<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 MARCH 31, 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 MAY 1, 1998
WAS 16,864,667 SHARES.






                        This report consists of 12 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..............   8


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................................................  11

Item 5.   Other Information..................................................................................  11

Item 6.   Exhibits and Reports on Form 8-K...................................................................  11





SIGNATURES    ...............................................................................................  12


</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 1998" refers to the period
beginning July 1, 1997 and ending June 30, 1998).


 
                                      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 MARCH 31,
                                   (UNAUDITED)
                  (THOUSANDS OF DOLLARS, EXCEPT PER SHARE DATA)



<TABLE>
<CAPTION>
                                                              THREE MONTHS                   NINE MONTHS
                                                       ---------------------------   ---------------------------
                                                           1998            1997          1998            1997
                                                           ----            ----          ----            ----
<S>                                                     <C>            <C>            <C>            <C>      
Net Sales ...........................................   $ 277,942      $ 281,774      $ 806,660      $ 814,005

Cost of Goods Sold:
   Materials, wages and other manufacturing costs ...     220,429        231,611        661,141        685,169
   Research, engineering and development expenses ...      11,425         11,402         32,889         33,087
                                                        ---------      ---------      ---------      ---------
                                                          231,854        243,013        694,030        718,256
                                                        ---------      ---------      ---------      ---------

     Gross income ...................................      46,088         38,761        112,630         95,749

Selling, General and Administrative Expenses ........      19,723         17,569         56,879         51,773
Non-recurring charge ................................          --         17,661             --         17,661
                                                        ---------      ---------      ---------      ---------
    Operating Income ................................      26,365          3,531         55,751         26,315
                                                        ---------      ---------      ---------      ---------

Other (Income) Expense:
   Royalty and dividend income ......................        (146)          (123)          (405)          (566)
   Interest expense .................................       3,169          3,024          9,327          9,752
   Other, net .......................................       1,997            351          6,063           (415)
                                                        ---------      ---------      ---------      ---------
                                                            5,020          3,252         14,985          8,771


Income before Taxes on Income .......................      21,345            279         40,766         17,544
Provision for Taxes on  Income ......................       7,786           (236)        15,635          9,289
                                                        ---------      ---------      ---------      ---------

   Net Income .......................................   $  13,559      $     515      $  25,131      $   8,255
                                                        =========      =========      =========      =========

Earnings Per Common Share:


Basic ...............................................   $    0.80      $    0.03      $    1.49      $    0.49
                                                        =========      =========      =========      =========


Diluted .............................................   $    0.80      $    0.03      $    1.48      $    0.49
                                                        =========      =========      =========      =========

Weighted average shares outstanding (in thousands):


Basic ...............................................      16,854         16,808         16,843         16,802
                                                        =========      =========      =========      =========


Diluted .............................................      16,987         16,829         16,943         16,830
                                                        =========      =========      =========      =========

Dividends declared per share ........................   $    0.17      $    0.17      $    0.51      $    0.51
                                                        =========      =========      =========      =========
</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)
                                                                                MARCH 31,        JUNE 30,
                                                                                  1998            1997
                                                                              -----------     -----------
ASSETS
Current Assets:
<S>                                                                            <C>            <C>      
   Cash and cash equivalents .............................................     $  11,756      $   6,972
   Receivables, less allowances of $3,782 at March 31 and $2,863 at
     June 30 (Note 4) ....................................................       146,155        174,696
   Inventories (Note 2) ..................................................        64,117         66,633
   Prepaid insurance, taxes, etc .........................................        32,551         23,685
                                                                               ---------      ---------
      Total current assets ...............................................       254,579        271,986

Property, Plant and Equipment, at cost ...................................       611,051        583,614
  Less - Accumulated depreciation ........................................      (298,841)      (280,608)
                                                                               ---------      ---------
                                                                                 312,210        303,006

Goodwill, net ............................................................        63,822         66,169
Other Assets .............................................................        53,778         50,698
                                                                               ---------      ---------
                                                                               $ 684,389      $ 691,859
                                                                               =========      =========
LIABILITIES AND SHAREHOLDERS' EQUITY 
Current Liabilities:
  Short-term notes payable ...............................................     $  23,179      $  19,645
  Current maturities of long-term debt ...................................         1,090          1,289
  Accounts payable and accrued expenses ..................................       188,368        201,629
  Dividend payable .......................................................         2,866          2,858
                                                                               ---------      ---------

   Total current liabilities .............................................       215,503        225,421

Long-term Debt, net of current maturities ................................       105,459        121,804

