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                                                                  Exhibit (4)(h)

                   SECOND AMENDMENT TO LIMITED TERM EXTENSION


                  This Second Amendment to Limited Term Extension (the "Second
Amendment") is entered into this 16th day of March, 1998 between National Auto
Credit, Inc. ("National"), as borrower, NAC, Inc. and NAC Investment Company, as
guarantors, The First National Bank of Chicago ("First Chicago"), Morgan
Guaranty Trust Company of New York ("Morgan"), The Bank of New York ("BNY"),
First Union National Bank ("First Union"), The Huntington National Bank
("Huntington"), Allstate Life Insurance Company ("Allstate"), Connecticut
General Life Insurance Company (on behalf of itself and one or more separate
accounts, collectively "Connecticut General"), Principal Mutual Life Insurance
Company ("Principal Mutual"), New York Life Insurance Company ("New York Life"),
New York Life Insurance and Annuity Corporation ("New York Annuity"), Lincoln
National Life Insurance Company ("Lincoln National") and Lincoln Life & Annuity
Company of New York ("Lincoln Life"), as lenders, and NBD Bank, ("NBD") as
issuer of letters of credit. Capitalized terms not otherwise defined herein
shall have the meanings ascribed to such terms in that certain Limited Term
Extension dated as of February 13, 1998 (as amended to the date hereof, the
"Extension").

                                    RECITALS
                                    --------

                  WHEREAS, National presently owes (i) approximately $35 million
in Principal Obligations on Loans extended by the Banks pursuant to the Credit
Agreement, and (ii) approximately $41.5 million in Principal Obligations on
loans extended by the Insurance Companies pursuant to the terms of the Note
Purchase Agreement and Notes.

                  WHEREAS, on February 13, 1998, National, the Lenders and NBD
entered into the Extension pursuant to which the Banks granted National a
limited extension of maturities and the Insurance Companies granted National a
limited extension of the Waiver Extension, all on the terms and conditions
specifically set forth therein.

                  WHEREAS, pursuant to the terms of the Extension, all Lender
Obligations became due and payable in full on March 6, 1998.

                  WHEREAS, on March 6, 1998, National, the Lenders and NBD
entered into the First Amendment to Limited Term Extension (the "First
Amendment") pursuant to which the Lenders granted National an additional limited
extension of maturities and the Insurance Companies granted National an
additional limited extension of the Waiver Extension, all on the terms and
conditions specifically set forth therein.

                  WHEREAS, National has requested the Lenders and NBD for an
additional extension of the Extension Termination Date.

                  WHEREAS, the Lenders and NBD are prepared to extend the
Extension Termination Date until May 29, 1998 on the terms and conditions
contained herein.


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                  NOW, THEREFORE, in consideration of the foregoing and for
other good and valuable consideration, the receipt and sufficiency of which are
hereby acknowledged, the parties hereto agree to amend the Extension as follows:

                  1. The definition of "Extension Default" is amended in its
entirety so that, as amended, it provides as follows:

         "EXTENSION DEFAULT" means (i) all "Defaults" as defined in the Credit
         Agreement, (ii) all "Defaults" as defined in the Note Purchase
         Agreement, (iii) National's failure to comply with any term or
         provision of this Limited Term Extension, or (iv) the payment by
         National of any portion of the principal obligations owed to Brown
         Brothers Harriman & Co.

                  2. The definition of "Extension Termination Date" is amended
in its entirety so that, as amended, it provides as follows:

         "EXTENSION TERMINATION DATE" means the earlier to occur of (i) May 29,
         1998, and (ii) the occurrence of an Extension Default.

                  3. The following definition is added to the Extension:

         "RECONSTITUTED SPECIAL COMMITTEE" means the special committee appointed
         by National's Board of Directors on March 11, 1998.

                  4. Paragraph 2 of the Extension is amended in its entirety so
that, as amended, it provides as follows:

                  "2. Upon the execution hereof, National shall pay to the
         Agent, for distribution to the Banks, and to the Insurance Companies,
         all interest accrued through March 19, 1998 on the Credit Agreement
         Obligations and the Note Obligations, respectively, at the rates set
         forth in paragraph 3 of the Extension."

                  5. Paragraph 3 of the Extension is amended in its entirety so
that, as amended, it provides as follows:

                  "3. From and after January 31, 1998, interest will accrue on
         the unpaid balance of all Lender Obligations at a per annum rate
         (computed on the basis of a 360-day year of twelve 30-day months) equal
         to the higher of (i) the Floating Rate, and (ii) 7.66%. Commencing on
         March 20, 1998 interest will be payable to all Lenders weekly, in
         arrears, on Friday of each week. From and after January 31,1998
         interest will accrue on the unpaid balance of any overdue Credit
         Agreement Obligation or Note Obligation at the rate applicable to such
         overdue Obligation under the terms of the Credit Agreement or Note
         Purchase Agreement, as the case may be."

                  6. Paragraph 4 of the Extension is amended in its entirety so
that, as amended, it provides as follows:


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                  "4. National shall make principal payments to the Lenders and
         NBD on the following dates and in the following amounts:

                             February 19, 1998                $1,000,000
                             March 6, 1998                    $5,500,000
                             March 19, 1998                   $6,000,000

         National shall make payments to the Lenders and NBD on the following
         dates and in the following amounts, to be applied first to accrued and
         unpaid interest, and the balance to principal:

                             March 20, 1998                   $625,000
                             March 27, 1998                   $625,000
                             April 3, 1998                    $625,000
                             April 10, 1998                   $625,000
                             April 17, 1998                   $625,000
                             April 24, 1999                   $625,000
                             May 1, 1998                      $625,000
                             May 8, 1998                      $625,000
                             May 15, 1998                     $625,000
                             May 22, 1998                     $625,000
                             May 29, 1998                     $625,000

         National shall also remit to the Lenders, for application to the
         Principal Obligations, all federal tax refunds (if any) received by
         National through May 29, 1998, when and as such refunds are received.
         Each principal payment will be distributed to the Lenders and NBD on a
         Pro Rata basis and will be applied by the Lenders against the Principal
         Obligations. Principal payments distributed to NBD in respect of the
         Reimbursement Obligation will be held by NBD as cash collateral to
         secure payment of the Reimbursement Obligation until the Letters of
         Credit are drawn. If one or more Letters of Credit expires or is
         returned to NBD undrawn, NBD will distribute the cash collateral then
         held by NBD in respect of such Letter(s) of Credit to all Lenders (and,
         to the extent that other Letters of Credit remain outstanding, to NBD)
         for reduction of Principal Obligations on a Pro Rata basis. The
         remaining balance of all Lender Obligations shall be due and payable in
         full on the Extension Termination Date; provided, however, that to the
         extent payment of the Note Obligations is voluntarily waived or
         extended by the Insurance Companies beyond the Extension Termination
         Date, the Extension Termination Date shall not constitute a "Settlement
         Date" for purposes of Section 8.6 of the Note Purchase Agreement."


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                  7. Paragraph 7 of the Extension is amended in its entirety so
that, as amended, it provides as follows:

                  "7. National shall update the Lenders, no less frequently than
         bi-weekly, which updates shall take the form of oral reports to counsel
         and, at the request of the Lenders, to the Lenders concerning (i) the
         business and operations of National, (ii) National's progress in its
         efforts to obtain financing, (iii) the Reconstituted Special
         Committee's internal review of National, (iv) National's negotiation of
         the terms and provisions of the settlement agreement that National
         intends to enter into with the United States Department of Labor, and
         (v) such other matters as the Lenders may reasonably request."

                  8. Paragraph 9 of the Extension is amended in its entirety so
that, as amended, it provides as follows:

                  "9. Notwithstanding any prior or future waiver of defaults by
         the Lenders (and without waiving or modifying rights available to the
         Lenders under the Credit Agreement and the Note Purchase Agreement),
         (i) National will, on a monthly basis or such shorter time as the
         Lenders may request, promptly pay statements (which statements may or
         may not be accompanied by the billing information described in the last
         sentence of this paragraph) for the reasonable fees and expenses
         incurred on behalf of the Lenders by the firms of Policano & Manzo,
         LLC, O'Melveny & Myers LLP, and Sidley & Austin, and (ii) National
         will, on a monthly basis, reimburse each Lender for its reasonable fees
         and expenses (including reasonable fees and expenses for outside and
         in-house counsel as well as travel and other expenses for each Lender's
         personnel) incurred by such Lender in connection with such Lender's
         loans to National in accordance with the terms of the Credit Agreement
         and the Note Purchase Agreement, as the case may be. Additionally, it
         is an express condition to the effectiveness of this Amendment that all
         outstanding statements for fees and expenses incurred by Policano &
         Manzo, LLC, O'Melveny & Myers LLP, and Sidley & Austin shall have been
         paid in full in connection with the matters set forth herein. The
         Lenders will, when or as soon as is reasonably practicable after
         statements have been submitted to National for payment, provide
         National with copies of the billing information submitted to the
         Lenders by Policano & Manzo, LLC, O'Melveny & Myers LLP, and Sidley &
         Austin; provided, however, that the Lenders shall be entitled to redact
         information which the Lenders believe to be subject to privilege or to
         be otherwise confidential."

                  9. The following paragraphs shall be added to the Extension as
paragraphs 13, 14, 15 and 16, respectively:

                  "13. National shall deliver to the Lenders, no later than May
         15, 1998, a comprehensive business plan reflecting National's projected
         operations, including all cash receipts and disbursements in a format
         and in detail reasonably acceptable to National and Policano & Manzo,
         LLC.

                  14. National shall promptly inform the former National
         directors who served on the Special Committee until March 9, 1998, as
         well as the professionals who had been retained by the Special
         Committee prior to March 9,1998, that National consents to such former
         directors and such professionals communicating directly with the
         Lenders concerning all facets of the Special Committee Report.

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                  15. National shall, and National shall cause Grant Thornton
         to, cooperate with Policano & Manzo, LLC in all respects. Without
         limiting the foregoing in any respect, National and Grant Thornton
         shall promptly provide Policano & Manzo, LLC with all information and
         reports (reasonably available to National and/or Grant Thornton) that
         may be reasonably requested by Policano & Manzo, LLC, including,
         without limitation, balance sheets, income statements and statements of
         changes in cash position and any financial information provided by
         National to prospective lenders.

