<PAGE>   1


                             AGREEMENT OF AMENDMENT


         This AGREEMENT OF AMENDMENT (this "Agreement") dated as of January 1,
1998, among DAIRY MART CONVENIENCE STORES, INC. (the "Company"), BANK OF BOSTON
CONNECTICUT, individually and as Agent under the Credit Agreement (as
hereinafter defined), HELLER FINANCIAL, INC. ("Heller") and STATE STREET BANK 
AND TRUST COMPANY ("State Street").

         WHEREAS, the Company, the banks and other financial institutions
listed on Schedule 1 thereto (collectively, with any banks or financial
institutions from time to time parties thereto, the "Banks"), and Bank of
Boston Connecticut ("BOBC"), as agent of the Banks thereunder (in such
capacity, the "Agent") entered into a certain Credit Agreement dated as of
April 24, 1996 (as amended the "Credit Agreement"); and

         WHEREAS, the Company, the Banks and the Agent wish to amend the Credit
Agreement as more fully set forth below.

         NOW THEREFORE, the parties hereto agree as follows:


                          I.  AGREEMENT OF THE PARTIES

         1. Unless the context shall otherwise require, all capitalized terms
used herein without definition shall have the meanings assigned to them in the
Credit Agreement.

         2. Section 1.1 of the Credit Agreement shall be, and hereby is, amended
by deleting the definitions of "Adjusted Consolidated Indebtedness" and 
"Minimum Consolidated Net Worth" in their entirety and substituting in lieu 
thereof the following:


            "ADJUSTED CONSOLIDATED INDEBTEDNESS" that amount which is equal to
            Consolidated Indebtedness reduced by an amount equal to the sum of
            (i) Cash and Cash Equivalents, and (ii) that portion of the
            Company's assets (as shown on its balance sheet) which represents
            real property owned by the Company and used for stores with respect
            to which the Company is party to a fully binding commitment to
            enter into a sale-leaseback arrangement within sixty days following
            the date of such calculation.

<PAGE>   2



            "MINIMUM CONSOLIDATED NET WORTH" (i) as at the FQED to occur on or
            about February 1, 1997: $7,500,000; (ii) as at the FQED to occur on
            or about April 30, 1997: $6,750,000; (iii) as at the FQED to occur
            on or about July 31, 1997: $7,900,000; (iv) as at the FQED to occur
            on or about October 31, 1997: $8,700,000; (v) as at the FQED to
            occur on or about January 31, 1998: $6,300,000; (vi) as at the FQED
            to occur on or about April 30, 1998: $4,800,000; (vii) as at the
            FQED to occur on or about July 31, 1998: $5,400,000; (viii) as at
            the FQED to occur on or about October 30, 1998: $5,850,000; and
            (ix) as at the FQED to occur on or about January 31, 1999:
            $5,600,000 and thereafter, $5,600,000 plus 50% of Cumulative 
<PAGE>   3

            Consolidated Net Income earned after the FQED ending approximately
            January 31, 1999.

         3. Section 7.1(a) of the Credit Agreement shall be, and hereby is,
amended by deleting such Section 7.1(a) in its entirety and substituting in lieu
thereof the following:

            (a) ADJUSTED CONSOLIDATED INDEBTEDNESS TO CONSOLIDATED EBITDA. For
            any period of four consecutive fiscal quarters ending on any FQED
            set forth below, permit the ratio of (i) Adjusted Consolidated
            Indebtedness at the end of such period to (ii) Consolidated EBITDA
            for such period to be more than the ratio set forth opposite such
            FQED:


-------------------------------------------------------------------------------
                   FQED                                              Ratio
-------------------------------------------------------------------------------
 The FQED ending on or about February 1, 1997                    4.50 to 1.00
-------------------------------------------------------------------------------
 The FQED ending on or about April 30, 1997                      5.25 to 1.00
-------------------------------------------------------------------------------
 The FQED ending on or about July 31, 1997                       3.80 to 1.00
-------------------------------------------------------------------------------
 The FQED ending on or about October 31, 1997                    4.60 to 1.00
-------------------------------------------------------------------------------
 The FQED ending on or about January 31, 1998                    5.00 to 1.00
 -------------------------------------------------------------------------------
 The FQED ending on or about April 30, 1998                      5.85 to 1.00
-------------------------------------------------------------------------------
 The FQED ending on or about July 31, 1998                       5.65 to 1.00
-------------------------------------------------------------------------------
 The FQED ending on or about October 30, 1998                    5.25 to 1.00
-------------------------------------------------------------------------------
 The FQED ending on or about January 31, 1999 and thereafter     4.65 to 1.00
-------------------------------------------------------------------------------


         4. Section 7.1(b) of the Credit Agreement shall be, and hereby is,
amended by deleting Section 7.1(b) in its entirety and substituting in lieu
thereof the following:

 
            (b) EBITDA TO INTEREST EXPENSE. For any period of four consecutive
            fiscal quarters ending on any FQED set forth below, permit the ratio
            of (i) Consolidated EBITDA for the applicable period to (ii)
            Consolidated Interest Expense for such period to be less than the
            ratio set forth opposite such FQED:


