<PAGE>   1
                                                                    EXHIBIT 25.1


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                       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, Suite 2310, 5 Empire State
             
             Plaza, Albany, New York 12223.  Board of Governors of the Federal

             Reserve System 20th and C Street NW, Washington, D.C., 20551 
      
             Federal Reserve Bank of New York, District No. 2, 33 Liberty
  
             Street, New York, N.Y. 10045.  Federal Deposit Insurance 
    
             Corporation, 550 Seventeenth Street NW 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.





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<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 2ND day
of JUNE, 1998.

                                   THE CHASE MANHATTAN BANK

                                   By  /s/ ANDREW M. DECK
                                     -------------------------------
                                           ANDREW M. DECK 
                                           VICE PRESIDENT


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<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 March 31, 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............................................. $ 12,037
     Interest-bearing balances ....................................    4,054
Securities:  ......................................................
Held to maturity securities........................................    2,340
Available for sale securities......................................   50,134
Federal funds sold and securities purchased under
     agreements to resell .........................................   24,982
Loans and lease financing receivables:
     Loans and leases, net of unearned income.....   $127,958
     Less: Allowance for loan and lease losses....      2,797
     Less: Allocated transfer risk reserve .......          0
                                                     --------
     Loans and leases, net of unearned income,
     allowance, and reserve .......................................   125,161
Trading Assets ....................................................    61,820
Premises and fixed assets (including capitalized
     leases).......................................................     2,961
Other real estate owned ...........................................       347
Investments in unconsolidated subsidiaries and
     associated companies..........................................       242
Customers' liability to this bank on acceptances
     outstanding ..................................................     1,380
Intangible assets .................................................     1,549
Other assets ......................................................    11,727
                                                                     --------
TOTAL ASSETS ......................................................  $298,734
                                                                     ========
</TABLE>



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<TABLE>

                                   LIABILITIES
<S>                                                                  <C>
Deposits
     In domestic offices ........................................     $96,682
     Noninterest-bearing ..................     $38,074
     Interest-bearing .....................      58,608
                                                -------
     In foreign offices, Edge and Agreement,
     subsidiaries and IBF's .....................................      72,630
     Noninterest-bearing ..................     $ 3,289
     Interest-bearing .....................      69,341

Federal funds purchased and securities sold under 
agreements to repurchase ........................................      42,735
Demand notes issued to the U.S. Treasury ........................         872
Trading liabilities .............................................      45,545

Other borrowed money (includes mortgage indebtedness
     and obligations under capitalized leases):
     With a remaining maturity of one year or less ..............       4,454
     With a remaining maturity of more than one year 
          through three years....................................         231
     With a remaining maturity of more than three years..........         106
Bank's liability on acceptances executed and outstanding.........       1,380
Subordinated notes and debentures ...............................       5,708
Other liabilities ...............................................      11,295

TOTAL LIABILITIES ...............................................     281,638
                                                                      -------

                                 EQUITY CAPITAL

Perpetual preferred stock and related surplus....................           0
Common stock ....................................................       1,211
Surplus  (exclude all surplus related to preferred stock)........      10,291
Undivided profits and capital reserves ..........................       5,579
Net unrealized holding gains (losses)
on available-for-sale securities ................................          (1)
Cumulative foreign currency translation adjustments .............          16

TOTAL EQUITY CAPITAL ............................................      17,096
                                                                     --------
TOTAL LIABILITIES AND EQUITY CAPITAL ............................    $298,734
                                                                     ========
</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.)


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