<PAGE>   1




                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                   FORM 10-K/A

[X]  Annual report pursuant to Section 13 or 15(d) of the Securities Exchange 
     Act of 1934

For the Fiscal Year Ended: SEPTEMBER 30, 1998    Commission File Number: 0-11309


                               GALILEO CORPORATION
             (Exact name of Registrant as specified in its charter)


DELAWARE                                                              04-2526583
(State of Incorporation)                       (IRS Employer Identification No.)


GALILEO PARK, P. O. BOX 550, STURBRIDGE, MASSACHUSETTS                     01566
(Address of Principal Executive Offices)                              (Zip Code)


Registrant's telephone number, including area code: (508) 347-9191

        Securities registered pursuant to Section 12(b) of the Act: NONE

           Securities registered pursuant to Section 12(g) of the Act:


                     COMMON STOCK, PAR VALUE $.01 PER SHARE
                     -------------------------------------- 
                                (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
the 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 [ ]

As of January 26, 1999, 10,082,265 shares of the Registrant's Common Stock were
outstanding, and the aggregate market value of such shares held by
non-affiliates of the Registrant on such date was $39.0 million.





                                  Page 1 of 11



<PAGE>   2

This Amendment No. 1 to the Annual Report on Form 10-K has been filed by the 
Registrant to amend the following sections as described:

PART III, Item 10. DIRECTORS OF THE REGISTRANT AND EXECUTIVE OFFICERS OF THE 
REGISTRANT is replaced with the following:

                              ELECTION OF DIRECTORS
    
    The following table indicates the names, experience and length of service 
of all directors of the Company. Pursuant to the Securities Purchase Agreement
between the Company and Andlinger Capital XIII LLC, the Company elected three
individuals selected by Andlinger Capital XIII LLC to the Board of Directors and
has agreed to nominate three designees (subject to adjustment) of Andlinger
Capital XIII LLC for election as directors of the Company as long as Andlinger
Capital XIII LLC continues to hold not less than 2,000,000 shares of Common
Stock of the Company (subject to certain adjustments). The directors selected by
Andlinger Capital XIII LLC are Mr. Andlinger, Mr. Ball and Mr. Magida.


<TABLE>
<CAPTION>
                                   BUSINESS EXPERIENCE DURING PAST FIVE           DIRECTOR
    NAME AND AGE                   YEARS AND OTHER DIRECTORSHIPS                    SINCE
<S>                                <C>                                               <C> 

Gerhard R. Andlinger ...........   Chairman and Chief Executive Officer              1999
     (68)                          of Andlinger & Company, Inc., a private 
                                   investment company.
       

Charles E. Ball ................   Principal of Andlinger & Company,  Inc.           1999
     (48)                          and an employee of ANC Management Corp.,  
                                   a management  company  affiliated
                                   with Andlinger & Company.

John F. Blais, Jr. .............   President of Optical Filter Corporation,          1998
     (60)                          one of the Company's subsidiaries.

Todd F. Davenport ..............   President and Founder of Cardiant Medical         1998
     (48)                          Corporation from April,  1995 to the  
                                   present, and President of St. Jude Medical, 
                                   Inc.,  (International Division) from 1992 
                                   to 1995.

Robert D. Happ .................   Former regional managing partner of               1955
     (58)                          KPMG Peat Marwick LLP, a public accounting    
                                   firm, from which he retired in 1994. Mr. Happ 
                                   is also a director of CAI Wireless Systems,   
                                   Inc., and CS Wireless Systems, Inc., both of  
                                   which are owners and operators of wireless    
                                   cable TV systems, and a Trustee of            
                                   Cambridgeport Mutual Holding Company, a mutual
                                   bank holding company.                         

