<PAGE>   1

                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                    ---------

                                    FORM 10-K

                        FOR ANNUAL AND TRANSITION REPORTS
                    PURSUANT TO SECTIONS 13 OR 15 (d) OF THE
                         SECURITIES EXCHANGE ACT OF 1934

               [ X ] ANNUAL REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934

                   FOR THE FISCAL YEAR ENDED DECEMBER 31, 1996
                                       OR
              [ ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934

                         COMMISSION FILE NUMBER 0-16358

                              ANDOVER BANCORP, INC.
             (Exact name of registrant as specified in its charter)

           DELAWARE                                             04-2952665     
(State or other jurisdiction of                              (I.R.S. Employer  
incorporation or organization)                              Identification No.)
                                                                               
     61 MAIN STREET, ANDOVER, MA                                   01810    
(Address of principal executive office)                         (Zip Code)  
                                                           
                                   
        REGISTRANT'S TELEPHONE NUMBER, INCLUDING AREA CODE: (508)749-2000

                                    --------- 

           SECURITIES REGISTERED PURSUANT TO SECTION 12(b) OF THE ACT:

                                      NONE

           SECURITIES REGISTERED PURSUANT TO SECTION 12(g) OF THE ACT:

                          COMMON STOCK, $0.10 PAR VALUE
                        PREFERRED STOCK PURCHASED RIGHTS
                                (Title of class)

     Indicate by check mark whether: the registrant (1) has filed all reports
required to be filed by Section 13 or 15 (d) of the Securities Exchange Act of
1934 during preceding 12 months (or for such shorter period that the Registrant
was required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days.  Yes X No 
                                        --   --
     Indicate by check mark if disclosure of delinquent filers pursuant to Item
405 of Regulation S-K is not contained herein, and will not be contained, to the
best of registrant's knowledge, in definitive proxy or information statements
incorporated by reference in Part III of this Form 10-K or any amendment to this
Form 10-K. [X]

     The aggregate market value of the voting stock held by non-affiliates of
the Registrant, based on the closing sale price for the Registrant's Common
Stock on March 3, 1997 as reported by NASDAQ, was $144,000,976.

     The number of shares outstanding of each of the Registrant's classes of
Common Stock, as of the latest practicable date, is:

                 Class: Common Stock, par value $0.10 per share
               Outstanding as of March 3, 1997: 5,142,892 shares

                       DOCUMENTS INCORPORATED BY REFERENCE
     Portions of the Andover Bancorp, Inc. Definitive Notice of Annual Meeting
and Proxy Statement for the 1997 Annual Meeting of Shareholders are incorporated
by reference into Part III of Form 10-K.

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                                    FORM 10-K
                              CROSS REFERENCE INDEX
                                     Part I
                                                                        Annual
                                                                        Report
                                                                          Page

Item 1   Business..........................................................  2

Item 2   Properties........................................................  9

Item 3   Legal Proceedings................................................  10

Item 4   Submission of Matters to a Vote of Security Holders.............   10

                                     Part II

Item 5   Market for Registrant's Common Equity and Related 
         Stockholder Matters..............................................  10

Item 6   Selected Financial Data............................................11

Item 7   Management's Discussion and Analysis of Financial Condition and
         Results of Operations..............................................12

Item 8   Financial Statements and Supplementary Data......................(See
                                                                 Item 14 below)

Item 9   Changes in and Disagreements with Accountants on Accounting and
         Financial Disclosure...............................................Non-
                                                                     Applicable

                                    Part III

The information called for by Part III (Items 10 through 13) is incorporated
herein by reference from Andover's Definitive Notice of Annual Meeting and Proxy
Statement for the 1997 Annual Meeting of Stockholders to be filed with the
Securities and Exchange Commission.

                                     Part IV

Item 14   Exhibits, Financial Statement Schedules and Reports on Form 8-K

(a)(1) Financial Statements -

               Independent Auditors' Report.................................34

               Consolidated Balance Sheets as of December 31, 1996 and
               1995.........................................................35

               Consolidated Statements of Operations for each of the
               years ended December 31, 1996, 1995 and 1994.................36

               Consolidated Statements of Changes in Stockholders' Equity
               for each of the years ended December 31, 1996, 1995 and 
               1994.........................................................37

               Consolidated Statements of Cash Flows for each of the
               years ended December 31, 1996, 1995 and 1994..............38-39

               Notes to Consolidated Financial Statements................40-63



<PAGE>   3



(2)  All financial statement schedules are omitted because they are not
     applicable, the data is not significant, or the required information is
     shown elsewhere in this report.
       
(b)  Reports on Form 8-K. There were no reports filed on Form 8-K during the
     three months ended December 31, 1996.
       
(c)  List of Exhibits
       
     Exhibits to the Form 10-K have been included only with the copies of the
     Form 10-K filed with the SEC. Upon request to Shareholder Relations,
     Andover Bancorp, Inc., 61 Main Street, Andover, Massachusetts 01810, copies
     of the individual exhibits will be furnished upon payment of a reasonable
     fee.
      
Exhibit No.    Description of Exhibits
-----------    -----------------------

3.1  Restated Certificate of Incorporation of Andover (incorporated herein by
     reference to Exhibit 3.1 to Post-Effective Amendment No. 1 to Andover's
     Registration Statement on Form S-4 No. 33-11891 filed on March 5, 1987).
       
3.2  By-laws of Andover, as amended and restated, January 23, 1997.
       
4.1  Specimen of Andover Bancorp, Inc. common stock certificate (incorporated
     herein by reference to Exhibit 4 to Andover's Registration Statement on
     Form S-4, Registration No. 33-11891, filed on February 11, 1987).
       
4.2  Shareholder Rights Agreement between Andover Bancorp, Inc. and The First
     National Bank of Boston (incorporated herein by reference to an Exhibit to
     Andover's Current Report on Form 8-K dated February 21, 1989).
       
4.3  Amendment to Shareholder Rights Agreement between Andover Bancorp, Inc. and
     The First National Bank of Boston (incorporated herein by reference to
     Exhibit 4.2 to Andover's Current Report on Form 8-K dated February 12,
     1990).
       
10.1 Employment Agreement between Andover, Andover Bank and Gerald T. Mulligan,
     dated May 16, 1991 (incorporated herein by reference to Exhibit 10.1 to
     Andover's Form 10-K for the fiscal year ended December 31, 1991).
       
10.2 Special Termination Agreement between Andover, Andover Bank and Gerald T.
     Mulligan, dated May 16, 1991, as amended and restated through January 23,
     1997.
       
10.3 Special Termination Agreement between Andover, Andover Bank and Joseph F.
     Casey, dated December 17, 1992, as amended and restated through January 23,
     1997.
       
10.4 Special Termination Agreement between Andover, Andover Bank and Michael J.
     Ecker, dated December 17, 1992, as amended and restated through January 23,
     1997.
       
10.5 Special Termination Agreement between Andover, Andover Bank and John R.
     Heerwagen, dated December 17, 1992, as amended and restated through January
     23, 1997.
       
10.6 Special Termination Agreement between Andover, Andover Bank and Octavio C.
     Bolivar, dated January 24, 1994, as amended and restated, January 23, 1997.
       
      
<PAGE>   4


10.7  Andover Savings Bank Employees' Stock Ownership Plan and Trust Agreement
      and Amendment No. 1 (incorporated herein by reference to Exhibit 10(c) to
      Andover's Annual Report on Form 10-K for the fiscal year ended  
      December 31, 1987).
       
10.8  Andover Bancorp, Inc. Stock Option Plan dated May 8, 1986, as amended May
      22, 1986, January 29, 1987, and November 2, 1987 (incorporated herein by
      reference to Exhibit 10(h) to Andover's Annual Report on Form 10-K for the
      fiscal year ended December 31, 1987).
       
10.9  Special Termination Agreement between Andover, Andover Bank and Raymond P.
      Smith, dated December 12, 1995, as amended and restated, January 23, 1997.
       
10.10 Andover Bancorp, Inc. 1995 Stock Incentive Plan, dated February 16, 1995
      (incorporated herein by reference to Exhibit 10.11 to Andover's Annual
      Report on Form 10-K for the fiscal year ended December 31, 1995).
      
10.11 Deferred Compensation Plan for Directors of Andover Bancorp, Inc. and its
      Subsidiaries, effective July 1, 1993, as amended and restated,  
      February 22, 1996 (incorporated herein be reference to Exhibit 10.12 to
      Andover's Annual Report on Form 10-K for the fiscal year ended
      December 31, 1995).
      
10.12 Andover Bancorp, Inc. Special Termination Plan, effective January 23,
      1997.
      
11    The computation of per share earnings can be readily determined from the
      material contained in the Annual Report on Form 10-K for the fiscal year
      ended December 31, 1996.
      
