<PAGE>   1
 
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                UNITED STATES SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
 
                                   FORM 10-Q
 
(Mark One)
 
            [X] QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF
                      THE SECURITIES EXCHANGE ACT OF 1934
 
               For the quarterly period ended SEPTEMBER 30, 1996
 
                                       OR
 
            [ ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF
                    THE SECURITIES AND EXCHANGE ACT OF 1934
 
           For the transition period from             to
 
                         Commission file number: 1-2917
 
                         THE STANDARD PRODUCTS COMPANY
             (Exact Name of Registrant as Specified in its Charter)
 
<TABLE>
<S>                                             <C>
                    OHIO                                         34-0549970
       (State or Other Jurisdiction of                          (IRS Employer
       Incorporation or Organization)                        Identification No.)
</TABLE>
 
                             2401 SOUTH GULLEY ROAD
                            DEARBORN, MICHIGAN 48124
             (Address of Principal Executive Offices and Zip Code)
 
       Registrant's telephone number, including area code: (313) 561-1100
 
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 [ ]
 
  THE NUMBER OF SHARES OF COMMON STOCK OUTSTANDING AS OF OCTOBER 31, 1996 WAS
                               16,806,323 SHARES.
 
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<PAGE>   2
 
                         THE STANDARD PRODUCTS COMPANY
                         QUARTERLY REPORT ON FORM 10-Q
 
                               TABLE OF CONTENTS
 
<TABLE>
<CAPTION>
                                                                                           PAGE
                                                                                           ----
<S>        <C>                                                                             <C>
PART I. FINANCIAL INFORMATION
Item 1.    Financial Statements
           Consolidated Statements of Operations........................................     3
           Consolidated Balance Sheets..................................................     4
           Consolidated Statements of Cash Flows........................................     5
           Notes to Consolidated Financial Statements...................................     6
           Managements's Discussion and Analysis of Financial Condition and Results of
Item 2.    Operations...................................................................     7
PART II. OTHER INFORMATION
Item 1.    Legal Proceedings............................................................     9
Item 2.    Changes in Securities........................................................     9
Item 3.    Defaults upon Senior Securities..............................................     9
Item 4.    Submission of Matters to a Vote of Security-Holders..........................     9
Item 5.    Other Information............................................................     9
Item 6.    Exhibits and Reports on Form 8-K.............................................     9
SIGNATURES..............................................................................    10
</TABLE>
 
UNLESS OTHERWISE INDICATED, REFERENCES TO "COMPANY" MEAN THE STANDARD PRODUCTS
COMPANY AND ITS SUBSIDIARIES AND REFERENCE TO A FISCAL YEAR MEANS THE COMPANY'S
YEAR ENDED JUNE 30 OF THE SAME YEAR (E.G., "FISCAL 1997" REFERS TO THE PERIOD
BEGINNING JULY 1, 1996 AND ENDING JUNE 30, 1997).
 
                                        2
<PAGE>   3
 
                         PART I. FINANCIAL INFORMATION
 
ITEM 1. FINANCIAL STATEMENTS
 
             THE STANDARD PRODUCTS COMPANY AND SUBSIDIARY COMPANIES
 
                     CONSOLIDATED STATEMENTS OF OPERATIONS
                                  (UNAUDITED)
                   (THOUSANDS OF DOLLARS, EXCEPT SHARE DATA)
 
