<PAGE>   1

================================================================================

                                  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, 1998

                                       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: 1-2917

                          THE STANDARD PRODUCTS COMPANY
             (Exact Name of Registrant as Specified in Its Charter)


            OHIO                                        34-0549970
(State or Other Jurisdiction of                       (IRS Employer
Incorporation or Organization)                      Identification No.)

                                                        
                             2401 SOUTH GULLEY ROAD
                            DEARBORN, MICHIGAN 48124
               (Address of Principal Executive Offices)(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 25, 1998 WAS
                              16,078,842 SHARES.



================================================================================

                        This report consists of 13 pages.


<PAGE>   2


                          THE STANDARD PRODUCTS COMPANY
                          QUARTERLY REPORT ON FORM 10-Q

                                TABLE OF CONTENTS

<TABLE>
<CAPTION>



PART I.  FINANCIAL INFORMATION                                                            PAGE
<S>      <C>                                                                                <C>
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

Item 2.  Management's Discussion and Analysis of Results of Operations and 
         Financial Condition................................................................9


PART II. OTHER INFORMATION

Item 1.  Legal Proceedings................................................................ 11

Item 2.  Changes in Securities............................................................ 11

Item 3.  Defaults upon Senior Securities.................................................. 11

Item 4.  Submission of Matters to a Vote of Security-Holders.............................. 12

Item 5.  Other Information................................................................ 12

Item 6.  Exhibits and Reports on Form 8-K................................................. 12





SIGNATURES  ...............................................................................13
</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 1999" refers to the period
beginning July 1, 1998 and ending June 30, 1999).




                                       2


<PAGE>   3


PART I. FINANCIAL INFORMATION

ITEM 1. FINANCIAL STATEMENTS



             THE STANDARD PRODUCTS COMPANY AND SUBSIDIARY COMPANIES
                      CONSOLIDATED STATEMENTS OF OPERATIONS
                       FOR THE PERIODS ENDED SEPTEMBER 30,
                                   (UNAUDITED)
                    (THOUSANDS OF DOLLARS, EXCEPT SHARE DATA)

<TABLE>
<CAPTION>


                                                                  THREE MONTHS ENDED SEPTEMBER 30,
                                                                  --------------------------------
                                                                      1998               1997
                                                                      ----               ----
<S>                                                               <C>                <C>
Net Sales......................................................   $   231,815        $   246,173

Cost of Goods Sold:
  Materials, wages and other manufacturing costs...............       198,831            208,512
  Research, engineering and development expenses...............        10,597             10,424
                                                                  -----------        -----------
                                                                      209,428            218,936
                                                                  -----------        -----------

    Gross income...............................................        22,387             27,237

Selling, General and Administrative Expenses ..................        18,173             17,323
                                                                  -----------        -----------
    Operating..................................................         4,214              9,914
                                                                  -----------        -----------
Income.........................................................


Other (Income) Expense:
  Royalty and dividend income..................................          (288)              (218)
  Interest expense.............................................         2,973              2,956
  Other, net...................................................           851              2,604
                                                                  -----------        -----------
                                                                        3,536              5,342
                                                                  -----------        -----------

Income before Taxes on Income..................................           678              4,572
Provision for Taxes on Income..................................           244              1,761
                                                                  -----------        -----------

  Net Income...................................................   $       434        $     2,811
                                                                  ===========        ===========

Earnings Per Common Share:
  Basic........................................................   $      0.03        $      0.17
                                                                  ===========        ===========
  Diluted......................................................   $      0.03        $      0.17
                                                                  ===========        ===========

Weighted average shares outstanding (in thousands):
  Basic........................................................        16,698             16,826
                                                                  ===========        ===========
  Diluted......................................................        16,747             16,879
                                                                  ===========        ===========

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>

                                                                   (UNAUDITED)
                                                                    SEPT. 30,         JUNE 30,
                                                                      1998              1998
                                                                  --------------    -------------
ASSETS
<S>                                                               <C>               <C>
Current Assets:
  Cash and cash equivalents...................................    $        --       $     1,625
  Receivables, less allowances of $4,175 at September 30 and
    $3,949 at June 30 (Note 4)................................        150,370           151,535
   Inventories (Note 2).......................................         61,563            61,139
   Prepaid insurance, taxes, etc..............................         30,537            25,319
                                                                  -----------       -----------
     Total current assets.....................................        242,470           239,618

