<PAGE>   1
                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                              Washington, DC 20549

                                    FORM 10-Q

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

For the quarterly period ended   May 23, 1997

                                       OR

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

For the transition period from        to

Commission file number  1-7623

                           GENOVESE DRUG STORES, INC.
             (Exact name of registrant as specified in its charter)

            DELAWARE                                            11-1556812
(State or other jurisdiction of                             (I.R.S. Employer
 incorporation or organization)                             Identification No.)

                   80 Marcus Drive, Melville, New York, 11747
                    (Address of principal executive offices)
                                   (Zip Code)

                                 (516) 420-1900
              (Registrant's telephone number, including area code)

                                      NONE
     (Former name, former address and former fiscal year, if changed since
                                  last report)

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 close of the period covered by this report.

<TABLE>
<CAPTION>
              CLASS                     OUTSTANDING AT MAY 23, 1997
----------------------------------      ---------------------------
<S>                                     <C>
COMMON STOCK:
Class A, par value $1.00 per share             6,340,136
Class B, par value $1.00 per share             6,037,100
</TABLE>
<PAGE>   2
                           GENOVESE DRUG STORES, INC.

                                      INDEX


                                                                     PAGE

PART I.    FINANCIAL INFORMATION

           Condensed Balance Sheets - May 23, 1997
           (Unaudited) and January 31, 1997                            2

           Condensed Statements of Income - Sixteen Weeks
           Ended May 23, 1997 and May 24, 1996 (Unaudited)             3

           Condensed Statements of Cash Flows -
           Sixteen Weeks Ended May 23, 1997
           and May 24, 1996  (Unaudited)                               4

           Notes to Unaudited Condensed Financial Statements           5

           Management's Discussion and Analysis of Financial
           Condition and Results of Operations                        6-7


PART II.   OTHER INFORMATION AND SIGNATURES                            8


Exhibit 11 - Statement Re:  Computation of Net Income
             Per Common Share                                          9
<PAGE>   3
                           GENOVESE DRUG STORES, INC.
                            CONDENSED BALANCE SHEETS
                             (Dollars in Thousands)


<TABLE>
<CAPTION>
                                                                 May 23,       January 31,
                                                                  1997            1997
                                                               -----------     -----------
                                                               (Unaudited)      (Note 1)
<S>                                                            <C>            <C>
                                     Assets
Current Assets:
        Cash                                                     $  1,970       $  2,368
        Receivables                                                20,614         21,179
        Merchandise inventory                                     105,381        113,182
        Prepaid expenses and other                                  4,341          4,527
                                                                 --------       --------

       Total Current Assets                                       132,306        141,256
                                                                 --------       --------

Property and Equipment, net                                        78,645         79,435
                                                                 --------       --------

Other Assets                                                       10,880          9,372
                                                                 --------       --------

          Total Assets                                           $221,831       $230,063
                                                                 ========       ========

                      Liabilities and Stockholders' Equity

Current Liabilities:
        Accounts payable, accrued expenses and other             $ 67,140       $ 87,958
        Current portion of long-term debt                             871            871
                                                                 --------       --------

                Total Current Liabilities                          68,011         88,829
                                                                 --------       --------

Long-Term Liabilities                                              66,289         55,073
                                                                 --------       --------

Deferred Income Taxes Payable                                       8,481          8,481
                                                                 --------       --------

Stockholders' Equity                                               79,050         77,680
                                                                 --------       --------
     Total Liabilities and Stockholders'
       Equity                                                    $221,831       $230,063
                                                                 ========       ========
</TABLE>

See accompanying notes to unaudited condensed financial statements.


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<PAGE>   4
                           GENOVESE DRUG STORES, INC.
                         CONDENSED STATEMENTS OF INCOME
                 (Dollars in Thousands Except Per Share Amounts)
                                   (Unaudited)


<TABLE>
<CAPTION>
                                            Sixteen Weeks Ended
                                       -----------------------------
                                         May 23,           May 24,
                                          1997              1996
                                       -----------       -----------
<S>                                    <C>               <C>
Sales                                  $   226,906       $   200,823
                                       -----------       -----------

Costs and Expenses:
  Cost of merchandise sold                 165,115           143,725
  Selling, general and
         administrative expenses            57,532            53,555
                                       -----------       -----------
                                           222,647           197,280
                                       -----------       -----------

Operating Profit                             4,259             3,543
Interest Expense                             1,011             1,249
                                       -----------       -----------

Income Before Income Taxes                   3,248             2,294
Income Taxes                                 1,419             1,009
                                       -----------       -----------

Net Income                             $     1,829       $     1,285
                                       ===========       ===========

Net Income Per Common Share (a)        $       .15       $       .11
                                       ===========       ===========

Average Number of Common Shares
  Outstanding (a)                       12,340,000        12,215,000
                                       ===========       ===========
Cash Dividends Paid Per Common
  Share (a)                            $       .06       $       .05
                                       ===========       ===========
</TABLE>

(a)      Adjusted, where appropriate, to retroactively reflect the effect of a
         10 percent stock dividend distributed on January 17, 1997.



