<PAGE>   1

                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                   FORM 10 - Q

Quarterly Report Pursuant to Section 13 or 15(d) of the Securities Exchange Act
of 1934

For the quarterly period ended DECEMBER 31, 1997

COMMISSION FILE NUMBER 0-11309

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

DELAWARE                                                       04-2526583
(State or other jurisdiction of                             (I.R.S. Employer
incorporation or organization)                              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


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 
                                          ---            ---

Indicate the number of shares outstanding of each of the Issuer's classes of
common stock, as of the latest practicable date.

             CLASS                           OUTSTANDING AT DECEMBER 31, 1997
--------------------------------           -------------------------------------
  COMMON STOCK, PAR VALUE $.01                      6,874,705 SHARES


                                  PAGE 1 OF 14

<PAGE>   2




                               GALILEO CORPORATION
                                      INDEX

                                                                      Page No.
PART I.  Financial Information:                                      ----------

Item 1. Financial Statements (unaudited)

   Consolidated Condensed Balance Sheets at December 31, 1997, and 
   September 30,1997..................................................... 3

   Consolidated Condensed Statements of Income for the three months 
   ended December 31, 1997, and 1996..................................... 4

   Consolidated Condensed Statements of Cash Flows for the
   three months ended December 31, 1997, and 1996........................ 5

   Notes to Consolidated Condensed Financial Statements.................. 6

Item 2.

   Management's Discussion and Analysis of Financial
   Condition and Results of Operations................................... 8

PART II. Other Information:

Item 6.

Exhibits and Reports on Form 8-K                                         12

Signatures                                                               13


                                       2


<PAGE>   3





                               GALILEO CORPORATION
                CONSOLIDATED CONDENSED BALANCE SHEETS (UNAUDITED)
                             (Dollars in thousands)

<TABLE>
<CAPTION>
                                                                  Dec. 31, 1997    Sept. 30, 1997
                                                                  -------------    --------------
ASSETS

<S>                                                                 <C>                <C>     
Current assets:
  Cash and cash equivalents                                         $  6,102           $  9,546
  Accounts receivable, net                                             6,894              5,639
  Inventories, net  (Note 2)                                           8,101              6,614
  Other current assets                                                    91                187
                                                                    --------           --------
  Total current assets                                                21,188             21,986
Property, plant and equipment, net                                    15,054             15,372
Excess of cost over the fair value of assets acquired, net             4,524              3,873
Other assets, net                                                      1,481              1,496
                                                                    --------           --------
Total assets                                                        $ 42,247           $ 42,727
                                                                    ========           ========

LIABILITIES AND SHAREHOLDERS' EQUITY

Current liabilities:
  Accounts payable and accrued liabilities                          $  4,880           $  5,669
  Note Payable                                                         1,287               --
                                                                    --------           --------
    Total current liabilities                                          6,167              5,669
Other liabilities                                                      1,089                956
Shareholders' equity:
  Common stock                                                            69                 69
  Additional paid-in capital                                          42,952             42,951
  Accumulated deficit                                                 (8,030)            (6,918)
                                                                    --------           --------
Total shareholders' equity                                            34,991             36,102
                                                                    --------           --------
Total liabilities and shareholders' equity                          $ 42,247           $ 42,727
                                                                    ========           ========
</TABLE>

See Notes to Consolidated Condensed Financial Statements


                                       3


<PAGE>   4



                               GALILEO CORPORATION
             CONSOLIDATED CONDENSED STATEMENTS OF INCOME (UNAUDITED)
                  (Amounts in thousands except per share data)
<TABLE>
<CAPTION>

                                                                            For the Three Months Ended
                                                                                  December 31,
                                                                             1997               1996
                                                                            -------           -------

<S>                                                                         <C>               <C>    
Net sales                                                                   $ 8,563           $ 9,711
Cost of sales                                                                 5,775             5,436
                                                                            -------           -------
Gross profit                                                                  2,788             4,275

Engineering expenses                                                          1,328             1,183
Selling and administrative expenses                                           2,620             2,161
Reduction in carrying value of certain long-lived assets  (Note 8)             --               2,226
                                                                            -------           -------
                                                                              3,948             5,570
                                                                            -------           -------
Operating loss                                                               (1,160)           (1,295)
Other income                                                                     57               250
                                                                            -------           -------
Loss before income taxes
                                                                             (1,103)           (1,045)
Provision for income taxes                                                        8               121
                                                                            -------           -------
Net loss                                                                    $(1,111)          $(1,166)
                                                                            =======           =======
Basic and diluted loss per share                                            $ (0.16)          $ (0.17)
                                                                           