Property, Plant and Equipment, at cost........................        650,136           624,188
 Less - Accumulated depreciation..............................       (307,268)         (293,836)
                                                                  -----------       -----------
                                                                      342,868           330,352

Goodwill, net.................................................         79,686            63,617
Other Assets..................................................         58,106            50,659
                                                                  -----------       -----------
                                                                  $   723,130       $   684,246
                                                                  ===========       ===========
LIABILITIES AND SHAREHOLDERS' EQUITY 
Current Liabilities:
 Short-term notes payable.....................................    $    25,854       $    14,994
 Current maturities of long-term debt.........................         39,762            14,031
 Accounts payable and accrued expenses........................        173,038           183,646
 Dividend payable.............................................          2,770             2,869
                                                                  -----------       -----------

  Total current liabilities...................................        241,424           215,540

Long-term Debt, net of current maturities.....................        117,086            92,457

Other Postretirement Benefits.................................         24,951            24,362

Deferred Income Taxes and Other Credits.......................         55,157            51,715

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,
    16,921,892 shares issued and 16,291,792 shares outstanding at 
    September 30 and 16,877,693 shares issued and outstanding
    at June 30................................................         16,922            16,878
  Paid-in capital.............................................         99,657            99,462
  Common stock held in Treasury, 630,100 shares at cost.......        (16,027)               --
  Retained earnings...........................................        200,263           202,599
  Accumulated other comprehensive income......................        (16,303)          (18,767)
                                                                  -----------       -----------
   Total shareholders' equity.................................        284,512           300,172
                                                                  -----------       -----------
                                                                  $   723,130       $   684,246
                                                                  ===========       ===========
</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,
                                                                  --------------------------------
                                                                      1998              1997
                                                                  --------------    --------------
<S>                                                               <C>               <C>
Cash Flows from Operating Activities:
Net income ...................................................    $       434       $     2,811
Adjustments to reconcile net income to net cash provided by 
(used for)
  operating activities:
  Depreciation and amortization...............................         13,325            15,410
  Deferred taxes and other credits............................           (105)             (729)
  Effect of changes in foreign currency.......................         (1,013)            1,804
  Other ......................................................         (4,887)              691
    Net changes in assets and liabilities:
       Receivables............................................          4,058            12,418
       Inventories............................................            412             4,990
       Accounts payable and accrued expenses..................        (13,019)          (19,827)
       Other current assets and liabilities...................         (6,797)              554
                                                                  -----------       -----------
           Net cash provided by (used by) operating activities         (7,592)           18,122

Cash Flows from Investing Activities:
  Purchase of property, plant and equipment, net..............        (15,884)          (15,325)
  Investment in affiliates and nonconsolidated entities.......           (969)             (180)
  Cash paid for acquisitions..................................        (19,450)               --
                                                                  -----------       -----------
        Net cash used by investing activities.................        (36,303)          (15,505)

Cash Flows from Financing Activities:
  Proceeds of long-term borrowings............................         50,239                --
  Repayment of long-term borrowings ..........................            (97)             (289)
  Net increase (decrease) in short-term borrowings............         10,860            (1,208)
  Stock repurchase............................................        (16,027)               --
  Cash dividends..............................................         (2,770)           (2,864)
                                                                  -----------       -----------
        Net cash provided by (used by) financing activities...         42,205            (4,361)

Effect of exchange rate changes on cash.......................             65               205
                                                                  -----------       -----------

Net decrease in cash and cash equivalents.....................         (1,625)           (1,539)

Cash and cash equivalents at the beginning of the period......          1,625             6,972
                                                                  -----------       -----------

Cash and cash equivalents at the end of the period............    $        --       $     5,433
                                                                  ===========       ===========
</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, 1998

                    (AMOUNTS IN THOUSANDS, EXCEPT SHARE DATA)