Other Postretirement Benefits ............................................        26,645         24,953

Deferred Income Taxes and Other Credits ..................................        52,294         51,324

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, 16,860,042 shares at March 31 and
     16,809,723 at June 30 ...............................................        16,860         16,810
   Paid-in capital .......................................................        99,106         98,066
   Retained earnings .....................................................       187,156        170,620
   Foreign currency translation adjustments ..............................       (14,365)       (12,870)
   Minimum pension liability .............................................        (4,269)        (4,269)
                                                                               ---------      ---------
    Total shareholders' equity ...........................................       284,488        268,357
                                                                               ---------      ---------
                                                                               $ 684,389      $ 691,859
                                                                               =========      =========
</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>
                                                                          NINE MONTHS ENDED MARCH 31,
                                                                          ---------------------------
                                                                             1998           1997
                                                                           ---------     ----------
Cash Flows from Operating Activities:
<S>                                                                        <C>           <C>     
Net income ...........................................................     $ 25,131      $  8,255
Adjustments to reconcile net income to net cash provided by (used for)
   operating activities:
   Depreciation and amortization .....................................       43,455        45,461
   Deferred taxes and other credits ..................................        1,064         1,775
   Effect of changes in foreign currency .............................         (914)         (955)
   Other .............................................................       (2,177)          (20)
   Net changes in assets and liabilities:
      Receivables ....................................................       28,541        18,345
      Inventories ....................................................        2,456        (7,331)
      Accounts payable and accrued expenses ..........................      (13,262)       (6,099)
      Other current assets and liabilities ...........................       (7,370)      (10,069)
                                                                           --------      --------
            Net cash provided by operating activities ................       76,924        49,362

Cash Flows from Investing Activities:
   Purchase of property, plant and equipment, net ....................      (49,674)      (39,573)
   Investment in affiliates and nonconsolidated entities..............       (1,307)         (150)
                                                                           --------      --------

         Net cash used by investing activities .......................      (50,981)      (39,723)

Cash Flows from Financing Activities:
   Proceeds of long-term borrowings ..................................       12,418        18,005
   Repayment of long-term borrowings .................................      (28,666)      (32,533)
   Net increase (decrease) in short-term borrowings ..................        3,534        15,625
   Cash dividends ....................................................       (8,595)       (8,571)
                                                                           --------      --------
         Net cash used by financing activities .......................      (21,309)       (7,474)

Effect of exchange rate changes on cash ..............................          150           565
                                                                           --------      --------

Net increase in cash and cash equivalents ............................        4,784         2,730

Cash and cash equivalents at the beginning of the period .............        6,972             0
                                                                           --------      --------

Cash and cash equivalents at the end of the period ...................     $ 11,756      $  2,730
                                                                           ========      ========
</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

                                 MARCH 31, 1998

                  (AMOUNTS IN THOUSANDS, EXCEPT PER 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 March 31, 1998 and June 30, 1997, the
results of its operations for the three and nine months ended March 31, 1998 and
1997, and cash flows for the nine months ended March 31, 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, 1997. Results for
interim periods are not necessarily indicative of those to be expected for the
year. Certain reclassifications have been made to prior year amounts to conform
with current year presentation.

(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>
                                            March 31, 1998  June 30, 1997
                                            --------------  -------------
<S>                                            <C>              <C>    
   Raw materials .......................       $25,532          $29,069
   Work-in-process and finished goods...        38,585           37,564
                                               -------          -------
       Totals ..........................       $64,117          $66,633
                                               =======          =======
</TABLE>

(3)      COMMITMENTS AND CONTINGENCIES

         On September 26, 1997, the Company entered into a $225 million,
five-year revolving credit agreement with a syndicate of seven banks. The new
agreement replaces the Company's $125 million credit agreement that was to
mature in January 1999. The agreement requires the Company to maintain certain
financial ratios and covenants as to net worth and leverage. The initial
interest rate charged under this agreement was LIBOR plus 0.225%, plus an annual
facility fee of 0.125% on the total commitment. At March 31, 1998, the Company
was in compliance with these various financial covenants. Under the most
restrictive covenants of the Company's various loan agreements, principally the
new Credit Agreement, $68,918 of retained earnings were not restricted at March
31, 1998 for the payment of dividends. Management expects that the Company will
remain in compliance with these financial covenants through the period ending
March 31, 1999.

         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.



                                       6

<PAGE>   7


(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
March 31, 1998, $50,000 had been advanced to the Funding Company. This
agreement, which was to expire September 1998, was extended through October
2000.