Weighted average shares                                                       6,874             6,836
</TABLE>

See Notes to Consolidated Condensed Financial Statements


                                       4


<PAGE>   5


                               GALILEO CORPORATION
           CONSOLIDATED CONDENSED STATEMENTS OF CASH FLOWS (UNAUDITED)
                             (Dollars in thousands)
<TABLE>
<CAPTION>

                                                                       For the three months ended
                                                                               December 31,
                                                                         1997              1996
                                                                       -------           --------
<S>                                                                    <C>               <C>      
Net loss                                                               $(1,111)          $ (1,166)
Adjustments to reconcile net loss to net
  cash provided (used) by operating activities:
     Depreciation and amortization                                         665                900
     Reduction in carrying value of certain long-lived assets               --              2,226
     Other adjustments, net                                                  4                 (1)
Increase (Decrease) in cash from changes in operating
  assets and liabilities:
     Accounts receivable                                                  (698)               279
     Inventories                                                           243               (713)
     Accounts payable and accrued liabilities                           (1,228)               412
     Other changes, net                                                   (141)               (90)
                                                                       -------           --------

       Total adjustments                                                (1,155)             3,013
                                                                       -------           --------

Net cash provided (used) by operating activities                       $(2,266)          $  1,847

Cash flows from investing activities:
  Acquisition of business                                                 (951)                --
  Capital expenditures                                                    (292)            (1,167)
                                                                       -------           --------

       Net cash used in investing activities                            (1,243)            (1,167)

Cash flows from financing activities:
  Payments on notes payable                                                 --               (542)
  Proceeds from issuance of common stock                                    21                102
  Other financing activities, net                                           --                (10)
                                                                       -------           --------

       Net cash provided (used) by financing activities                     21               (450)
                                                                       -------           --------

  Effect of exchange rate changes on cash                                   44                 --
                                                                       -------           --------

Net increase (decrease) in cash and cash equivalents                    (3,444)               230

Cash and cash equivalents at beginning of period                       $ 9,546           $ 18,652
                                                                       =======           ========

Cash and cash equivalents at end of period                             $ 6,102           $ 18,882
                                                                       =======           ========
</TABLE>



See Notes to Consolidated Condensed Financial Statements


                                       5


<PAGE>   6


                               GALILEO CORPORATION
              NOTES TO CONSOLIDATED CONDENSED FINANCIAL STATEMENTS
                  (Dollars in thousands except per share data)

1.   In the opinion of management, the accompanying unaudited consolidated
     condensed financial statements contain all adjustments (consisting of only
     normal recurring adjustments) necessary to present fairly Galileo
     Corporation's (the Company) financial position as of December 31, 1997, and
     the results of operations and cash flows for the three month period ended
     December 31, 1997, in conformity with generally accepted accounting
     principles for interim financial information applied on a consistent basis.
     The results of operations for the three months ended December 31, 1997, are
     not necessarily indicative of the results to be expected for the full year.
     These financial statements should be read in conjunction with the Company's
     1997 Annual Report to Shareholders and Form 10-K for the fiscal year ended
     September 30, 1997.

2.   Classification of inventories is:
<TABLE>
<CAPTION>

                                      December 31, 1997      September 30, 1997
                                      -----------------      ------------------

<S>                                         <C>                  <C>   
             Finished goods                 $3,119               $2,755
             Work-in-progress                  640                  660
             Raw materials                   4,342                3,199
                                            ------               ------
                                            $8,101               $6,614
                                            ======               ======
</TABLE>


3.   In February 1997 the Company received written notification from its then
     largest customer, Xerox Corporation, that Xerox had developed internal
     production capabilities for dicorotron assemblies and would no longer
     purchase these assemblies from the Company. These assemblies accounted for
     approximately $3,750 or 39% of the company revenues of $9,711 for the three
     months ended December 31, 1996. The Company completed final shipments to
     Xerox during its second quarter of fiscal 1997.

