<PAGE>   1

                                                                    EXHIBIT 10.2

                             AGREEMENT OF AMENDMENT

         This AGREEMENT OF AMENDMENT (this "Agreement") dated as of January 31,
1997 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 I 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 is amended by deleting the
definitions of "Applicable Margin" and "Minimum Consolidated Net Worth" in their
entirety and substituting in lieu thereof the following:

                  "APPLICABLE MARGIN" at any time, for Alternate Base Rate Loans
or Libor Loans, as the case may be, a rate per annum equal to the rate set forth
below opposite the applicable ratio of Consolidated Indebtedness to Consolidated
EBITDA for the period of four consecutive fiscal quarters ending on the FQED
immediately preceding such time:


<PAGE>   2



<TABLE>
<CAPTION>
  LEVEL            RATIO OF CONSOLIDATED INDEBTEDNESS TO                   APPLICABLE MARGIN FOR       APPLICABLE
                           CONSOLIDATED EBITDA                             ALTERNATIVE BASE RATE    MARGIN FOR LIBOR
                                                                                   LOANS                  LOANS

<S>         <C>                                                                    <C>                    <C>  
    I       Less than 3.0 to 1.00                                                  0.00%                  2.00%
----------- ------------------------------------------------------------ -------------------------- ------------------
    II      Less than 3.50 to 1.00, but greater than or equal to 3.00              0.00%                  2.25%
            to 1.00
----------- ------------------------------------------------------------ -------------------------- ------------------
   III      Less than 4.00 to 1.00, but greater than or equal to 3.50              0.00%                  2.50%
            to 1.00
----------- ------------------------------------------------------------ -------------------------- ------------------
    IV      Less than 4.50 to 1.00, but greater than or equal to 4.00              0.25%                  2.75%
            to 1.00
----------- ------------------------------------------------------------ -------------------------- ------------------
    V       Greater than or equal to 4.50 to 1.00                                   .50%                  3.00%
----------- ------------------------------------------------------------ -------------------------- ------------------
</TABLE>



PROVIDED, HOWEVER, that notwithstanding the foregoing, until the Company
delivers to the Agent the certificates required by Section 6.2(b) hereof
following the completion of the Company's fiscal year ending approximately
January 31, 1997, the Applicable Margin for Alternate Base Rate Loans and the
Applicable Margin for LIBOR Loans shall be not less than that set forth in Level
IV above.

         "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 April 30,
1997: $6,750,000; (iii) as at the FQED to occur on July 31, 1997: $7,900,000;
(iv) as at the FQED to occur on October 31, 1997: $8,700,000; (v) as at the FQED
to occur on January 31, 1998: $7,700,000; (vi) as at the FQED to occur on April
30, 1998: $7,100,000; and (vii) as at any FQED to occur on July 31, 1998 and all
FQEDs thereafter: $7,100,000 plus 50% of cumulative Consolidated Net Income
earned after the end of the Company's FQED ending approximately April 30, 1998.

         3. Section 1.1 of the Credit Agreement is further amended by adding the
following additional definitions:

         "ADJUSTED CONSOLIDATED INDEBTEDNESS" that amount which is equal to
Consolidated Indebtedness reduced by an amount equal to Cash and Cash
Equivalents.

         "CASH" when used in connection with any Person, all monetary and
nonmonetary items owned by that Person that are treated as cash in accordance
with GAAP.

         4. Section 6 of the Credit Agreement shall be, and hereby is, amended
by adding the following:

                  Section 6.11 SALE OF NORTHEAST REGIONAL DIVISION. Sell its
Northeast Regional Division and provide evidence satisfactory to the Bank that
it has raised gross cash receipts of at least $37,500,000 from such sale on or
before June 30, 1997. In the event that such sale does not occur by such date,
the Company and the Banks agree that Section 7.1 (along with the definition of
Minimum Consolidated Net Worth) and Section 7.8 shall automatically be amended
effective with the FQED to occur on October 31, 1998 to reflect the terms and
conditions set forth therein immediately prior to the effectiveness of the
Amendment to the Agreement effective as of January 31, 1997.