<TABLE>
<CAPTION>
                                                                          THREE MONTHS ENDED
                                                                            SEPTEMBER 30,
                                                                        ----------------------
                                                                          1996          1995
                                                                        --------      --------
<S>                                                                     <C>           <C>
Net Sales............................................................   $265,611      $238,760
Cost of Goods Sold:
  Materials, wages and other manufacturing costs.....................    230,745       219,778
  Research, engineering and development expenses.....................      9,574         9,577
                                                                        --------      --------
                                                                         240,319       229,355
                                                                        --------      --------
     Gross income....................................................     25,292         9,405
Selling, General and Administrative Expenses (Note 4)................     17,303        17,143
                                                                        --------      --------
                                                                           7,989        (7,738)
                                                                        --------      --------
Other (Income) Expense:
  Royalty and dividend income........................................       (245)         (119)
  Net interest expense...............................................      3,247         3,733
  Other, net.........................................................       (456)          435
                                                                        --------      --------
                                                                           2,546         4,049
                                                                        --------      --------
Income (Loss) before Taxes on Income.................................      5,443       (11,787)
Provision for Taxes on Income........................................      4,046        (2,003)
                                                                        --------      --------
  Net Income (Loss)..................................................   $  1,397      $ (9,784)
                                                                        ========      ========
Earnings Per Common Share............................................      $0.08        $(0.58)
                                                                        ========      ========
Weighted average shares outstanding (in thousands)...................     16,792        16,746
                                                                        ========      ========
Dividends declared per share.........................................      $0.17         $0.17
                                                                        ========      ========
</TABLE>
 
        The accompanying notes are an integral part of these statements.
 
                                        3
<PAGE>   4
 
             THE STANDARD PRODUCTS COMPANY AND SUBSIDIARY COMPANIES
 
                          CONSOLIDATED BALANCE SHEETS
                             (THOUSANDS OF DOLLARS)
 
<TABLE>
<CAPTION>
                                                                        SEPTEMBER 30,    JUNE 30,
                                                                            1996           1996
                                                                        -------------    ---------
                                                                         (UNAUDITED)
<S>                                                                     <C>              <C>
                               ASSETS
Current Assets:
  Cash and cash equivalents..........................................     $   8,137      $  --
  Receivables, less allowances of $2,690 at September 30 and $2,958
     at June 30 (Note 4).............................................       169,074        180,787
  Inventories........................................................        66,950         60,377
  Prepaid insurance, taxes, etc......................................        24,149         19,680
                                                                          ---------      ---------
       Total current assets..........................................       268,310        260,844
                                                                          ---------      ---------
Property, Plant and Equipment, at cost...............................       559,245        548,816
  Less -- Accumulated depreciation...................................      (260,406)      (250,278)
                                                                          ---------      ---------
                                                                            298,839        298,538
Goodwill, net........................................................        71,226         71,653
Other Assets.........................................................        51,682         53,660
                                                                          ---------      ---------
                                                                          $ 690,057      $ 684,695
                                                                          =========      =========
                LIABILITIES AND SHAREHOLDERS' EQUITY
Current Liabilities:
  Short-term notes payable...........................................     $   6,744      $   1,198
  Current maturities of long-term debt...............................         2,764          2,450
  Accounts payable...................................................        93,368         99,093
  Accrued payrolls...................................................        22,846         26,651
  Accrued expenses...................................................        83,528         74,565
  Dividend payable...................................................         2,857          2,853
                                                                          ---------      ---------
       Total current liabilities.....................................       212,107        206,810
                                                                          ---------      ---------
Long-term Debt, net of current maturities............................       139,698        143,041
Other Postretirement Benefits........................................        26,146         26,023
Deferred Income Taxes and Other Credits..............................        54,613         50,056
Commitments and Contingent Liabilities (Note 3)
Shareholders' Equity:
  Serial preferred shares, without par value, authorized 6,000,000
     voting and 6,000,000 non-voting shares, none issued.............       --              --
  Common shares, par value $1 per share; authorized 50,000,000
     shares, issued and outstanding, 16,804,123 shares at September
     30 and 16,784,867 at June 30....................................        16,804         16,785
  Paid-in capital....................................................        97,329         96,906
  Retained earnings..................................................       153,209        154,669
  Foreign currency translation adjustments...........................        (6,572)        (6,318)
  Minimum pension liability..........................................        (3,277)        (3,277)
                                                                          ---------      ---------
       Total shareholders' equity....................................       257,493        258,765
                                                                          ---------      ---------
                                                                          $ 690,057      $ 684,695
                                                                          =========      =========
</TABLE>
 
        The accompanying notes are an integral part of these statements.
 
