of Chemical Bank and The Chase Manhattan Bank
(National Association), Chemical Bank, the surviving corporation, was renamed
The Chase Manhattan Bank).

         3. None, authorization to exercise corporate trust powers being
contained in the documents identified above as Exhibits 1 and 2.

         4. A copy of the existing By-Laws of the Trustee (see Exhibit 4 to Form
T-1 filed in connection with Registration Statement No. 333-06249, which is
incorporated by reference).

         5. Not applicable.

         6. The consent of the Trustee required by Section 321(b) of the Act
(see Exhibit 6 to Form T-1 filed in connection with Registration Statement No.
33-50010, which is incorporated by reference. On July 14, 1996, in connection
with the merger of Chemical Bank and The Chase Manhattan Bank (National
Association), Chemical Bank, the surviving corporation, was renamed The Chase
Manhattan Bank).

         7. A copy of the latest report of condition of the Trustee, published
pursuant to law or the requirements of its supervising or examining authority.

         8. Not applicable.

         9. Not applicable.

                                       SIGNATURE

         Pursuant to the requirements of the Trust Indenture Act of 1939 the
Trustee, The Chase Manhattan Bank, a corporation organized and existing under
the laws of the State of New York, has duly caused this statement of eligibility
to be signed on its behalf by the undersigned, thereunto duly authorized, all in
the City of New York and State of New York, on the 1st day of September, 1998.

                                       THE CHASE MANHATTAN BANK

                                       By /s/ ANDREW M. DECK
                                         -----------------------------
                                              Andrew M. Deck
                                              Vice President


                                     -3-

<PAGE>   4


                              Exhibit 7 to Form T-1


                                Bank Call Notice

                             RESERVE DISTRICT NO. 2
                       CONSOLIDATED REPORT OF CONDITION OF

                            The Chase Manhattan Bank
                  of 270 Park Avenue, New York, New York 10017
                     and Foreign and Domestic Subsidiaries,
                     a member of the Federal Reserve System,

                   at the close of business June 30, 1998, in
        accordance with a call made by the Federal Reserve Bank of this
        District pursuant to the provisions of the Federal Reserve Act.

<TABLE>
<CAPTION>
                                                          DOLLAR AMOUNTS
                     ASSETS                                 IN MILLIONS

<S>                                                           <C>  
Cash and balances due from depository institutions:
     Noninterest-bearing balances and
     currency and coin ..................................     $ 12,546
     Interest-bearing balances ..........................        6,610
Securities:
Held to maturity securities .............................        2,014
Available for sale securities ...........................       46,342
Federal funds sold and securities purchased under
     agreements to resell ...............................       27,489
Loans and lease financing receivables:
     Loans and leases, net of unearned income ...........     $129,281
     Less: Allowance for loan and lease losses ..........        2,796
     Less: Allocated transfer risk reserve ..............            0
                                                              --------
     Loans and leases, net of unearned income,
     allowance, and reserve .............................      126,485
Trading Assets ..........................................       58,015
Premises and fixed assets (including capitalized
     leases) ............................................        3,001
Other real estate owned .................................          260
Investments in unconsolidated subsidiaries and
     associated companies ...............................          255
Customers' liability to this bank on acceptances
     outstanding ........................................        1,245
Intangible assets .......................................        1,492
Other assets ............................................       16,408
                                                              --------
TOTAL ASSETS ............................................     $302,162
                                                              ========
</TABLE>


                                       -4-




<PAGE>   5

<TABLE>
<CAPTION>

                                LIABILITIES

<S>                                                           <C>      
Deposits
     In domestic offices ...................................  $  99,347
     Noninterest-bearing ...................................  $  41,566
     Interest-bearing ......................................     57,781
     In foreign offices, Edge and Agreement,                  ---------
     subsidiaries and IBF's ................................     80,602
Noninterest-bearing ........................................  $   4,109
     Interest-bearing ......................................     76,493

Federal funds purchased and securities sold under agree-
ments to repurchase ........................................     37,760
Demand notes issued to the U.S. Treasury ...................      1,000
Trading liabilities ........................................     42,941

Other borrowed money (includes mortgage indebtedness
     and obligations under capitalized leases):
     With a remaining maturity of one year or less .........      4,162
With a remaining maturity of more than one year ............
          through three years ..............................        213
     With a remaining maturity of more than three years ....        106
Bank's liability on acceptances executed and outstanding          1,245
Subordinated notes and debentures ..........................      5,408
Other liabilities ..........................................     11,796

TOTAL LIABILITIES ..........................................    284,580
                                                              ---------
                               EQUITY CAPITAL

Perpetual preferred stock and related surplus ..............          0
Common stock ...............................................      1,211
Surplus  (exclude all surplus related to preferred stock)...     10,441
Undivided profits and capital reserves .....................      5,916
Net unrealized holding gains (losses)
on available-for-sale securities ...........................         (2)
Cumulative foreign currency translation adjustments ........         16

TOTAL EQUITY CAPITAL .......................................     17,582
                                                              ---------
TOTAL LIABILITIES AND EQUITY CAPITAL .......................  $ 302,162
                                                              =========
</TABLE>

I, Joseph L. Sclafani, E.V.P. & Controller of the above-named
bank, do hereby declare that this Report of Condition has
been prepared in conformance with the instructions issued
by the appropriate Federal regulatory authority and is true
to the best of my knowledge and belief.

                               JOSEPH L. SCLAFANI

We, the undersigned directors, attest to the correctness
of this Report of Condition and declare that it has been
examined by us, and to the best of our knowledge and
belief has been prepared in conformance with the instructions
issued by the appropriate Federal regulatory
authority and is true and correct.

                               WALTER V. SHIPLEY       )
                               THOMAS G. LABRECQUE     ) DIRECTORS
                               WILLIAM B. HARRISON, JR.)
                                      -5-