(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, 1998 and June 30, 1998,
and the results of its operations for the three months ended September 30, 1998
and 1997 and cash flows for the three months ended September 30, 1998 and 1997.
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, 1998. 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, 1998    June 30, 1998
                                                        ------------------    -------------
    <S>                                                     <C>                <C>
    Raw materials...................................        $    26,268        $    24,898
    Work-in-process and finished goods..............             35,295             36,241
                                                            -----------        -----------
        Totals......................................        $    61,563        $    61,139
                                                            ===========        ===========
</TABLE>

(3)     COMMITMENTS AND CONTINGENCIES

        At September 30, 1998, the Company was in compliance with these various
financial covenants. Under the most restrictive of the revised covenants of the
Company's various loan agreements, principally the bank revolving credit
agreement, $32,728 of retained earnings were not restricted at September 30,
1998 for the payment of dividends. Management expects that the Company will
remain in compliance with these financial covenants through the period ending
September 30, 1999.

        The Company and its subsidiaries are involved in certain legal actions
and claims. In the opinion of management, any liability that 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, transferred 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. At
September 30, 1998, $50,000 had been advanced to the Funding Company. This
agreement has been extended to November 2000.



                                       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 accounts receivable ($4,175 and
$3,949 at September 30, 1998 and June 30, 1998, respectively) based on the
expected collectibility of all trade accounts receivable, including receivables
sold.

 (5)    NEW ACCOUNTING STANDARDS

        The FASB issued SFAS No. 131, "Disclosures about Segments of an
Enterprise and Related Information." This standard requires extensive disclosure
of operating segments based on the "management approach." This approach
organizes segments within a company for making operating decisions and assessing
performance. Reportable segments can be based on products and services,
geography, legal structure or any other manner in which management disaggregates
the company. This Statement requires reporting segment profit or loss, certain
specific revenue and expense items and segment assets. It also requires
reconciliations of total segment revenues, total segment profit or loss, total
segment assets and other amounts disclosed for segments to corresponding amounts
reported in the Consolidated Financial Statements. Restatement of comparative
information for earlier periods presented is required in the initial year of
application. Interim information is not required until the second year of
application, at which time comparative information is required.

        The FASB has also issued SFAS No. 132, "Employer's Disclosures about
Pensions and Other Postretirement Benefits." This standard revises employers'
disclosures on pension and other postretirement benefit plans. The objective of
the statement is to standardize the disclosure requirements and report
additional information on changes in the benefit obligations and fair value of
plan assets.

        SFAS Nos. 131 and 132 are effective for fiscal years beginning after
December 15, 1997.

        The FASB also issued SFAS No. 133, "Accounting for Derivative
Instruments and Hedging Activities." This standard provides a comprehensive and
consistent standard for the recognition and measurement of derivatives and
hedging activities. This standard is effective for fiscal years beginning after
June 15, 1999.

        The Company has not determined the impact that the adoption of these new
standards will have on its Consolidated Financial Statements or disclosures.

(6)     EARNINGS PER SHARE

        The Company has adopted the provisions of SFAS No. 128, "Earnings per
Share." The information required by this pronouncement is presented on the face
of the Company's "Consolidated Statements of Operations" found on page 3 of this
document. A reconciliation of the numerators and denominators of the basic and
diluted earnings per share are as follows:

<TABLE>
<CAPTION>

                                               THREE MONTHS ENDED
                                      --------------------------------------
                                      SEPTEMBER 30, 1998     SEPTEMBER 30,    
                                      ------------------     -------------
                                                                 1997
                                                                 ----
         <S>                               <C>                <C>
         Net Income.................        $    434           $  2,811
                                            --------           --------
         Basic:
              Basic Shares..........          16,698             16,826
                                            --------           --------
              Basic EPS.............        $   0.03           $   0.17
                                            --------           ---------

         Diluted:
              Basic Shares..........          16,698             16,826
              Stock Options.........              49                 53
                                            --------           --------
                                              16,747             16,879
                                            --------           --------

         Diluted EPS................        $   0.03           $   0.17
                                            --------           --------
</TABLE>



                                       7

<PAGE>   8


(7)     COMPREHENSIVE INCOME

        Effective July 1, 1998, the Company adopted SFAS No. 130, "Reporting
Comprehensive Income," which establishes standards for the display of
comprehensive income for financial statement purposes. Comprehensive income is
defined as all changes in a company's net assets except changes resulting from
transactions with shareholders. It differs from traditionally defined net income
in that certain items recorded in shareholders' equity become part of
comprehensive income.