Stephen A. Magida ..............   Self-employed attorney since May 1994. Prior      1999
     (55)                          thereto, Mr. Magida had been a partner of    
                                   Dechert Price & Rhoads, attorneys.           
                                   
W. Kip Speyer ..................   President and Chief Executive Officer of the      1998
     (50)                          Company. Mr. Speyer is also President of       
                                   Leisegang Medical, Inc., one of the Company's  
                                   subsidiaries.                                  
                                   
                        
</TABLE>
                        

SECTION 16(a) BENEFICIAL OWNERSHIP REPORTING COMPLIANCE


     The Company's executive officers and directors and persons who own
beneficially more than 10% of the Company's Common Stock are required under
Section 16(a) of the Securities Exchange Act of 1934 to file reports of
ownership and changes in ownership of Company securities with the Securities and
Exchange Commission. One report covering the purchase of 2,000 shares of Common
Stock by Allen E. Busching was filed after the time such filing was required.




                                  2

<PAGE>   3


PART III, Item 11. EXECUTIVE COMPENSATION is replaced with the following:

                        EXECUTIVE COMPENSATION

         The Compensation Committee Report on Executive Compensation set forth
below describes the Company's compensation policies applicable to executive
officers and the Committee's basis for Mr. Hanley's compensation as Chief
Executive Officer for the fiscal year ended September 30, 1998.

             COMPENSATION COMMITTEE REPORT ON EXECUTIVE COMPENSATION

         The Compensation Committee of the Board of Directors, which consists of
the nonemployee directors, determines the compensation of all executive officers
of the Company, administers the Company's Stock Option Plan, including the grant
of stock options thereunder, and acts on other compensation matters.

         The Committee reviews the compensation of all executive officers at
least once a year. The Company's executive compensation contains the following
three elements: base salary, bonus earned under the Company's Variable Pay Plan
and periodic stock option grants. In setting base salary compensation for
executive officers, the Committee may review publicly available executive
compensation surveys of technology oriented manufacturing companies with annual
sales comparable to those of the Company. The Committee considers making an
adjustment to the base salary of each executive officer based upon the
relationship of current compensation to the comparable compensation levels
reported in the surveys and a subjective judgement on the officer's performance
during the last year.

         In fiscal year 1998, Mr. Hanley and the other executive officers
voluntarily reduced their base salaries by 20%, effective July 27, 1998, in view
of the financial performance of the Company. Consequently, Mr. Hanley's base
salary was reduced from $220,000 to $176,000. These voluntary salary reductions
were accepted by the Compensation Committee.

         The Variable Pay Plan for executive officers is part of a variable pay
plan in effect for all of the Company's employees. Under this plan, executive
officers are compensated based on the earnings per share results of the Company
versus the earnings per share goal in the Company's Operating Plan for the
fiscal year. Specifically, the Chief Executive Officer's variable pay bonus is
determined by multiplying his base salary by the following two factors: first,
his participation rate percentage, which was 50% of his base salary for 1998,
and second, the pay-out percentage, which is determined by a formula specified
in the Plan based on the Company's actual earnings per share versus the earnings
per share in the Company's Operating Plan for fiscal year 1998. The
participation rate times the payout percentage times base compensation equals
the Variable Pay Plan bonus. For fiscal year 1998, because the Company did not
meet the earnings per share objective contained in its 1998 Operating Plan, Mr.
Hanley and the other executive officers did not receive a variable pay bonus.

         In fiscal year 1998, the Committee granted a stock option to purchase
10,000 shares of Common Stock of the Company to Mr. Riedel. In granting this
stock option, the Committee took into account the level of Mr. Riedel's base
salary and the number of stock options previously granted to him and currently
held by the other officers. The Company has no specific plan or formula for
determining the frequency of grants or number of options granted.




                                        By the Compensation Committee,

                                        William T. Burgin
                                        Allen E. Busching
                                        Kenneth W. Draeger
                                        Robert D. Happ






                                       3
<PAGE>   4

                           SUMMARY COMPENSATION TABLE

         The following table sets forth certain compensation information for the
Chief Executive Officer of the Company and each of the other executive officers
of the Company whose salary and bonus exceeded $100,000 for the fiscal year
ended September 30, 1998:

<TABLE>
<CAPTION>
                                                                                    LONG-TERM
                                                                                   COMPENSATION      
                                                                                      AWARDS         
                                                                                   ------------
                                                          ANNUAL COMPENSATION       SECURITIES    
                                                          -------------------       UNDERLYING      ALL OTHER   
              NAME AND                                    SALARY        BONUS        OPTIONS      COMPENSATION(1)
         PRINCIPAL POSITION                     YEAR        ($)          ($)           (#)             ($)
         ------------------                     ----      ------        -----      -----------    --------------
<S>                                             <C>       <C>         <C>             <C>             <C>   

William T. Hanley ............................  1998      213,318          --             --          12,043
   President and Chief Executive Officer        1997      189,252          --         60,000          14,130
                                                1996      180,000     113,400         25,000          13,686

Gregory Riedel(2) ............................  1998      145,404          --         10,000           3,679
   Vice President, Finance and                  1997      118,285      17,000         30,000           2,700
   Chief Financial Officer

Josef W. Rokus ...............................  1998      116,333          --             --          12,476
   Vice President, Corporate Development        1997      104,619      18,000         10,000          13,821
   and Secretary                                1996      100,000      37,800             --          12,051
   
</TABLE>

(1)  All Other Compensation in 1998 includes Company matching funds under the
     Company's 401(k) Plan, vacation and paid absence allowance payouts and the
     Company portion of split dollar life insurance premiums as follows:


<TABLE>
<CAPTION>
                                                           VACATION AND       LIFE
                                           401(K) PLAN     PAID ABSENCE     INSURANCE
         NAME OF                          CONTRIBUTIONS     ALLOWANCES      PREMIUMS
         OFFICER                               ($)              ($)            ($)
         -------                          -------------    ------------     ---------
<S>                                          <C>                              <C>  

 William T. Hanley.....................      3,555                --          8,487
 Gregory Riedel........................      3,403                --            276
 Josef W. Rokus........................      2,613             1,385          8,479
 
</TABLE>


(2)  Mr. Riedel joined the Company on December 9, 1996.






                                       4
<PAGE>   5

                        OPTION GRANTS IN FISCAL YEAR 1998

         The following table sets forth certain information concerning options
granted to executive officers of the Company in fiscal year 1998:



<TABLE>
<CAPTION>
                                                                                        POTENTIAL REALIZABLE VALUE AT    
                                                                                     ASSUMED ANNUAL RATES OF STOCK PRICE 
                                              INDIVIDUAL GRANTS                        APPRECIATION FOR OPTION TERM(2)  
                            ------------------------------------------------------   -----------------------------------  
                                           % OF TOTAL
                            SECURITIES       OPTIONS
                            UNDERLYING     GRANTED TO    EXERCISE OR
                              OPTIONS     EMPLOYEES IN    BASE PRICE
                            GRANTED(#)     FISCAL YEAR    ($/SHARE)     EXPIRATION     0%          5%            10%
     Name                      (1)            1998                         DATE       ($)         ($)            ($)
     ----                   ----------    ------------   -----------    ----------   -----     ---------       --------
<S>                           <C>             <C>          <C>            <C>         <C>     <C>             <C>      

Gregory Riedel........        10,000          4.7%         4.625          8/06/08      0       29,086(3)       73,711(3)
</TABLE>
_______________

(1)  One grant of 10,000 shares was made to Mr. Riedel on August 6, 1998.
     Options become exercisable as to 25% of the shares annually beginning one
     year after grant.

(2)  Based upon the last trading price ($3.625) of the Company's Common Stock on
     September 30, 1998, the dollar amounts under these columns are the result
     of calculations at the 5% and 10% rates prescribed by the rules of the
     Securities and Exchange Commission and, therefore, are not intended to
     forecast possible future appreciation, if any, in the price of the Common
     Stock. No gain to the optionee is possible without an increase in the price
     of the Common Stock, which will benefit all shareholders proportionately.

(3)  In order to realize the potential values set forth in the 5% and 10%
     columns of this table, the per share price of the Common Stock would be
     $7.53 and $12.00, or 63% and 159% above the exercise price, respectively.