                                        4
<PAGE>   5
 
             THE STANDARD PRODUCTS COMPANY AND SUBSIDIARY COMPANIES
 
                     CONSOLIDATED STATEMENTS OF CASH FLOWS
                                  (UNAUDITED)
                             (THOUSANDS OF DOLLARS)
 
<TABLE>
<CAPTION>
                                                                            THREE MONTHS ENDED
                                                                              SEPTEMBER 30,
                                                                           --------------------
                                                                             1996        1995
                                                                           --------    --------
<S>                                                                        <C>         <C>
Net cash provided by (used for) operating activities:
  Net income (loss).....................................................   $  1,397    $ (9,784)
  Adjustments to reconcile net income to net cash provided by operating
     activities:
     Depreciation and amortization......................................     16,141      10,765
     Deferred taxes and other credits...................................      3,885         799
     Effect of changes in foreign currency..............................       (226)        605
     Other operating items..............................................      2,708       1,556
                                                                           --------    --------
       Net cash provided by operations..................................     23,905       3,941
                                                                           --------    --------
Net cash provided by (used for) changes in operating assets and
  liabilities:
     Receivables (Note 4)...............................................     11,713      38,758
     Inventories........................................................     (6,639)     (3,292)
     Accounts payable and accrued expenses..............................       (963)       (520)
     Other..............................................................     (4,469)     (1,462)
                                                                           --------    --------
       Net cash provided by (used for) changes in operating assets and
        liabilities.....................................................       (358)     33,484
                                                                           --------    --------
       Net cash provided by operating activities........................     23,547      37,425
                                                                           --------    --------
Net cash used for investments:
  Purchase of property, plant and equipment, net........................    (15,162)    (17,063)
  Investments in affiliates.............................................       (350)       (340)
                                                                           --------    --------
       Net cash used for investments....................................    (15,512)    (17,403)
                                                                           --------    --------
Net cash provided by (used for) financing:
  Proceeds of long-term borrowings......................................      7,490      14,456
  Net increase (decrease) in short-term borrowings......................      5,546      (3,230)
  Repayment of long-term borrowings (Note 4)............................    (10,063)    (40,131)
  Cash dividends........................................................     (2,857)     (2,847)
                                                                           --------    --------
       Net cash provided by (used for) financing........................        116     (31,752)
                                                                           --------    --------
Effect of exchange rate changes on cash.................................        (14)        192
                                                                           --------    --------
Increase (decrease) in cash and cash equivalents........................      8,137     (11,538)
Cash and cash equivalents at the beginning of the period................      --         19,546
                                                                           --------    --------
Cash and cash equivalents at the end of the period......................   $  8,137    $  8,008
                                                                           ========    ========
</TABLE>
 
        The accompanying notes are an integral part of these statements.
 
                                        5
<PAGE>   6
 
             THE STANDARD PRODUCTS COMPANY AND SUBSIDIARY COMPANIES
 
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                               SEPTEMBER 30, 1996
                             (THOUSANDS OF DOLLARS)
 
(1) BASIS OF PRESENTATION
 
     The accompanying consolidated financial statements have been prepared by
management and in the opinion of management, contain all adjustments, consisting
of normal recurring adjustments, necessary to present fairly the financial
position of the Company as of September 30, 1996 and June 30, 1996, and the
results of its operations for the three months ended September 30, 1996 and 1995
and cash flows for the three months ended September 30, 1996 and 1995. The
consolidated financial statements should be read in conjunction with the
consolidated financial statements and notes thereto included in the Company's
Annual Report on Form 10-K for the fiscal year ended June 30, 1996. Results for
interim periods are not necessarily indicative of those to be expected for the
year.
 