4.   In October 1997 the Company acquired all of the outstanding shares of
     Leisegang Feinmechanik-Optik GmbH & Co., KG ("Leisegang GmbH") for $2,250
     in cash. Leisegang GmbH was a privately held manufacturer and distributor
     of colposcopes and accessories. These diagnostic products are sold to
     OB/GYN physicians' offices and hospitals primarily through a worldwide
     network of sales representatives and distributors. The acquisition was
     accounted for using the purchase method of accounting. The excess of the
     cost over the fair value of net assets acquired 

                                       6

<PAGE>   7


     amounted to $684 at December 31, 1997. Included in notes payable is $1,287
     associated with the final acquisition payment due in October 1998.

5.   In January 1998 the Company entered into a $12,000 revolving credit
     facility with a bank. Any loans thereunder may be converted to a three year
     term loan after two years and will bear interest at the prime rate through
     June 30, 1998, with a Company option thereafter for LIBOR-based rates under
     certain conditions. This facility will be used for acquisitions and working
     capital and will provide additional flexibility to carry out current
     Company growth initiatives.

6.   In January 1998 the Company acquired all the outstanding shares of OFC
     Corporation ("OFC") for approximately $6,000 in cash and 1.15 million
     shares of Galileo Common Stock. OFC designs, manufactures and markets a
     broad range of optical components and systems which incorporate the latest
     advances in photonic technology and optical coatings. The acquisition will
     be accounted for using the purchase method of accounting.

7.   In February 1998 the Company acquired all the outstanding shares of Les
     Entreprises Galencia, Inc. ("Galenica") for approximately $3,200 in cash.
     Galenica manufactures and markets a broad line of disposable single-use
     vaginal specula, the most frequently used diagnostic instrument by OB/GYN
     physicians, clinics and hospitals. The acquisition will be accounted for
     using the purchase method of accounting.

8.   For the three months ended December 31, 1996, the Company adopted Statement
     of Financial Accounting Standard No. 121, "Accounting for the Impairment of
     Long-Lived Assets and for the Long-Lived Assets to be Disposed of." This
     statement requires impairment losses be recognized for long-lived assets,
     when indicators of impairment are present and the fair market values of
     assets are estimated to be less than carrying amounts. The adoption of this
     Standard resulted in a $2,226, or $0.32 per share, nonrecurring, pretax,
     noncash, charge in the quarter, which reduced certain robotic assembly
     equipment for the Company's Medical Products Group to its estimated fair
     market value. Excluding the impact of this charge, net income for the three
     months ended December 31, 1996, was $1,060, or $0.15 per share.

9.   In 1997, the Financial Accounting Standards Board issued Statement of
     Financial Accounting Standards No. 128, "Earnings per Share." Statement 128
     replaced the previously reported primary and fully diluted earnings per
     share with basic and diluted earnings per share. Unlike primary earnings
     per share, basic earnings per share excludes any dilutive effect of
     options, warrants, and convertible securities. Diluted earnings per share
     is very similar to the previously reported fully diluted earnings per
     share. All earnings per share amounts for all periods of have been
     presented, and where necessary, restated to conform to Statement 128
     requirements.



                                       7

<PAGE>   8


         MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
                             RESULTS OF OPERATIONS

OVERVIEW

Galileo Corporation (the "Company") develops, manufactures and markets
fiberoptic and electro-optic products which transmit, sense or intensify light
or images. The Company's products are currently sold primarily to original
equipment manufacturers (OEMs) for use in medical, scientific, analytical,
electronic imaging and office product applications. The Company's core
competencies in glass sciences and experience in fiberoptic and photonic
technology are fundamental to developing and manufacturing its products.

On February 11, 1997, the Company received written notification from its then
largest customer, Xerox Corporation ("Xerox"), that Xerox had developed internal
production capabilities for dicorotron assemblies and would no longer purchase
these assemblies from the Company. These assemblies accounted for approximately
$20.4 million, or 48% of the Company's fiscal 1996 revenues. Reduced revenues
from this product materially adversely affected the Company's financial
performance for fiscal 1997 and resulted in a loss for the fiscal year. In
connection with this loss of business, the Company adopted a reorganization plan
and recorded a charge of $6.9 million in the three months ended March 31, 1997.
The charge included a noncash $6.5 million provision for related long-lived
assets, other assets and inventory, and a $0.4 million provision for related
severance and other obligations.

The Company's Medical Products consist of a variety of endoscopes in support of
minimally invasive medical procedures. Scopes are valuable in any medical
procedure where video imaging can provide accurate diagnosis, improve surgical
performance and reduce patient discomfort. In addition, the fiscal 1996
acquisition of Leisegang Medical, the fiscal 1997 acquisition of the
Sani-Spec(TM) product line from C.R. Bard, Inc., and the fiscal 1998 acquisition
of Leisegang GmbH, more fully discussed below, position the Company as a
supplier of medical instrument equipment, principally to the obstetric and
gynecological markets. The Company believes that its medical products offer
significant future growth opportunities.

Leisegang Medical, headquartered in Boca Raton, FL, was a privately-held
distributor and manufacturer of OB/GYN diagnostic and surgical equipment.
Included in its product line are colposcopes produced by Leisegang GmbH, a
related company based in Berlin, Germany. In October 1997 the Company announced
the acquisition of Leisegang GmbH. Leisegang GmbH was a privately-held
manufacturer and worldwide distributor of colposcopes and accessories and the
supplier of colposcopes for Leisegang Medical. These products are sold to OB/GYN
physicians' offices and hospitals through an internal sales force, sales
representatives and distributors.


                                       8

<PAGE>   9


Leisegang Medical is well known and highly respected in the gynecological
equipment market, estimated to be $200 million annually, and is a leader in
sales to physicians' offices. In addition to colposcopes, its products include
biopsy instruments, ultrasound, video equipment, laser and electro-surgical
systems and accessories, cryosurgery equipment, surgical instruments, rigid and
flexible hysteroscopes, and fetal heart monitors. These acquisitions also
provide Galileo with new distribution channels that enhance the brand name
recognition and market penetration of the Company's medical imaging and sensing
products.

On February 28, 1997, the Company acquired the Sani-Spec(TM) product line. This
product line includes a comprehensive suite of women's health-related products
used by OB/GYN physicians, clinics and hospitals including Sani-Spec single-use
vaginal specula, Sani-Scope(TM) anoscopes, Spec Light(TM) speculum lights and
Pap Smear kits. The product line is marketed through a nationwide network of
approximately 80 dealers and has been a market leader for over 20 years.

The Company's Scientific Detector and Spectroscopy Products include detectors
and sensors which are used in various instruments in a wide range of markets
including semiconductor processing, life sciences, food processing, bulk and
specialty chemicals, petroleum refining, biotechnology, failure analysis and
quality and process control.

The Company's Fluorolase(R) fiberoptic-based optical amplifier product is
targeted at applications for telecommunications as well as high-speed data and
video transmission. Currently, this product is being tested in these markets,
and the Company believes that the Fluorolase product offers significant future
growth opportunities.

In addition to investing in research and development activities for all of its
products, the Company is exploring other acquisition opportunities to enhance
product offerings to customers.

This Report on Form 10-Q contains certain forward-looking statements concerning,
among other things, the Company's plans and objectives for future operations,
planned products and services, expansion into new markets and anticipated
customer demand for its existing and future products and services. Certain
factors that could cause the Company's actual results to differ from those
projected in these forward-looking statements are set forth in Management's
Discussion and Analysis of Financial Condition and Results of Operations
included in the Company's September 30, 1997, SEC Form 10-K and incorporated
herein.


                                       9

<PAGE>   10


RESULTS OF OPERATIONS

Sales for the three months ended December 31, 1997, of $8.6 million, decreased
$1.1 million, or 12%, from $9.7 million for the comparable prior-year period.
Reduced revenues resulted primarily from the loss of the Company's largest
customer more fully discussed in the "Overview" section above. Excluding sales
activity for this customer in the prior-year period, revenues for the three
months ended December 31, 1997, increased 45% over the prior year from both
revenues derived from new products and revenues from acquisitions as outlined in
the "Overview" section above.

Gross profit (as a percentage of revenues) of 32.6% for the three months ended
December 31, 1997, decreased from 44.0% for the comparable prior-year period,
primarily due to the impact of reduced revenues on fixed manufacturing expenses.

Engineering expenses increased to $1.3 million primarily due to increased
spending to support the development of the medical and telecommunications
products.

Selling and administrative expenses increased to $2.6 million resulting from the
consolidation of operating expenses from acquisitions made during fiscal 1997.