See accompanying notes to unaudited condensed financial statements.



                                       -3-
<PAGE>   5
                           GENOVESE DRUG STORES, INC.
                       CONDENSED STATEMENTS OF CASH FLOWS
                             (Dollars in Thousands)
                                   (Unaudited)

<TABLE>
<CAPTION>
                                                              Sixteen Weeks Ended
                                                            ------------------------
                                                             May 23,         May 24,
                                                              1997            1996
                                                            --------        --------
<S>                                                         <C>             <C>
Cash Flows From Operating Activities:
  Net income                                                $  1,829        $  1,285
  Adjustments to reconcile net income to
    net cash provided by (used for) operating
    activities:
     Depreciation and amortization                             3,918           3,397
     Provision for LIFO inventory valuation                    1,600           1,200
     Provision for other noncash expenses                         41              93
     Changes in certain assets and liabilities:
       Receivables                                               563          (2,129)
       Merchandise inventory                                   5,794           1,519
       Prepaid expenses and other                                 25           1,676
       Other assets                                           (1,859)           (965)
       Supplier advances                                       6,224            --
       Accounts payable, accrued expenses
        and other                                            (21,340)        (11,458)
                                                            --------        --------
Net cash used for operating activities                        (3,205)         (5,382)
                                                            --------        --------
Cash Flows From Investing Activities:
  Purchase of property and equipment                          (6,155)         (4,985)
  Proceeds from the sale of the Living Color
    photo processing lab                                       3,952            --
                                                            --------        --------

Net cash used for investing activities                        (2,203)         (4,985)
                                                            --------        --------
Cash Flows From Financing Activities:
  Net increase in bank borrowings                              5,514          10,600
  Repayments of long term liabilities                           (286)           (222)
  Issuance of Common Stock - Employee Stock Ownership
   and Appreciation Rights Plan                                  356               5
  Treasury stock purchased                                      (120)             (1)
  Payment of cash dividends                                     (740)           (666)
                                                            --------        --------

Net cash provided by financing activities                      5,010           9,716
                                                            --------        --------

Net Increase (Decrease) in Cash                                 (398)           (651)
Cash at Beginning of Period                                    2,368           2,251
                                                            --------        --------

Cash at End of Period                                       $  1,970        $  1,600
                                                            ========        ========
Supplemental Disclosure:
  Interest paid                                             $  1,019        $  1,186
                                                            ========        ========

  Income taxes paid                                         $  5,619        $  3,422
                                                            ========        ========
</TABLE>


See the accompanying notes to unaudited condensed financial statements.



                                       -4-
<PAGE>   6
                           GENOVESE DRUG STORES, INC.
                NOTES TO UNAUDITED CONDENSED FINANCIAL STATEMENTS


1.       The condensed balance sheet as of May 23, 1997, the condensed
         statements of income for the sixteen week periods ended May 23, 1997
         and May 24, 1996 and the condensed statements of cash flows for the
         sixteen week periods ended May 23, 1997 and May 24, 1996 have been
         prepared in accordance with generally accepted accounting principles
         for interim financial information and with the instructions to Form
         10-Q and Article 10 of Regulation S-X by the Company, without audit.
         The balance sheet as of January 31, 1997 was derived from the audited
         balance sheet included in the Company's Annual Report on Form 10-K. In
         the opinion of management, all adjustments (which include only normal
         recurring adjustments) necessary to present fairly the financial
         condition, results of operations and cash flows at May 23, 1997 and for
         the periods presented have been made.

         Certain information and footnote disclosures normally included in
         financial statements prepared in accordance with generally accepted
         accounting principles have been condensed or omitted. These condensed
         financial statements should be read in conjunction with the financial
         statements and notes thereto included in the Company's Annual Report on
         Form 10-K for the year ended January 31, 1997.

2.       The results of operations for the sixteen weeks ended May 23, 1997 and
         May 24, 1996 are not necessarily indicative of the results to be
         expected for the full year.

3.       Merchandise inventory is valued at the lower of cost or market, cost
         being determined by the last in first out (LIFO) method. LIFO inventory
         costs are determined at the end of each fiscal year when inflation
         rates are finalized. Therefore, LIFO inventory costs and cost of
         merchandise sold for interim periods are estimated and adjusted based
         on periodic physical inventories. At May 23, 1997 and January 31, 1997,
         inventories would have been greater by $20,300,000 and $18,700,000,
         respectively, if they had been valued at replacement costs.

4.       During the quarter ended May 23, 1997, the Company sold the assets of
         its Living Color photo processing plant. Simultaneously with the sale
         of the processing plant, the Company entered into an agreement whereby
         the Company will outsource all of its out of store photofinishing.