        Comprehensive income consists of the following:

<TABLE>
<CAPTION>

                                                             THREE MONTHS ENDED
                                                  ------------------------------------------
                                                   SEPTEMBER 30, 1998   SEPTEMBER 30, 1997     
       <S>                                              <C>                   <C>
       Net Income............................           $     434             $   2,811
                                                        ---------             ---------
       Other comprehensive income:
            Foreign currency translation                    2,464                   402
              adjustment.....................
            Minimum pension liability 
              adjustment.....................               --                     --
                                                        ---------             ---------
       Other comprehensive income............               2,464                   402
                                                        ---------             ---------
       Comprehensive income..................           $   2,898             $   3,213
                                                        =========             =========
</TABLE>




                                       8


<PAGE>   9


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 1999 decreased
by 5.8%, or $14.4 million, to $231.8 million compared to the first quarter of
fiscal year 1998. Sales for the Company's Transportation Equipment segment
totaled $197.9 million for the first quarter of fiscal 1999 compared with $213.3
million for the same period last year, a decrease of $15.5 million, or 7.3%. The
overall decline is primarily attributable to deteriorating economic conditions
in Brazil and lower volumes in North American automotive operations. Sales for
the Company's Tread Rubber segment increased 3.4% to $33.9 million. This
increase is attributable to Oliver Rubber's new agreement with Michelin North
America, Inc. to provide for the extrusion and pressing of tread rubber for
resale.

        Sales of the Company's North American automotive operations decreased
$16.3 million, or 13.0%, as a result of several factors. The United Auto Workers
("UAW") strike against General Motors, which continued into the first quarter,
reduced sales by an estimated $4.4 million. Translation losses related to a
weaker Canadian dollar accounted for another $4.4 million of the sales decline.
This group also experienced sales volume losses of $3.7 million related to
programs for which it was not the carryover supplier, particularly the Jeep(R)
Grand Cherokee. Automotive sales in Europe increased $2.5 million, or 5.4%, due
primarily to increased sales volumes as a result of new platform launches,
principally the Opel Astra and Toyota Avensis. Currency translations from the
strengthened French franc and British pound against the U.S. dollar contributed
an additional $0.9 million in sales. Sales at the Company's Brazilian
subsidiaries declined substantially to $13.4 million, a decrease of $6.3
million, or 32.0% over the first quarter of last year. This decrease is
primarily attributable to lower volumes for the Fiat Palio and other platforms
as a result of reduced production by South American OEMs. The production decline
was caused by deteriorating Brazilian economic conditions, which has reduced the
demand for high price items such as automobiles. These conditions appear likely
to continue for the remainder of the fiscal year 1999 and the Company presently
anticipates that lower sales volumes and reduced earnings from its Brazilian
subsidiary will continue for the remainder of the year. Sales at the Company's
Holm Industries subsidiary increased by approximately $5.3 million from the same
period last year. Approximately $2.9 million of this increase resulted from the
addition of the recently acquired OEM/Miller business unit and the remainder
resulted from increased volumes on appliance and air conditioning sealing
components.

        Based on published industry data, management believes that car and light
truck production in the United States and Canada decreased by approximately 3.0%
during the quarter when compared to the same period in the prior year. Car
production was flat, while light truck production decreased by 6.0%. Several key
vehicles for which the Company supplies components had weakened sales during the
quarter, including the Ford Escort and Windstar and the Chevrolet Lumina.

        Gross income for the Company's first quarter of fiscal 1999 decreased
$4.9 million to $22.4 million, or 9.7% of net sales, from $27.2 million, or
11.1% of net sales for the same period in fiscal 1998. Principal factors
affecting the decline were significantly lower sales volumes in North America
and Brazil, where the level of fixed costs creates exposure to the company in
periods of weakened sales volumes. In addition, launch costs of approximately
$3.1 million in Europe associated with numerous new platforms being launched
simultaneously reduced profitability.

