CUSTODIAL AGREEMENT



                       NATIONAL AUTO FINANCE COMPANY, INC.
                                     COMPANY




                                       AND




                       OMNI FINANCIAL SERVICES OF AMERICA
                                    CUSTODIAN




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

                          DATED AS OF JANUARY 20, 1998


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         THIS CUSTODIAL AGREEMENT ("Agreement"), dated as of January 20, 1998,
is entered into by and between OMNI FINANCIAL SERVICES OF AMERICA, INC. as
custodian ("Custodian" or "OFSA"), and NATIONAL AUTO FINANCE COMPANY, INC. as
servicer (the "Company" or "NAFI").

                                    RECITALS

      A. National Financial Auto Funding Trust ("National Financial"), a
Delaware business trust, intends to transfer, set over, assign and otherwise
convey the accounts designated in Schedule 1 to the Servicing Agreement (as
defined below) (the "Assigned Accounts") to National Auto Finance 1998-1 Trust
(the "Trust") pursuant to the Sale and Servicing Agreement, dated as of December
15, 1997 (the "Sale and Servicing Agreement"), by and among the Trust, National
Financial, NAFI and Harris Trust and Savings Bank, as trust collateral agent
(the "Trust Collateral Agent").

      B. NAFI and OFSA have agreed pursuant to the Amended and Restated
Servicing Agreement (the "Servicing Agreement") dated as of December 5, 1994, as
amended and supplemented, that OFSA shall provide certain accounting and
collection services with respect to the Assigned Accounts following assignment
of the Assigned Accounts by National Financial to the Trust. 

      C. NAFI desires to have OFSA take possession of the Receivable Files as
custodian and bailee of the Trust Collateral Agent and NAFI and the Trust
Collateral Agent, as assignee of NAFI in accordance with the terms and
conditions hereof.

      D. Capitalized terms used but not defined herein shall have the same
meanings ascribed thereto in the Sale and Servicing Agreement.


                             STATEMENT OF AGREEMENT

      A. The Custodian shall maintain custody and possession of the Receivable
Files as custodian for the benefit of, and bailee for, NAFI and the Trust
Collateral Agent, as assignee of NAFI.

      B. The Custodian shall maintain possession of the related Receivable Files
at its offices in Memphis, Tennessee or at such other offices of the Custodian
as shall from time to time be identified to NAFI by written notice; provided
that, if such other offices are outside of Tennessee, the Custodian must get
NAFI's prior written consent. The Custodian may temporarily move individual
Receivable Files or any portion thereof without notice as necessary to conduct
collection and other servicing activities in accordance with its customary
practices and procedures. It is intended that by the Custodian's agreements
pursuant to this agreement that the Trust Collateral Agent will be deemed to
have possession of the Receivable Files for purposes of Section 9-305 of the UCC
as in effect in the state in which the Receivable Files are located.

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      C. As custodian and bailee, the Custodian shall have and perform the
following powers and duties:

          (i) hold the Receivable Files on behalf of NAFI and the Trust
          Collateral Agent, as assignee of NAFI maintain accurate records
          pertaining to each Receivable to enable it to comply with the terms
          and conditions of this custodial agreement and maintain a current
          inventory thereof (by computer records or otherwise);

          (ii) implement policies and procedures with respect to the reasonable
          and customary handling and custody of the Receivable Files;

          (iii) attend to details in maintaining custody of the Receivable Files
          on behalf of NAFI; and

          (iv) at all times maintain the original of each fully executed
          Receivable and store such original Receivable in a secure place.

      D. The Custodian shall:

          (i) act with reasonable care, using that degree of skill and care that
          it exercises with respect to similar contracts owned and/or serviced
          by it;

          (ii) promptly report to NAFI any material failure by it to hold the
          Receivable Files as herein provided;

          (iii) promptly take appropriate action to remedy any such failure; and

          (iv) in acting as custodian and bailee of the Receivable Files, not
          assert, and shall cause a related subservicer not to assert, any
          beneficial ownership interests in the Receivables or the Receivable
          Files.