                  16. The Lenders hereby agree:

                  (a) to extend the time limit, imposed by Section 5.1(d)(iii)
         of the Credit Agreement and Section 7.1(b) of the Note Purchase
         Agreement, within which National must deliver audited financial
         statements (meeting the requirements set forth in Section 5.1(d)(iii)
         of the Credit Agreement and Section 7.1(b) of the Note Purchase
         Agreement) to the Lenders until two business days after National's
         independent auditors issue their audit opinion to National; provided,
         however, that in no event will the time limit extend beyond the
         Extension Termination Date;

                  (b) to extend the time limit, imposed by Section 5.1(d)(vii)
         of the Credit Agreement and Section 7.1(j) of the Note Purchase
         Agreement, within which National must deliver the prescribed claims
         analysis to the Lenders until two business days after National's
         independent auditors issue their audit opinion to National; provided,
         however, that in no event will the time limit extend beyond the
         Extension Termination Date;

                  (c) to suspend National's obligation to comply with the fixed
         charge coverage ratio covenants contained in Section 5.2(b) of the
         Credit Agreement and Section 10.5(d) of the Note Purchase Agreement
         until the Extension Termination Date; and

                  (d) that, in light of the foregoing extensions and suspension,
         neither (i) National's failure to deliver audited financials meeting
         the requirements set forth in Section 5.1(d)(iii) of the Credit
         Agreement and Section 7.1(b) of the Note Purchase Agreement within 100
         days after the end of its 1998 fiscal year, (ii) National's failure to
         deliver the specified claims analysis within 30 days of the end of its
         1998 fiscal year, nor (iii) National's failure to comply with the fixed
         charge coverage ratios during the term of this Extension shall
         constitute an Extension Default."

                  10. Except to the extent that they are amended by the terms of
this Second Amendment, the terms and provisions of the Extension shall remain in
full force and effect.

                  11. This Second Amendment is a contract made under, and shall
be governed by and construed in accordance with, the law of the State of
Illinois applicable to contracts made and to be performed entirely within such
State and without giving effect to choice of law principles of such State.


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                                       NATIONAL AUTO CREDIT, INC.

                                       By:
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                                       Its
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                                       NAC, INC.

                                       By:
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                                       Its
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                                       NAC INVESTMENT COMPANY

                                       By:
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                                       Its
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                                       THE FIRST NATIONAL BANK OF CHICAGO, as
                                       Administrative Agent and as a Lender

                                       By:
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                                       Its
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                                       MORGAN GUARANTY TRUST COMPANY OF
                                       NEW YORK,  as Documentation Agent and as
                                       a Lender

                                       By:
                                          --------------------------------------
                                       Its
                                          --------------------------------------


                                       THE BANK OF NEW YORK

                                       By:
                                          --------------------------------------
                                       Its
                                          --------------------------------------


                                       FIRST UNION NATIONAL BANK (formerly known
                                       as First Union National Bank of North
                                       Carolina)

                                       By:
                                          --------------------------------------
                                       Its
                                          --------------------------------------


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                                       THE HUNTINGTON NATIONAL BANK

                                       By:
                                          --------------------------------------
                                       Its
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                                       ALLSTATE LIFE INSURANCE COMPANY

                                       By:
                                          --------------------------------------
                                       Its
                                          --------------------------------------

                                       By:
                                          --------------------------------------
                                       Its
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                                       CONNECTICUT GENERAL LIFE INSURANCE
                                       COMPANY BY CIGNA INVESTMENTS, INC.

                                       By:
                                          --------------------------------------
                                       Its
                                          --------------------------------------


                                       CONNECTICUT GENERAL LIFE INSURANCE
                                       COMPANY ON BEHALF OF ONE OR MORE SEPARATE
                                       ACCOUNTS BY CIGNA INVESTMENTS, INC.

                                       By:
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                                       Its
                                          --------------------------------------


                                       PRINCIPAL MUTUAL LIFE INSURANCE COMPANY

                                       By:
                                          --------------------------------------
                                       Its
                                          --------------------------------------

                                       By:
                                          --------------------------------------
                                       Its
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                                       NEW YORK LIFE INSURANCE COMPANY

                                       By:
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                                       Its
                                          --------------------------------------

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                                       NEW YORK LIFE INSURANCE AND ANNUITY
                                       CORPORATION BY NEW YORK LIFE INSURANCE
                                       COMPANY

                                       By:
                                          --------------------------------------
                                       Its
                                          --------------------------------------


                                       LINCOLN NATIONAL LIFE INSURANCE COMPANY

                                       By:
                                          --------------------------------------
                                       Its
                                          --------------------------------------


                                       LINCOLN LIFE & ANNUITY COMPANY OF
                                       NEW YORK

                                       By:
                                          --------------------------------------
                                       Its
                                          --------------------------------------


                                       NBD BANK

                                       By:
                                          --------------------------------------
                                       Its
                                          --------------------------------------