Other income principally relates to interest earned on investments. For both the
current and comparable prior year periods, the Company's effective tax rate
differs from the statutory rate primarily due to available tax loss
carryforwards. The provisions principally relate to state and franchise taxes.

FINANCIAL CONDITION

The Company's working capital at December 31, 1997, of $15.0 million, decreased
from $16.3 million at September 30, 1997. The change in working capital was
primarily the result of the acquisition of Leisegang GmbH described in more
detail in the "Overview" section above and operating losses for the year to
date.

Capital spending for the three months ended December 31, 1997, amounted to $0.3
million. This compares with $1.2 million of capital expenditures for the
comparable prior-year period. Capital spending for fiscal 1997 primarily relates
to machinery and equipment to support the development of new medical scopes and
the Company's telecommunications products.

As more fully described in the "Subsequent Events" section below, in January
1998 the Company entered into a $12 million credit facility with a bank. The
Company considers its working capital and available credit facility to be
adequate to support its currently planned operations.


                                       10


<PAGE>   11


SUBSEQUENT EVENTS

In January 1998 the Company entered into a $12 million revolving credit facility
with a bank. Any loans thereunder may be converted to a three-year term loan
after two years and will bear interest at the prime rate through June 30, 1998,
with a Company option thereafter for LIBOR-based rates under certain conditions.
This facility will be used for acquisitions and working capital and will provide
additional flexibility to carry out current Company growth initiatives.

In January 1998 the Company acquired all the outstanding shares of OFC
Corporation ("OFC") for approximately $6 million in cash and 1.15 million shares
of Galileo Common Stock. OFC designs, manufactures and markets a broad range of
optical components and systems which incorporate the latest advances in photonic
technology and optical coatings. The acquisition will be accounted for using the
purchase method of accounting.

In February 1998 the Company acquired all the outstanding shares of Les
Entreprises Galencia, Inc. ("Galenica") for approximately $3.2 million in cash.
Galenica manufactures and markets a broad line of disposable single-use vaginal
specula, the most frequently used diagnostic instrument by OB/GYN physicians,
clinics and hospitals. The acquisition will be accounted for using the purchase
method of accounting.








                                       11

<PAGE>   12


                           PART II. OTHER INFORMATION

ITEM 4. SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS.

     The following matters were submitted to a vote of the Company's
     shareholders at the Annual Meeting of Shareholders held on January 22,
     1998:

     1.   The following persons were elected as directors of the Company:
<TABLE>
<CAPTION>

                                            FOR                   WITHHOLD
                                         ---------                --------

         <S>                             <C>                       <C>   
          William T. Burgin              5,906,164                 63,851
          Allen E. Busching              5,904,765                 65,250
          Kenneth W. Draeger             5,904,765                 65,550
          William T. Hanley              5,906,714                 63,301
          Robert D. Happ                 5,906,765                 63,250
</TABLE>

     2.   Amendment to the 1991 Employee Stock Option Plan to increase the
          aggregate number of shares of common stock that may be subject to
          grants under the plan from 550,000 to 750,000 was approved by a vote
          of 5,120,933 in favor, 499,352 against, 38,114 abstaining and 311,616
          shares not voting.

ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K

               a. Exhibits:

                    27   Financial Data Schedule (EDGAR filing only)

               b. Reports on Form 8-K

                    1.   On October 20, 1997, the Registrant filed a Form 8-K
                         for the acquisition of Leisegang Feinmechanik-Optik
                         GmbH & Co. KG.



                                       12



<PAGE>   13





                                   SIGNATURES



Pursuant to the requirements 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.


                                        GALILEO CORPORATION


    Dated:  February 12, 1998           /s/ William T. Hanley
                                        ---------------------------------------
                                        William T. Hanley, President and
                                        Chief Executive Officer (Principal
                                        Executive Officer)


                                        /s/ Gregory Riedel
                                        ---------------------------------------
                                        Gregory Riedel, Vice President,
                                        Finance and Chief Financial Officer
                                        (Principal Financial and Accounting
                                        Officer)



                                       13

<PAGE>   14



                               GALILEO CORPORATION
                                INDEX TO EXHIBITS

       EXHIBIT NO.                                               PAGE NO.

           27              Financial Data Schedule                 EDGAR
                                                                  Filing
                                                                   Only











                                       14