      E. The Custodian agrees to indemnify the Company and the Trust Collateral
Agent, its respective officers, directors, employees and agents for any and all
liabilities, obligations, losses, damages, payments, costs or expenses of any
kind whatsoever which may be imposed on or incurred by the Company and the Trust
Collateral Agent arising from the gross negligence or willful misconduct of the
Custodian in maintaining custody of the Receivable Files pursuant to this
Agreement; provided, however, that the Custodian will not be liable to the
extent that any such amount resulted from the gross negligence or willful
misconduct of the Company and provided further that the Custodian will not be
liable for any such liability, obligation, loss, damage, payment, cost or
expense that resulted from any act or omission to act by it done in conformity
with the written instructions of the Company.

      F. If at any time the Company notifies the Custodian that other custodial
arrangements have been made for the holding of the Receivable Files, such

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Custodian shall cooperate with the Company in such new custodial arrangement at
the expense of the Company. Such Custodian shall cooperate with the Company to
assure that the various documents contained in such Receivable Files are made
available to the Company, as necessary for the performance of the Company's
duties under the other custodial agreements.

      G. The Custodian shall not without the prior written consent of the
Company and the Trust Collateral Agent, deliver or release to any Person any
Receivables or related Title Documents (or any security interest in the related
Financed Vehicle) except (i) in the ordinary course of its business in
connection with the release of collateral securing such Receivable after
satisfaction of the related indebtedness thereunder or in connection with
correcting vehicle lienholder or similar information on a Receivable or title
document or (ii) upon written notice from the Seller or NAFI that such contract
has been retransferred to the Seller in accordance with the Sale and Servicing
Agreement.

      H. The Custodian shall retain possession of the Receivable File for each
Assigned Account until written notice from NAFI that the related account has
been determined to be a contract with respect to which any of the following has
occurred during the due period: (i) 91 days have elapsed since repossession of
the related financed vehicle, (ii) NAFI has in good faith determined that all
amounts that it expects to recover under such contract have been received, or
(iii) 90% of any scheduled payment on such contract is 120 days or more (or, if
the related Obligor is a debtor under Chapter 13 of the U.S. Bankruptcy Code,
180 days or more) delinquent as of the end of such due period; provided that
OFSA shall not be required to continue collection efforts beyond its standard
collection practices (as provided in the Servicing Agreement) except at NAFI's
expense.


                            MISCELLANEOUS PROVISIONS

      A. Effect of Invalidity of Provisions. In case any one or more of the
provisions contained in this Agreement should be or become invalid, illegal or
unenforceable in any respect, the validity, legality and enforceability of the
remaining provisions contained herein or therein shall in no way be affected,
prejudiced or disturbed thereby.

      B. Governing Law. This Agreement shall be governed by and construed in
accordance with the laws of the State of New York, without regard to conflict of
laws rules.

      C. Termination. It is agreed that either party hereto may terminate this
Agreement without cause upon 60 days prior written notice to the other party,
provided that NAFI delivers prior written notice of such termination to the
Insurer and the Custodian delivers the Receivable Files to the Trust Collateral
Agent or at the direction of the Trust Collateral Agent prior to expiration of
such 60 day period and termination of this Agreement.

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Notwithstanding the preceding sentence, if the Trust Collateral Agent or its
designee has not received the Receivable Files prior to expiration of such 60
day period, this Agreement will continue in full force and effect until actual
receipt of the Receivables Files by the Trust Collateral Agent or its designee.


      D. Assignment. This Agreement may be assigned only with the prior written
consent of the other party hereto and the Trust Collateral Agent; provided that,
the Company may assign all its rights under this Agreement to the Trust
Collateral Agent, to which the Custodian hereby expressly consents. The Trust
Collateral Agent as assignee of the Company can enforce the rights under this
Agreement directly against the Custodian.



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         IN WITNESS WHEREOF, the Company and Custodian have caused this
Agreement to be duly executed as of the date and year first above written.



                                     NATIONAL AUTO FINANCE COMPANY, INC.

                                       By:
                                      Name:
                                     Title:



                                     OMNI FINANCIAL SERVICES OF AMERICA, INC.

                                       By:
                                      Name:
                                     Title: