<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, 1997
                                       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: (978)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
                                (Title of Class)

                        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. [ ]

     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 2, 1998 as reported by NASDAQ, was $205,734,632.

     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 2, 1998: 5,175,714 shares


                       DOCUMENTS INCORPORATED BY REFERENCE

     Portions of the Andover Bancorp, Inc. Definitive Notice of Annual Meeting
and Proxy Statement for the 1998 Annual Meeting of Shareholders are incorporated
by reference into Part III of Form 10-K.





<PAGE>   2

                                    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 Consolidated 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 1998 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...............................    36

               Consolidated Balance Sheets as of December 31, 1997 
               and 1996...................................................    37

               Consolidated Statements of Operations for each of 
               the years ended December 31, 1997, 1996 and 1995...........    38

               Consolidated Statements of Changes in 
               Stockholders' Equity for each of the years ended 
               December 31, 1997, 1996 and 1995...........................    39

               Consolidated Statements of Cash Flows for each of 
               the years ended December 31, 1997, 1996 and 1995........... 40-41

               Notes to Consolidated Financial Statements................. 42-67



                                        2


<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, 1997.

(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
          (incorporated herein by reference to Exhibit 3.2 to Andover's Form
          10-K for the fiscal year ended December 31, 1996).

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 (incorporated herein by reference to Exhibit 10.2 to
          Andover's Form 10-K for the fiscal year ended December 31, 1996).

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 (incorporated herein by reference to Exhibit 10.3 to
          Andover's Form 10-K for the fiscal year ended December 31, 1996).

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 (incorporated herein by reference to Exhibit
          10.4 to Andover's Form 10-K for the fiscal year ended December 31,
          1996).




                                        3


<PAGE>   4

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 (incorporated herein by reference to Exhibit 10.5 to
          Andover's Form 10-K for the fiscal year ended December 31, 1996).

10.6      Special Termination Agreement between Andover, Andover Bank and
          Octavio C. Bolivar, dated January 24, 1994, as amended and restated,
          January 23, 1997 (incorporated herein by reference to Exhibit 10.6 to
          Andover's Form 10-K for the fiscal year ended December 31, 1996).

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 (incorporated herein by reference to Exhibit 10.9 to
          Andover's Form 10-K for the fiscal year ended December 31, 1996).

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 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 (incorporated herein by reference to Exhibit 10.12 to Andover's
          Form 10-K for the fiscal year ended December 31, 1996).

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, 1997.

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. 1997 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, 1997.

23.1      Consent of KPMG Peat Marwick LLP.


27        Financial Data Schedule



                                        4



<PAGE>   5


                                   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 13, 1998                          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 13, 1998
--------------------------        Executive Officer and
Gerald T. Mulligan                Director (Principal
                                  Executive Officer)

/s/ Joseph F. Casey               Chief Financial Officer        March 13, 1998
--------------------------        and Treasurer (Principal
Joseph F. Casey                   Financial and Accounting
                                  Officer)

/s/ Thomas F. Caffrey             Director                       March 13, 1998
--------------------------
Thomas F. Caffrey


/s/ Naomi A. Gardner              Director                       March 13, 1998
--------------------------
Naomi A. Gardner


/s/ Cornelius J. McCarthy         Director                       March 13, 1998
--------------------------
Cornelius J. McCarthy


/s/ Clifford E. Elias             Director                       March 13, 1998
--------------------------
Clifford E. Elias


/s/ Robert J. Scribner            Director                       March 13, 1998
--------------------------
Robert J. Scribner


/s/ Fred P. Shaheen               Director                       March 13, 1998
--------------------------
Fred P. Shaheen




                                      5


<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
                (incorporated herein by reference
                to Exhibit 3.2 to Andover's Form
                10-K for the fiscal year ended
                December 31, 1996).                                         --

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
                (incorporated herein by reference to
                Exhibit 10.2 to Andover's Form 10-K for
                the fiscal year ended December 31, 1996).                   --





                                      6


<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
                (incorporated herein by reference to
                Exhibit 10.3 to Andover's Form 10-K for
                the fiscal year ended December 31, 1996).                  --

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 (incorporated herein by reference
                to Exhibit 10.4 to Andover's Form 10-K for
                the fiscal year ended December 31, 1996).                  --

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 (incorporated herein by reference
                to Exhibit 10.5 to Andover's Form 10-K for
                the fiscal year ended December 31, 1996).                  --

10.6            Special Termination Agreement between
                Andover, Andover Bank and Octavio C.
                Bolivar, dated January 24, 1994 as
                amended and restated, January 23, 1997
                (incorporated herein by reference
                to Exhibit 10.6 to Andover's Form 10-K for
                the fiscal year ended December 31, 1996).                  --

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 (incorporated herein by reference
                to Exhibit 10.9 to Andover's Form 10-K for
                the fiscal year ended December 31, 1996).                  --




                                      7


<PAGE>   8
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 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
                (incorporated herein by reference
                to Exhibit 10.12 to Andover's Form 10-K for
                the fiscal year ended December 31, 1996).                   --

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, 1997.                                          --

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. 1997 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.                    9

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, 1997.                        --

23.1            Consent of KPMG Peat Marwick LLP.                           89



                                      8