(2) INVENTORIES
 
     Inventories are stated at the lower of cost or market. The majority of
domestic inventories are valued using the last-in, first-out (LIFO) method and
the remaining inventories are valued using the first-in, first-out (FIFO)
method. The major components of inventory are as follows:
 
<TABLE>
<CAPTION>
                                                                 SEPTEMBER 30,      JUNE 30,
                                                                     1996             1996
                                                                 -------------      --------
        <S>                                                      <C>                <C>
        Raw materials.........................................      $28,073           27,186
        Work-in-process and finished goods....................       38,877           33,191
                                                                    -------          -------
             Totals...........................................      $66,950         $ 60,377
                                                                    =======          =======
</TABLE>
 
(3) COMMITMENTS AND CONTINGENCIES
 
     At September 30, 1996, management believes that the Company was in
compliance with its various financial covenants. Under the most restrictive
covenants of the Company's various loan agreements, principally the Revolving
Credit Agreement, $56,077 of retained earnings were not restricted at September
30, 1996 for the payment of dividends, and the ratio of current assets to
current liabilities was in excess of the minimum requirement of 1.25 to 1.
Management expects that the Company will remain in compliance with its financial
covenants in all material respects through the period ending September 30, 1997.
 
     The Company and its subsidiaries are involved in certain legal actions and
claims. In the opinion of management, any liability which may ultimately be
incurred would not materially affect the financial position or results of
operations of the Company.
 
(4) ACCOUNTS RECEIVABLE SECURITIZATION
 
     In September 1995, the Company and certain of its U.S. subsidiaries entered
into an agreement to sell, on an ongoing basis, all of their accounts receivable
to The Standard Products Funding Corporation (Funding Co.), a wholly owned
subsidiary of the Company. Accordingly, the Company and those subsidiaries,
irrevocably and without recourse, transfer all of their U.S. dollar denominated
trade accounts receivable (principally representing amounts owed by original
equipment customers in the U.S. automotive and related industries) to the
Funding Co. The Funding Co. has sold and, subject to certain conditions, may
from time to time sell an undivided interest in those receivables to the Clipper
Receivables Corporation. The Funding Co. is permitted to receive advances of up
to $50,000 for the sale of such undivided interest. On September 30, 1996,
$50,000 had been advanced to the Funding Company. Unless extended by amendment,
the agreement expires in September 1998.
 
                                        6
<PAGE>   7
 
     Proceeds from the sales of receivables have been used to reduce outstanding
borrowings under the Company's Revolving Credit Agreement and are reflected as
operating cash flows in the accompanying consolidated statement of cash flows.
Costs of the program which primarily consist of the purchasers' financing and
administrative costs, have been classified as Selling, General and
Administrative Expenses in the accompanying consolidated statement of income.
 
     The Company maintains an allowance for doubtful accounts receivable ($2,690
and $2,958 at September 30, 1996 and June 30, 1996, respectively) based on the
expected collectibility of all trade accounts receivable, including receivables
sold.
 
(5) NEW ACCOUNTING STANDARDS
 
     The Financial Accounting Standards Board (FASB) has issued Statement of
Financial Accounting Standards (SFAS) No. 121 "Accounting for the Impairment of
Long-Lived Assets and for Long-Lived Assets to Be Disposed Of." This standard
requires that long-lived assets held by and used by an entity may be reviewed
for impairment whenever events or changes in circumstances indicate that the
carrying amount of an asset may not be recoverable. SFAS No. 121 also requires
that long-lived assets to be disposed of be reported at the lower of carrying
amount or fair value less costs to sell.
 
     The FASB also issued SFAS No. 123, "Accounting for Stock-Based
Compensation" which was effective for the Company beginning July 1, 1996. SFAS
No. 123 requires expanded disclosures of stock-based compensation arrangements
with employees and encourages (but does not require) compensation cost to be
measured based on the fair value of the equity instrument awarded. Companies are
permitted, however, to continue to apply APB Opinion No. 25, which recognizes
compensation cost based on the intrinsic value of the equity instrument awarded.
The Company will continue to apply APB Opinion No. 25 to its stock based
compensation awards to employees and will disclose the required pro forma effect
on net income and earnings per share.
 
ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF RESULTS OF OPERATIONS AND
FINANCIAL CONDITION
 
(1) RESULTS OF OPERATIONS
 
     The Company's net sales for the first quarter of fiscal 1997 increased by
11.2% or $26.9 million to $265.6 million compared to the first quarter of fiscal
year 1996. This increase is primarily attributable to 1) significantly increased
volumes in North American Automotive Operations from the Company's participation
on the Ford Taurus/Sable and Chrysler minivan models, 2) revenues from the
Company's new Brazilian plant in Varginha which was not in production in the
first quarter of fiscal 1996, and 3) a 14.2% increase in sales in the Company's
Tread Rubber segment primarily attributable to the previously announced contract
with Treadco, Inc. the nation' largest independent truck-tire retreader.
 
     The Company's gross profit for the first quarter of fiscal 1997 increased
$15.9 million to $25.3 million or 9.5% of net sales, from $9.4 million or 3.9%
of net sales for the same period in fiscal 1996. The increase in gross margins
came primarily from North American Automotive operations, where increased
volumes, cost reduction programs, reduced launches from fiscal 1996 and process
improvements all contributed to improved profitability. These gains were
partially offset by continued ramp up costs at the Company's Varginha
manufacturing facility.
 
     The Company provides design and development work on behalf of its
customers. First quarter engineering and product development expense remained
flat compared to the same period of the prior year, reflecting the constant
stream of activity in this area.
 
     Selling, General and Administrative expenses increased slightly to $17.3
million over the same period of fiscal 1996. However, as a percentage of net
sales, these costs decreased from 7.2% to 6.5% for the first quarter. Charges
for the first quarter of the current year include increased costs in the
Company's Tread Rubber segment attributable to the new Treadco business. These
were partially offset by one-time expenditures in fiscal 1996 for the start-up
of the Company's new Brazilian subsidiary as well as legal and other expenses
related to the formation of the Company's subsidiary for the sale of accounts
receivable.
 
                                        7
<PAGE>   8
 
     Other income increased $0.9 million due the increase in earnings of NISCO,
the Company's 50% owned U.S. based joint venture with Nishikawa Rubber Company
of Japan. Royalty income was also up slightly over prior year levels.
 
     Interest expense decreased $0.5 million over the first quarter of fiscal
1996 due to the lower levels of debt carried by the Company. This resulted from
the use of proceeds from the sale of accounts receivable late in the first
quarter of fiscal year 1996 to pay down the company's credit lines. This was
partially offset by slightly higher U.S. borrowing rates.
 
(2) FINANCIAL CONDITION
 
     The Company's operations provided $23.5 million in cash during the first
quarter of fiscal 1997. This is $13.9 million less than the same quarter of the
prior year. The decrease is attributable to the $50 million received from the
sale of the Company's accounts receivable in the prior year (See note 4). This
was partially offset by improved operating results, a one-time benefit from the
acceleration of customer payments on receivable balances, and increased
depreciation and amortization over prior year levels. The increase in
depreciation relates primarily to the start of production in Brazil where the
Company's investment in capital equipment totaled $43.0 million in fiscal 1996.
 
     The Company's capital expenditures totaled $15.2 million, a reduction of
$1.9 million from the prior year. This decrease results form the completion of
construction of the Brazilian plant in Varginha which was still in process
during the prior year. The Company continued its investment in new technology by
upgrading its mixing capabilities in its plants in the United Kingdom and
beginning construction of a new plant in Mexico as part of a 70% owned joint
venture with the Nishikawa Rubber Company of Japan. Fiscal year capital
expenditures are expected to be approximately $65 million.
 