        Research, engineering and development expenses for the quarter increased
$0.2 million, to $10.6 million over the same period in fiscal 1997. The increase
is primarily attributable to a decrease in recoverable engineering costs from
original equipment manufacturers ("OEMs").

        Selling, general and administrative expenses for the first quarter
increased $0.9 million, or 4.9%, to $18.2 million. The increases were
attributable to increased professional fees, facility costs, depreciation and
the addition of OEM/Miller.




                                       9


<PAGE>   10




        Other income and expense for the current quarter was $3.5 million in
expense, a decrease of $1.8 million over the same period a year ago. This
decrease is primarily attributable to improved results at NISCO, the Company's
joint venture with Nishikawa Rubber Company of Japan, which improved by $1.4
million over the same period last year and gains of $0.3 on fixed asset
dispositions. Interest expense was flat compared to the same period a year ago
as increased interest expense from higher borrowing in Europe was offset by
lower borrowing levels in the United States.

        The Company's tax provision for the first quarter of fiscal 1999 of $0.2
million represents an effective rate of 36% compared to 38.5% for the same
period a year ago. The change is primarily due to utilization of U.S. tax
credits.

(2)     FINANCIAL CONDITION

        Cash used by operations for the first three months of fiscal 1999 was
$7.6 million. This represents a decrease from the same period in fiscal 1998 of
$25.7 million. This decrease was the result of several factors including
accounts receivable, prepaid items, tooling and inventory. The change in
accounts receivables is directly attributable to the decline in sales levels and
associated collections when compared to prior year levels, while the change in
prepaids and tooling were due to timing of payments with suppliers and
customers. The change in inventory resulted from levels remaining flat in the
current year after declining in the previous year. The prior year decline was
due to lowering of inventory as a result of U.S. plant closings.

        Capital spending for the first three months of fiscal 1998 totaled $15.9
million, an increase of $0.6 million over the same period last year. The Company
expects capital spending for fiscal 1999 to approximate $65.0 million. This
includes capital required in connection with the addition of equipment at its
Mexican facility as it ramps up to full production, expenditures required in
support of the new General Motors Silverado and Sierra truck platforms, and the
upgrade of facilities in England related to the introduction of various new
platforms. The Company has also invested $19.5 million on acquisitions in the
first quarter of the current year.

        Cash generated from financing activities resulted in a net inflow of
$42.2 million for the first quarter of the fiscal year. The funds were generated
through borrowings under the Company's revolving credit line and other
short-term financing arrangements. These funds were used to fund an acquisition,
reacquire shares of the Company's stock, provide for working capital, and pay
dividends. At September 30, 1998, debt represented 39.1% of total capitalization
compared with 28.8% at June 30, 1998.

        The Company has determined that the functional currency of its Brazilian
and Mexican subsidiaries is the U.S. dollar. Accordingly, the results for these
operations have been translated utilizing a remeasurement process prescribed by
Statement of Financial Accounting Standard ("SFAS") No. 52. The criteria for
determining highly inflationary status and the functional currency of an
operation are detailed in SFAS No. 52. The Company will continue to translate
its results using the remeasurement process until the criteria supporting a U.S.
dollar functional currency are no longer met.

(3)     YEAR 2000

        The "Year 2000" problem relates to computer systems that have time and
date-sensitive programs that were designed to read years beginning with "19,"
but may not properly recognize the year 2000. If a computer system or software
application used by the Company or a third party dealing with the Company fails
because of the inability of the system or application to properly read the year
"2000," the results could conceivably have a material adverse effect on the
Company.

        The Company provided an extensive description of its Year 2000 plans and
progress to date as part of its Management Discussion and Analysis ("MD&A") in
its Form 10-K for the fiscal year ended June 30, 1998, which was filed in
September 1998. The Company continues to make progress on its plan in accordance
with the timetable described in that MD&A. Based on this progress, management
believes that a contingency plan with respect to its information technology and
production processes is not necessary at this time. In addition, the Company has
not encountered any specific problems with any of its suppliers that would
require development of a contingency plan.