<PAGE>   3




         5. Sections 7.1 (a), (b) and (c) of the Credit Agreement shall be, and
hereby are, amended by deleting such Sections 7.1(a) (b) and (c) in their
entirety and substituting in lieu thereof the following:

                  Section 7.1(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:

<TABLE>
<CAPTION>
                                 FQED                                                      RATIO

<S>                                                                                     <C>     
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                                            4.30 to 1.00
------------------------------------------------------------------------ -------------------------------------------
The FQED ending on or about January 31, 1998                                            4.20 to 1.00
------------------------------------------------------------------------ -------------------------------------------
The FQED ending on or about April 30, 1998                                              4.40 to 1.00
------------------------------------------------------------------------ -------------------------------------------
The FQED ending on or about July  31, 1998                                              4.10 to 1.00
------------------------------------------------------------------------ -------------------------------------------
The FQED ending on or about October 31, 1998                                            4.00 to 1.00
------------------------------------------------------------------------ -------------------------------------------
The FQED ending on or about January 31, 1999 and thereafter                             3.90 to 1.00
------------------------------------------------------------------------ -------------------------------------------
</TABLE>


         Section 7.1 (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:

<TABLE>
<CAPTION>
                                 FQED                                                      RATIO

<S>                                                                                     <C>     
The FQED ending on or about February 1, 1997                                            2.00 to 1.00
------------------------------------------------------------------------ -------------------------------------------
The FQEDs ending on or about April 30, 1997, July 31, 1997 and October                  1.60 to 1.00
31, 1997
------------------------------------------------------------------------ -------------------------------------------
The FQED ending on or about January 31, 1998                                            1.80 to 1.00
------------------------------------------------------------------------ -------------------------------------------
The FQED ending on or about April 30, 1998                                              2.00 to 1.00
------------------------------------------------------------------------ -------------------------------------------
The FQED ending on or about July 31, 1998                                               2.10 to 1.00
------------------------------------------------------------------------ -------------------------------------------
The FQED ending on or about October 31, 1998 and thereafter                             2.25 to 1.00
------------------------------------------------------------------------ -------------------------------------------
</TABLE>


         Section 7.1 (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 EBITDAR 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 


<PAGE>   4



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:

<TABLE>
<CAPTION>
                                      FQED                                         RATIO

<S>                                                                                <C>     
The FQED ending on or about February 1, 1997                                       1.20 to 1.00
---------------------------------------------------------------------------------- ---------------------------------
The FQED ending on or about April 30, 1997 and thereafter                          1.25 to 1.00
---------------------------------------------------------------------------------- ---------------------------------
</TABLE>


         6. Section 7.8 of the Credit Agreement shall be, and hereby is, amended
by deleting such Section 7.8 in its entirety and substituting in lieu thereof
the following:

                  LIMITATION ON CAPITAL EXPENDITURES. Make or commit to make (by
way of the acquisition of securities of a Person or otherwise) any Capital
Expenditures (excluding any expenses incurred in connection with normal
replacement and maintenance programs properly charged to current operations) in
the aggregate for the Company and its Subsidiaries during any of the fiscal
years of the Company set forth below in an amount in excess of that set forth
opposite such fiscal year:

<TABLE>
<CAPTION>
                         FISCAL YEAR                   MAXIMUM CAPITAL EXPENDITURES

<S>                                                             <C>        
1997                                                            $28,500,000
------------------------------------------------- ---------------------------------------
1998                                                            $34,500,000
------------------------------------------------- ---------------------------------------
1999 and thereafter                                             $33,000,000
------------------------------------------------- ---------------------------------------
</TABLE>


PROVIDED, HOWEVER, that in the event the Company and its Subsidiaries shall make
Capital Expenditures in any fiscal year of less than the maximum amount set
forth above, an amount equal to the difference between such maximum amount and
the actual Capital Expenditures made during such fiscal year shall be available
(in addition to the maximum amount stated above) to the Company for Capital
Expenditures during (but only during) the immediately following fiscal year.

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

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

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

         10. 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.


<PAGE>   5



                  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.

                   REMAINDER OF PAGE INTENTIONALLY LEFT BLANK




<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:
                                       ----------------------------------------
                                          Name:    James M. Schulte
                                          Title:   Vice President and Treasurer

                                    BANK OF BOSTON CONNECTICUT,
                                    Individually and as Agent

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

                                    HELLER FINANCIAL, INC.

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



                                    STATE STREET BANK AND TRUST COMPANY

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