12    As the Company does not have any debt securities registered under Section
      12 of the Securities Act of 1933, no ratio of earnings to fixed charges
      appears in this Annual Report on Form 10-K.
      
13    Andover Bancorp, Inc. 1996 Annual Report, which, except for those portions
      expressly incorporated herein by reference, is furnished only for the
      information of the Securities and Exchange Commission and is not deemed to
      be filed.
      
21    The Company has two subsidiaries, Andover Bank and Andover Bank NH. 
      Andover Bank is a Massachusetts savings bank in stock form while Andover
      Bank NH is a New Hampshire guaranty savings bank in stock form. Both
      subsidiaries are included in the Consolidated Financial Statements filed
      in the Annual Report on Form 10-K for the fiscal year ended 
      December 31, 1996.
     
23.1  Consent of KPMG Peat Marwick LLP.



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                                   SIGNATURES
                                   ----------

     Pursuant to the requirements of Section 13 of the Securities Exchange Act
of 1934, the Company has duly caused this report to be signed on its behalf by
the undersigned, thereunto duly authorized.

                                                          ANDOVER BANCORP, INC.



March 14, 1997                                By:/s/Gerald T. Mulligan
                                                 -----------------------------
                                                 Gerald T. Mulligan, President
                                                 and Chief Executive Officer

     Pursuant to the requirements of the Securities Exchange Act of 1934, this
Report has been signed below by the following persons on behalf of the Company
and in the capacities and on the dates indicated.

Signature                      Title                            Date
---------                      -----                            ----
                                                             
                                                             
/s/Gerald T. Mulligan          President, Chief                 March 14, 1997
------------------------       Executive Officer and
Gerald T. Mulligan             Director (Principal
                               Executive Officer)
                                                             
                                                             
/s/Joseph F. Casey             Chief Financial Officer          March 14, 1997
------------------------       and Treasurer (Principal
Joseph F. Casey                Financial and Accounting
                               Officer)
                                                             
                                                             
/s/Thomas F. Caffrey           Director                         March 14, 1997
------------------------
Thomas F. Caffrey                                            
                                                             
                                                             
                                                             
/s/Naomi A. Gardner            Director                         March 14, 1997
------------------------
Naomi A. Gardner                                             
                                                             
                                                             
                                                             
/s/Cornelius J. McCarthy       Director                         March 14, 1997
------------------------
Cornelius J. McCarthy                                        
                                                             
                                                            

/s/Clifford E. Elias           Director                         March 14, 1997
------------------------
Clifford E. Elias



/s/Fred P. Shaheen             Director                         March 14, 1997
------------------------
Fred P. Shaheen


<PAGE>   6

                              EXHIBITS TO FORM 10-K
                             Andover Bancorp, Inc.
                             ---------------------

                                  EXHIBIT INDEX
                                  -------------

Exhibit No.   Description of Exhibit                              Page No.    
-----------   ----------------------                              --------
                                                                 
3.1           Restated Certificate of Incorporation              
              of Andover (incorporated herein by                 
              reference to Exhibit 3.1 to Post-                  
              Effective Amendment No. 1 to Andover's             
              Registration Statement on Form S-4,                
              No. 33-11891 filed on March 5, 1987).                  --
                                                                 
3.2           By-laws of Andover, as amended                     
              and restated, January 23, 1997.                         9
                                                                 
4.1           Specimen of Andover Bancorp, Inc.                  
              common stock certificate (incorporated             
              herein by reference to Exhibit 4 to                
              Andover's Registration Statement on                
              Form S-4, Registration No. 33-11891,               
              filed on February 11, 1987).                           --
                                                                 
4.2           Shareholder Rights Agreement between               
              Andover Bancorp, Inc. and The First                
              National Bank of Boston (incorporated              
              herein by reference to an Exhibit to               
              Andover's Current Report on Form 8-K               
              dated February 21, 1989).                              --
                                                                 
4.3           Amendment to Shareholder Rights                    
              Agreement between Andover Bancorp, Inc.            
              and The First National Bank of Boston              
              (incorporated herein by reference to               
              Exhibit 4.2 to Andover's Current Report            
              on Form 8-K dated February 12, 1990).                  --
                                                                 
10.1          Employment Agreement between Andover,              
              Andover Bank and Gerald T. Mulligan,               
              dated May 16, 1991 (incorporated herein            
              by reference to Exhibit 10.1 to                    
              Andover's Form 10-K for the fiscal                 
              year ended December 31, 1991).                         --
                                                                 