                                       10

<PAGE>   11


        The Company believes that its program to monitor the compliance of its
suppliers with Year 2000 requirements will minimize the risks associated with
noncompliance. Management believes that the cost of Year 2000 compliance for
it's information and production systems is not likely to be material to its
consolidated results of operations and financial position.

        Although the Company has made progress in identifying its Year 2000
problems, and believes this issue is not likely to pose a significant problem
for it, there can be no absolute assurance that the Company and all of its
vendors and suppliers will identify and remediate in a timely fashion all
potential Year 2000 issues.

(4)     CAUTIONARY STATEMENT FOR PURPOSES OF "SAFE HARBOR" UNDER THE PRIVATE 
SECURITIES REFORM ACt OF 1995

        Certain statements in this Management's Discussion and Analysis, the
attached Consolidated Financial Statements, in the Company's press releases and
in oral statements made by or with the approval of an authorized executive
officer of the Company, constitute "forward-looking statements," as that term is
defined under the Private Securities Litigation Reform Act of 1995. These may
include statements projecting, forecasting or estimating Company performance and
industry trends. The achievement of the projections, forecasts or estimates is
subject to certain risks and uncertainties. Actual results and events may differ
materially from those projected, forecasted or estimated. The applicable risks
and uncertainties include general economic and industry conditions that affect
all international businesses, as well as matters that are specific to the
Company and the markets it serves. In addition, please see the "Year 2000"
section for a description of the risks and uncertainties associated with this
issue.

        General risks that may impact the achievement of such forecasts include
compliance with new laws and regulations; significant raw material price
fluctuations; currency exchange rate fluctuations; limits on repatriation of
funds; and political uncertainties. Specific risks to the Company include risk
of recession in the economies in which its products are sold, especially in
emerging markets where recent currency weakness may lead to recessionary
conditions; the concentration of a substantial percentage of the Company's sales
with a few major OEM customers; labor relations at the Company, its customers
and its suppliers; competition in pricing and new product development from
larger companies with substantial resources; and continued globalization of the
automotive supply base resulting in new competition in certain locations.


PART II.  OTHER INFORMATION

Item 1.     Legal Proceedings

            None.

Item 2.     Changes in Securities

            None.

Item 3.     Defaults upon Senior Securities

            None.



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<PAGE>   12


Item 4.    Submission of Matters to a Vote of Security Holders

           The Company held its annual meeting of shareholders on October 20,
           1998. At this meeting, an election was held to elect five directors
           to serve three-year terms expiring at the 2001 annual meeting. The
           voting results for each item are summarized in the table below:

           ELECTION OF DIRECTORS:           FOR            WITHHELD           
                                            ---            --------
           John Doddridge               13,806,533        1,046,088
           Leigh H. Perkins             14,575,049          277,572
           Alfred M. Rankin, Jr.        14,573,895          278,726
           John D. Sigel                13,631,970        1,220,651
           W. Hayden Thompson           14,575,049          277,572

Item 5.     Other Information

            None.

Item 6.     Exhibits and Reports on Form 8-K

            (a)  Exhibits

            Exhibit No.
            Under Reg. S-K   Form 10-Q
               Item 601      Exhibit No.         Description   
               --------      -----------    -----------------------
                 27             27          Financial Data Schedule

            (b)  Reports on Form 8-K

            None.




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<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.



                                                   THE STANDARD PRODUCTS COMPANY




      Dated:   November 13, 1998            by       /s/ Donald R. Sheley, Jr. 
                                                  ------------------------------
                                                         Donald R. Sheley, Jr.
                                                         Vice President, Finance
                                                         Chief Financial Officer


                                                     /s/ Bernard J. Theisen 
                                                  ------------------------------
                                                         Bernard J. Theisen
                                                         Corporate Controller
                                                    Principal Accounting Officer







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<PAGE>   14
                               INDEX TO EXHIBITS


EX-27                                                    FINANCIAL DATA SCHEDULE