                                       5

<PAGE>   6

               AGGREGATED OPTION EXERCISES IN LAST FISCAL YEAR AND
                          FISCAL YEAR-END OPTION VALUES


         The following table provides information as to options exercised by
each of the named executive officers in fiscal year 1998 and the value of the
remaining options held by each such executive officer at year-end, measured
using the last trading price ($3.625) of the Company's Common Stock on September
30, 1998:

<TABLE>
<CAPTION>
                                                              NO. OF SECURITIES                                          
                                                           UNDERLYING UNEXERCISED             VALUE OF UNEXERCISED,     
                                                              OPTIONS HELD AT                IN-THE-MONEY OPTIONS AT 
                            SHARES                            FISCAL YEAR-END                    FISCAL YEAR-END           
                          ACQUIRED ON      VALUE       -------------------------------     ----------------------------
                           EXERCISE      REALIZED      EXERCISABLE       UNEXERCISABLE     EXERCISABLE    UNEXERCISABLE
      NAME                    (#)           ($)             (#)                (#)             ($)            ($)
      ----                -----------    --------      -----------       -------------     -----------    ------------- 
<S>                           <C>           <C>           <C>               <C>                 <C>               <C>

William T. Hanley........     --            --            71,250            63,750              --             --

Gregory Riedel...........     --            --             7,500            32,500              --             --

Josef W. Rokus...........     --            --            18,250             8,750              --             --

</TABLE>


                               PENSION PLAN TABLE

         The following table shows the estimated annual benefits payable under
the Company's Pension Plan:

<TABLE>
<CAPTION>
                                                  YEARS OF SERVICE
                              ------------------------------------------------------------
      REMUNERATION               15           20            25            30          35
      ------------            -------      -------       -------       -------     -------
       <S>                    <C>          <C>           <C>           <C>         <C>     

       $125,000 ............  $27,300      $36,400       $45,500       $51,750     $58,000 
        150,000 ............   33,300       44,400        55,500        63,000      70,500    
        175,000 ............   35,700       47,600        59,500        67,500      75,500  
        200,000 ............   35,700       47,600        59,500        67,500      75,500  
        225,000 ............   35,700       47,600        59,500        67,500      75,500  
        250,000 ............   35,700       47,600        59,500        67,500      75,500                                       
        300,000 ............   35,700       47,600        59,500        67,500      75,500  
        400,000 ............   35,700       47,600        59,500        67,500      75,500  
        450,000 ............   35,700       47,600        59,500        67,500      75,500  
        500,000 ............   35,700       47,600        59,500        67,500      75,500  

</TABLE>

         All employees who joined the Company prior to January 1, 1995 and who
work at least 1,000 hours per year are eligible for participation in the
Company's Pension Plan. Upon retirement at age 65, the Pension Plan will pay an
annual pension equal to the sum of (a) 1% of the employee's average total salary
during the highest five consecutive years in his last ten years of service
multiplied by credited years of service and (b) 6/10 of 1% of such average total
compensation in excess of the employee's Social Security-covered compensation
multiplied by credited years of service (up to a maximum of 25 years). Only base
salary is covered by the Pension Plan. Years of service for the persons named in
the Summary Compensation Table above and eligible for participation in the
Pension Plan are as follows: Mr. Hanley, 16 and Mr. Rokus, 14.






                                       6
<PAGE>   7


                         OTHER COMPENSATION ARRANGEMENTS

         Mr. Hanley resigned as President and Chief Executive Officer of the
Company on November 18, 1998. Pursuant to a Consulting Agreement dated November
24, 1998 between Mr. Hanley and the Company, Mr. Hanley has agreed to act as a
consultant to the Company for a fee of $10,000 per month for a period of twelve
months.

         On January 1, 1999, Mr. Rokus entered into an Employment Agreement with
the Company pursuant to which the Company has agreed to pay Mr. Rokus an annual
salary of $130,000. The Employment Agreement terminates on December 31, 1999. In
the event Mr. Rokus is terminated by the Company without cause prior to such
date, the Company has agreed to pay Mr. Rokus his salary through such date.