5.       On June 16, 1997, the Company's Board of Directors declared a cash
         dividend of $.07 per common share payable on July 8, 1997 to holders of
         record as of July 1, 1997.



                                       -5-
<PAGE>   7
                          MANAGEMENT'S DISCUSSION AND
                      ANALYSIS OF FINANCIAL CONDITION AND
                             RESULTS OF OPERATIONS


FOR THE SIXTEEN WEEKS ENDED MAY 23, 1997

Sales increased by 13.0% for the first quarter. On a comparable store basis
(stores opened during all of fiscal 1997), sales increased by 8.7%. The sales
contribution of the 19 stores opened in fiscal 1996, 1997 and 1998 to date, in
addition to the seasoned stores sales growth, were the main components of the
sales increase.

Cost of merchandise sold, expressed as a percentage of sales, increased to 72.8%
for the first quarter this year versus 71.6% last year. The most significant
factors effecting gross margins were decreases in the gross margins related to
pharmacy merchandise caused by reductions in third party reimbursement rates, an
increase in pharmacy sales as a percentage of total sales, and an increase in
the percentage of third party sales as a percentage of total pharmacy sales.
Gross margins on non pharmacy merchandise increased.

Selling general and administrative expenses as a percentage of sales decreased
to 25.4% this year versus 26.7% in the prior year. This decrease was the result
of cost controls put in place during the past few years, particularly with
respect to payroll costs and certain fixed costs being absorbed by a larger
sales base.

Interest expense was $1,012,000 versus $1,249,000 in the prior year. This
decrease was due to lower average levels of borrowings in this year's quarter.

Net income for the first quarter was $1,829,000 or $.15 per share. Last year's
net income for the quarter, was $1,285,000 or $.11 per share.

FINANCIAL CONDITION

The Company's operating, investing and financing activities for the sixteen
weeks ended May 23, 1997 utilized net cash of $398,000 as follows:

-        Operating activities utilized $3,205,000 primarily due to the reduction
         of accounts payable and accrued expenses which was particularly offset
         by reductions in the merchandise inventory and receivables, receipt of
         supplier advances and cash generated by operations.

-        Investing activities utilized $2,203,000 due to purchases of property
         and equipment of $6,155,000 offset by proceeds from the sale of the
         Living Color photo processing lab of $3,952,000.

-        Financing activities provided $5,010,000 from additional bank
         borrowings and the issuance of common stock, partially offset



                                       -6-
<PAGE>   8
         by the repayment of long-term debt, the purchase of treasury stock and
         the payment of cash dividends.

Working capital at May 23, 1997 increased to $64.3 million. The working capital
ratio was 1.95 to 1.0 at May 23, 1997 versus of 1.59 to 1.0 at January 31, 1997.

The Company maintains a revolving term loan agreement with three banks under
which the banks are committed to lend up to $90 million to the Company. As of
May 23, 1997, the Company had borrowings of $49.8 million under this facility.

The Company anticipates that its working capital needs for the remainder of
fiscal 1998 will be satisfied through operating results and, as necessary,
through borrowings under facilities available to the Company.

RECENT ACCOUNTING PRONOUNCEMENTS

In February 1997, the Financial Accounting Standards Board issued Statement of
Financial Accounting Standards No. 128 "Earnings per Share" ("SFAS 128"). SFAS
128 establishes standards for computing and presenting earnings per share
("EPS"). SFAS 128 replaces the presentation of primary EPS with the presentation
of basic EPS and requires the presentation of basic EPS and diluted EPS on the
face of the income statement.

This statement will be effective for the Company's fiscal year ending January
30, 1998. Early application for the quarter ended May 23, 1997 is not permitted.

If SFAS 128 had been adopted for the quarters ended May 23, 1997 and May 24,
1996, earnings per share would have been:

<TABLE>
<CAPTION>
                                    May 23,      May 24,
Sixteen Weeks Ended                  1997         1996
-------------------                 -------      -------
<S>                                 <C>          <C>
Basic EPS                             $.15         $.11
                                      ====         ====

Diluted EPS                           $.15         $.10
                                      ====         ====
</TABLE>


                                       -7-
<PAGE>   9
PART II.  OTHER INFORMATION


Item 6.  Exhibits and Reports on Form 8-K

The following exhibits are included herein:

(11) Statement re:  computation of net income per common share.

There were no reports on Form 8-K filed during the sixteen weeks ended May 23,
1995.



                                   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.


                                 GENOVESE DRUG STORES, INC.
                                       (Registrant)



Date:   July 2, 1997             By:  /s/ Jerome Stengel
                                      -----------------------------
                                             Jerome Stengel
                                      (Vice President & Treasurer)
                                      (Principal Financial Officer)


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