10.2          Special Termination Agreement between              
              Andover, Andover Bank and Gerald T.                
              Mulligan, dated May 16, 1991, as amended           
              and restated through January 23, 1997.                 26
                                                                 
                                                                 
                                                                 
                                                                 
                                                                 
                                                                 
                                                                 
<PAGE>   7
                                                                 
                                                                 
                                                                 
10.3          Special Termination Agreement between              
              Andover, Andover Bank and Joseph F. Casey,         
              dated December 17, 1992, as amended and            
              restated through January 23, 1997.                     32
                                                                 
10.4          Special Termination Agreement between              
              Andover, Andover Bank and Michael J.               
              Ecker, dated December 17, 1992, as                 
              amended and restated through January               
              23, 1997.                                              38
                                                                 
10.5          Special Termination Agreement between              
              Andover, Andover Bank and John R.                  
              Heerwagen, dated December 17, 1992, as             
              amended and restated through January               
              23, 1997.                                              44
                                                                 
10.6          Special Termination Agreement between              
              Andover, Andover Bank and Octavio C.               
              Bolivar, dated January 24, 1994 as                 
              amended and restated, January 23, 1997.                50
                                                                 
10.7          Andover Savings Bank Employees' Stock              
              Ownership Plan and Trust Agreement and             
              Amendment No. 1 (incorporated herein by            
              reference to Exhibit 10(c) to Andover's            
              Annual Report on Form 10-K for the                 
              fiscal year ended December 31, 1987).                  --
                                                                 
10.8          Andover Bancorp, Inc. Stock Option Plan            
              dated May 8, 1986, as amended May 22,              
              1986, January 29, 1987 and November 2,             
              1987 (incorporated herein by reference             
              to Exhibit 10(h) to Andover's Annual               
              Report on Form 10-K for the fiscal year            
              ended December 31, 1987).                              --
                                                                 
10.9          Special Termination Agreement between              
              Andover, Andover Bank and Raymond P.               
              Smith, dated December 12, 1995, as                 
              amended and restated, January 23,                  
              1997.                                                  56
                                                                 
10.10         Andover Bancorp, Inc. 1995 Stock                   
              Incentive Plan, dated February 16, 1995            
              (incorporated herein by reference to               
              Exhibit 10.11 to Andover's Annual Report           
              on Form 10-K for the fiscalyear ended              
              December 31, 1995).                                    --
                                                                 
                                                                 
                                                                 
                                                                 
                                                                 
                                                                 
                                                                 
                                                                 
                                                                 
                                                                 
<PAGE>   8
                                                                 
                                                                 
10.11         Deferred Compensation Plan for Directors           
              of Andover Bancorp, Inc. and its                   
              Subsidiaries, effective July 1, 1993, as           
              amended and restated, February 22, 1996            
              (incorporated herein by reference to               
              Exhibit 10.12 to Andover's Annual Report           
              on Form 10-K for the fiscal year ended             
              December 31, 1995).                                    --
                                                                 
10.12         Andover Bancorp, Inc. Special Termination          
              Plan, effective January 23, 1997.                      62
                                                                 
11            The computation of per share earnings              
              can be readily determined from the                 
              material contained in the Annual Report            
              on Form 10-K for the fiscal year ended             
              December 31, 1996.                                     --
                                                                 
12            As the Company does not have any debt              
              securities registered under Section 12             
              of the Securities Act of 1933, no ratio            
              of earnings to fixed charges appears in            
              this Annual Report on Form 10-K.                       --
                                                                 
13            Andover Bancorp, Inc. 1996 Annual Report           
              which, except for those portions                   
              expressly incorporated herein by                   
              reference, is furnished only for the               
              information of the Securities and Exchange         
              Commission and is not deemed to be filed.              66      
                                                                 
21            The Company has two subsidiaries, Andover          
              Bank and Andover Bank NH.  Andover Bank is         
              a Massachusetts savings bank in stock form         
              while Andover Bank NH is a New Hampshire           
              guaranty savings bank in stock form.  Both         
              subsidiaries are included in the                   
              Consolidated Financial Statements filed in         
              the Annual Report on Form 10-K for the             
              fiscal year ended December 31, 1996.                   --
                                                                 
23.1          Consent of KPMG Peat Marwick LLP.                     142