     The Company is party to a Revolving Credit Agreement (Credit Agreement)
with a group of banks that have committed to make available for borrowing up to
$125 million. The Credit Agreement expires in January 1999 but contains
provisions for extension provided certain requirements are satisfied. The terms
of the Credit Agreement require the Company to maintain certain financial
covenants as to net worth, leverage and working capital. At September 30, 1996,
borrowings under the agreement totaled $37 million. The Company and its
subsidiaries also have short-term lines of credit available from various banking
sources.
 
     At September 30, 1996, the Company was in compliance with the various
covenants under the agreements pursuant to which it may borrow money. Management
expects that it will remain in compliance during the coming year.
 
                                        8
<PAGE>   9
 
                           PART II. OTHER INFORMATION
 
ITEM 1. LEGAL PROCEEDINGS
 
     None.
 
ITEM 2. CHANGES IN SECURITIES
 
     None.
 
ITEM 3. DEFAULTS UPON SENIOR SECURITIES
 
     None.
 
ITEM 4. SUBMISSION OF MATTERS TO A VOTE OF SECURITY-HOLDERS
 
     The Company held its annual meeting of shareholders on October 22, 1996. At
this meeting, an election was held (i) to elect four directors to serve
three-year terms expiring at the 1999 annual meeting, and (ii) to consider a
proposal to approve the Company's 1996 Employee Stock Option Plan and to reserve
350,000 authorized but unissued Common Shares, $1 par value, for purposes of
such plan. The voting results for each item are summarized in the table below:
 
<TABLE>
<CAPTION>
                   ELECTION OF DIRECTORS:                 FOR          WITHHELD
        --------------------------------------------   ----------      ---------
        <S>                                            <C>             <C>            
        John D. Drinko..............................   15,194,169       433,019
        Curtis E. Moll..............................   15,349,828       277,360
        Malcolm R. Myers............................   15,349,628       277,560
        Theodore K. Zampetis........................   15,344,620       282,568
</TABLE>
 
<TABLE>
<CAPTION>
                                                          FOR           AGAINST       ABSTAIN  
                                                       ----------      ---------      -------- 
        <S>                                            <C>             <C>            <C>      
        APPROVAL OF STOCK OPTION PLAN:..............   15,354,168       193,316        91,053 
</TABLE>
 
ITEM 5. OTHER INFORMATION
 
     None.
 
ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K
 
     (a) Exhibits:
 
<TABLE>
<CAPTION>
     EXHIBIT NO.
    UNDER REG. S-K      FORM 10-Q
       ITEM 601        EXHIBIT NO.                              DESCRIPTION
    --------------     ------------     ------------------------------------------------------------
    <C>                <C>              <S>
           4                 4          Third Agreement of Amendment, dated as of October 25, 1996,
                                        among The Standard Products Company, as borrower, and
                                        National City Bank as agent for itself, KeyBank National
                                        Association, Comerica Bank and NBD Bank.
          27                27          Financial Data Schedule
</TABLE>
 
     (b) Reports on Form 8-K:
 
     None.
 
                                        9
<PAGE>   10
 
                                   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.
 
                                          THE STANDARD PRODUCTS COMPANY
 
Dated: November 14, 1996                        /s/ DONALD R. SHELEY, JR.
                                          --------------------------------------
                                                  Donald R. Sheley, Jr.
                                                  Vice President-Finance
                                                 Chief Financial Officer
 
                                                  /s/ BERNARD J. THEISEN
                                          --------------------------------------
                                                    Bernard J. Theisen
                                            Corporate Controller and Assistant
                                                        Secretary
                                               Principal Accounting Officer
 
                                       10
<PAGE>   11
                                EXHIBIT INDEX



<TABLE>
<CAPTION>
EXHIBIT NO.                              DESCRIPTION
-----------                              -----------
<S>                              <C>
     4                           Third Agreement of Amendment

    27                           FINANCIAL DATA SCHEDULE

</TABLE>