                                       7

<PAGE>   8


PART III, Item 12. SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS AND
MANAGEMENT is replaced with the following:


                                 SHARE OWNERSHIP

         The following table sets forth certain information regarding the
ownership of the Company's Common Stock as of January 26, 1999 by (i) persons
known by the Company to be beneficial owners of more than 5% of its Common
Stock, (ii) the directors and nominees for election as directors of the Company,
(iii) the executive officers of the Company, and (iv) all executive officers and
directors of the Company as a group:

<TABLE>
<CAPTION>
                                                         SHARES OF COMMON STOCK
                                                          BENEFICIALLY OWNED(1)
                                                        ------------------------
BENEFICIAL OWNER                                          SHARES         PERCENT
----------------                                        -------------    ------- 
<S>                                                     <C>       <C>     <C>   

Andlinger Capital XIII LLC ..........................   4,000,000 (2)     33%(3)
  105 Harbor Drive                                                          
  Stamford, Connecticut 06902

Eaton Vance Management ..............................     627,958 (4)      5%
  24 Federal Street
  Boston, Massachusetts 02110                                               

Dimensional Fund Advisors Inc. ......................     495,200 (4)      5%
  1299 Ocean Avenue                                                          
  Santa Monica, California 90401

Gerhard R. Andlinger ................................   4,000,000 (5)     33%(3)

Charles E. Ball .....................................   4,000,000 (6)     33%(3)

John F. Blais, Jr. ..................................     816,652 (4)      8%

Todd F. Davenport ...................................         -0-          0%

William T. Hanley ...................................     105,978 (7)      1%

Robert D. Happ ......................................      13,750 (8)      *

Stephen A. Magida ...................................   4,023,000 (9)     33%(3)

Gregory Riedel ......................................      15,104(10)      *

Josef W. Rokus ......................................      26,943(11)      *

W. Kip Speyer .......................................     137,906(12)      1%

Stephen P. Todd .....................................         -0-          0%

All executive officers and directors ................   5,018,251(13)     41%
  as a group (8 persons)                            

</TABLE>



--------------------------------------------------------------------------------
*  Indicates less than 1%





                                        8


<PAGE>   9


(1)  Unless otherwise indicated, each beneficial owner has sole voting and
     investment power with respect to the shares listed in the table.

(2)  Includes 2,000,000 shares Andlinger Capital XIII LLC has the right to
     acquire upon exercise of a warrant. Mr. John P. Kehoe, with an address at
     766 Madison Avenue, New York, New York 10021, may be deemed to have shared
     voting and dispository power of such shares. Mr. Kehoe disclaims beneficial
     ownership of such 4,000,000 shares.

(3)  Based on 12,082,265 shares outstanding, which includes 2,000,000 shares
     Andlinger Capital XIII LLC has the right to acquire upon exercise of a
     warrant.

(4)  Based on information provided by the beneficial owner.

(5)  Includes 4,000,000 shares (2,000,000 of which may be acquired upon exercise
     of a warrant) held by Andlinger Capital XIII LLC. Mr. Andlinger shares
     voting and dispository power for the 4,000,000 shares.

(6)  Includes 4,000,000 shares (2,000,000 of which may be acquired upon exercise
     of a warrant) held by Andlinger Capital XIII LLC. Mr. Ball may be deemed to
     have shared voting and dispository power of such shares. Mr. Ball disclaims
     beneficial ownership of such 4,000,000 shares.

(7)  Includes 77,500 shares subject to options granted to Mr. Hanley under the
     1981 Employee Stock Option Plan and the 1991 Employee Stock Option Plan and
     2,478 shares owned by Mr. Hanley's spouse. Mr. Hanley resigned from the
     Company on November 18, 1998.

(8)  Includes 8,750 shares subject to options granted to Mr. Happ under the 1996
     Director Stock Option Plan.

(9)  Includes (a) 23,000 shares held of record by seven irrevocable trusts of
     which Mr. Magida is sole trustee for the benefit of the family members of
     Mr. Andlinger; and (b) 4,000,000 shares (2,000,000 of which may be acquired
     upon exercise of a warrant) held by Andlinger Capital XIII LLC, for which
     Mr. Magida shares voting and dispository power.

(10) Includes 7,500 shares subject to options granted to Mr. Riedel under the
     1991 Employee Stock Purchase Plan, 1,604 shares held under the Employee
     Stock Purchase Plan and 1,000 shares owned by Mr. Riedel's children. Mr.
     Riedel resigned from the Company on November 2, 1998.