                                       2
<PAGE>   4


-------------------------------------------------------------------------------
                   FQED                                              Ratio
-------------------------------------------------------------------------------
 The FQED ending on or about February 1, 1997                    2.00 to 1.00
-------------------------------------------------------------------------------
 The FQED ending on or about April 30, 1997, July 30,            1.60 to 1.00
 1997 and October 31, 1997
-------------------------------------------------------------------------------
 The FQED ending on or about January 31, 1998                    1.60 to 1.00
-------------------------------------------------------------------------------
 The FQED ending on or about April 30, 1998                      1.40 to 1.00
-------------------------------------------------------------------------------
 The FQED ending on or about July 31, 1998                       1.45 to 1.00
-------------------------------------------------------------------------------
 The FQED ending on or about October 30, 1998                    1.60 to 1.00
-------------------------------------------------------------------------------
 The FQED ending on or about January 31, 1999                    2.00 to 1.00
-------------------------------------------------------------------------------
            

         5. Section 7.1(c) of the Credit Agreement shall be, and hereby is,
amended by deleting Section 7.1(c) in its entirety and substituting in lieu
thereof the following:


            (c) FIXED CHARGE COVERAGE. For any period of four consecutive
            fiscal quarters ending on any FQED set forth below, permit the
            ratio of (i) Consolidated EDITDAR minus the amount of any federal,
            state and local income taxes levied by a Governmental Authority on
            the revenues of the Company which are actually paid by the Company
            or its consolidated Subsidiaries in cash during such period, to
            (ii) Consolidated Interest Expense, plus all principal payments
            required to be made during the period on account of any Consolidated
            Indebtedness, plus the amount of any Consolidated Rent Expense
            during the period, to be less than the ratio set forth opposite such
            FQED:

-------------------------------------------------------------------------------
                   FQED                                              Ratio
-------------------------------------------------------------------------------
 The FQED ending on or about February 1, 1997                    1.20 to 1.00
-------------------------------------------------------------------------------
 The FQED ending on or about April 30, 1997, July 31,            1.25 to 1.00
 1997 and October 31, 1997
-------------------------------------------------------------------------------
 The FQED ending on or about January 1, 1998                     1.25 to 1.00
-------------------------------------------------------------------------------
 The FQED ending on or about April 30, 1998                      1.05 to 1.00
-------------------------------------------------------------------------------
 The FQED ending on or about July 31, 1998                       1.15 to 1.00
 -------------------------------------------------------------------------------


                                       3
<PAGE>   5
--------------------------------------------------------------------------------
The FQED ending on or about October 30, 1998                     1.20 to 1.00
--------------------------------------------------------------------------------
The FQED ending on or about January 31, 1999 and                 1.25 to 1.00
thereafter
--------------------------------------------------------------------------------


     6.  Except as specifically amended or modified by this Agreement, all 
terms and conditions set forth in the Credit Agreement and the Security 
Document remain in full force and effect.

     7.  This Agreement shall be governed by and construed in accordance with 
the laws of the State of Connecticut.

     8.  The Company shall reimburse the Agent for the fees and expenses of its 
counsel in connection with this Agreement.

     9.  This Agreement may be executed in two or more counterparts, each of 
which shall constitute an original but all of which when taken together shall 
constitute but one agreement.

         II. REPRESENTATIONS AND WARRANTIES OF COMPANY

     The Company represents and warrants as follows:

     1.  The representations and warranties set forth in the Credit Agreement 
are true and correct in all material respects on the date hereof as if made on 
the date hereof.

     2.  After giving effect to this Agreement, no Event of Default has occurred
and is continuing, and no event or condition has occurred or exists which would 
constitute an Event of Default but for the giving of notice or passage of time 
or both.

             III. CONDITIONS TO EFFECTIVENESS

     This Agreement shall be effective upon satisfaction of the following 
conditions:

     1.  The Agent shall have received counterparts of this Agreement which, 
when taken together, bear the signatures of all parties hereto.

     2.  The representations and warranties of the Company set forth in 
Section II of this Agreement shall be true and correct in all respects.

                                       4
<PAGE>   6
    IN WITNESS WHEREOF, the parties have caused this agreement to be executed 
and delivered as of the date first above written.

                                      DAIRY MART CONVENIENCE STORES, INC.

                                      By: /s/ Susan D. Adams
                                          ---------------------
                                          Name: Susan Adams
                                          Title: Vice President


                                      BANK OF BOSTON CONNECTICUT,
                                      Individually and as Agent

                                      By: /s/ Scott S. Barnett
                                          ----------------------
                                          Name: Scott S. Barnett
                                          Title: Vice President


                                      HELLER FINANCIAL, INC.

                                      By: /s/ William P. Watkins
                                          ------------------------
                                          Name: William P. Watkins
                                          Title: Vice President



                                      STATE STREET BANK AND TRUST COMPANY

                                      By: /s/ Karen F. Booth
                                          ------------------------
                                          Name: Karen Booth
                                          Title: Vice President


                                       5