(11) Includes 18,250 shares subject to options granted to Mr. Rokus under the
     1981 Employee Stock Option Plan and the 1991 Employee Stock Option Plan and
     3,893 shares held under the Employee Stock Purchase Plan.

(12) Includes 35,000 shares subject to options granted to Mr. Speyer under the
     1991 Employee Stock Option Plan.

(13) Includes 62,000 shares subject to options granted to officers and directors
     under the 1981 Employee Stock Option Plan, the 1991 Employee Stock Option
     Plan and the 1996 Director Stock Option Plan and 2,000,000 shares which may
     be acquired by Andlinger Capital XIII LLC upon exercise of a warrant.
     Excludes all shares and options to purchase shares held by Mr. Hanley and 
     Mr. Riedel or their families.







                                       9


<PAGE>   10

PART III, Item 13. CERTAIN RELATIONSHIPS AND RELATED TRANSACTIONS is replaced
with the following:

     1.   On November 16, 1998, Mr. Speyer entered into an Employment Agreement
     with the Company pursuant to which Mr. Speyer agreed to become President
     and Chief Executive Officer of the Company. The Company has agreed to pay
     Mr. Speyer an annual salary of $250,000, with the opportunity to receive
     incentive bonus compensation up to 40% of his salary. The Employment
     Agreement terminates on September 30, 2001. If the Employment Agreement is
     terminated by the Company without cause prior to such date, the Company has
     agreed to pay Mr. Speyer his salary through such date, including the full
     amount of his bonus if all applicable goals are achieved.

     2.   OFC, a wholly-owned subsidiary, has sales, marketing, administrative
     and manufacturing facilities in Natick, Massachusetts and additional
     manufacturing facilities in Keene, New Hampshire. OFC leases approximately
     25,000 square feet of office space from a realty trust of which the sole
     beneficiary is John F. Blais, Jr., the former majority stockholder of OFC
     and currently its president and a director of the Company. The lease, which
     expires in December 2006, provides for monthly payments of $19,500 subject
     to annual adjustment to reflect changes in the fair market value of the
     real estate. The Company is responsible for certain insurance, utilities
     and other operating costs. Rents paid to the realty trust during fiscal
     1998 were approximately $179,000.









                                       10

<PAGE>   11




                                   SIGNATURES



Pursuant to the requirements of Section 13 or 15(d) of the Securities Exchange
Act of 1934, the Registrant has duly caused this report to be signed on its
behalf by the undersigned, thereunto duly authorized.





Dated: January 26, 1999                     GALILEO CORPORATION




                                            /s/ W. Kip Speyer
                                            ------------------------------------
                                            W. Kip Speyer, President
                                            and Chief Executive Officer





Pursuant to the requirements of the Securities Exchange Act of 1934, this report
has been signed by the following persons on behalf of the Registrant and in the
capacities indicated on January 26, 1999.




                                            /s/ W. Kip Speyer
                                            ------------------------------------
                                            W. Kip Speyer, President and
                                            Chief Executive Officer and Director
                                            (Principal Executive Officer)


                                            /s/ Stephen P. Todd
                                            ------------------------------------
                                            Stephen P. Todd, Interim Chief 
                                            Financial Officer (Principal 
                                            Financial and Accounting Officer)


                                            /s/ Gerhard R. Andlinger 
                                            ------------------------------------
                                            Gerhard R. Andlinger
                                            Chairman of the Board


                                            /s/ Charles E. Ball 
                                            ------------------------------------
                                            Charles E. Ball
                                            Director


                                            /s/ John F. Blais, Jr.
                                            ------------------------------------
                                            John F. Blais, Jr.
                                            Director


                                            /s/ Todd F. Davenport 
                                            ------------------------------------
                                            Todd F. Davenport
                                            Director


                                            /s/ Robert D. Happ  
                                            ------------------------------------
                                            Robert D. Happ
                                            Director


                                            /s/ Stephen A. Magida 
                                            ------------------------------------
                                            Stephen A. Magida
                                            Director






                                       11