         Proceeds from the sales of receivables have been used to reduce
outstanding borrowings under the Company's Revolving Credit Agreement. 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 ($3,782 and
$2,863 at March 31, 1998 and June 30, 1997, 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. 130, "Reporting Comprehensive Income."
This standard establishes guidelines for the display of comprehensive income for
financial statement purposes. The objective of the statement is to report a
measure of all changes in equity of an enterprise that result from transactions
and other economic events of the period other than transactions with owners.

         The FASB also 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. Both standards are effective for fiscal years beginning after
December 15, 1997.

(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                     NINE MONTHS
                            --------------------------      ----------------------------
                              1998             1997            1998              1997
                              ----             ----            ----              ----

<S>                         <C>              <C>              <C>              <C>    
Net Income                  $13,559          $   515          $25,131          $ 8,255
                            -------          -------          -------          -------
Basic:
     Basic Shares            16,854           16,808           16,843           16,802
                            -------          -------          -------          -------
     Basic EPS              $  0.80          $  0.03          $  1.49          $  0.49
                            -------          -------          -------          -------

Diluted:
     Basic Shares            16,854           16,808           16,843           16,802
     Stock Options              133               21              100               28
                            -------          -------          -------          -------
                             16,987           16,829           16,943           16,830
                            -------          -------          -------          -------
Diluted EPS                 $  0.80          $  0.03          $  1.48          $  0.49
                            -------          -------          -------          -------
</TABLE>



                                       7
<PAGE>   8

 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 third quarter of fiscal 1998 decreased
by $3.8 million, or 1.4%, to $277.9 million, compared to the third quarter of
fiscal year 1997. Sales for the Company's Transportation Equipment segment
totaled $247.0 million in this year's third quarter, versus $251.7 million for
the same period last year. The sales decline was the result of general volume
decreases in the Company's North American and European automotive groups, and
currency translation losses arising from operations in Canada and France. In
North America, sales decreased $7.1 million to $146.6 million, as volumes were
down $8.3 million and translation losses on a weakened Canadian dollar
diminished sales another $2.8 million. The volume decrease was the result of
lower sales on several different automobile platforms, none of which were
individually significant. European automotive operations experienced a sales
decrease of $1.9 million, or 3.1% to $59.6 million, primarily as a result of
translation losses on the weakened French franc, which totaled $3.1 million, and
customer price reductions of $0.8 million. This decline was partially offset by
improved volumes of $1.5 million in the United Kingdom on SAAB and Rover models,
and $0.9 million in France on several new Renault platforms. The Company's
overall sales decrease was partially offset by improvements at its Brazilian
subsidiary, where sales increased $2.9 million, or 20.1% over prior year levels.
This increase is largely attributable to volume gains, on the Fiat Palio
platform. The weakened Brazilian currency has not had a significant impact on
operations as production releases from Fiat remain high. Sales at the Company's
Holm Industries subsidiary were 8.8% higher than in the same period last year,
primarily due to higher volumes from existing customers. Sales by the Company's
Tread Rubber segment increased 2.8% to $31.0 million, reflecting increased
equipment sales as well as improved volumes on the segment's precure products.

         Based on published industry data, management believes that car and
light truck production in the United States and Canada increased by
approximately 0.7% during the quarter when compared to the same period in the
prior year. Car production decreased by 4.6%, while light truck production
increased by approximately 6.2%.Year-to-date car production is down 2.6% while
light truck production has increased by 8.9%. Certain key vehicles for which the
Company supplies components, such as the Chrysler minivan and Ford F-Series
pickup had weakened build rates during the quarter, while others such as the
Ford Taurus, Chrysler Neon, and Jeep(R) Cherokee experienced increases.

         For the first nine months of fiscal 1998, sales of the Transportation
Equipment segment were $709.0 million, or 0.9% below prior year levels. This
reduction is attributable to North America and European operations where
year-to-date sales have decreased by $26.5 million, or 4.3%. The principal cause
of this decrease is translation losses from the Canadian dollar and French Franc
which weakened against the U.S. dollar. Volume decreases in North America on the
Ford F-series truck platform also contributed to the decline. This decrease was
partially offset by Renault volume increases in France of $6.8 million and
substantial year-over-year volume increases in Brazil of 42.3% or $17.3 million,
primarily as a result of increased production of the Fiat Palio. In addition,
sales to existing customers at Holm Industries increased by 6.2%. Sales in the
Tread Rubber segment decreased 1.1%, to $97.6 million, from the same period in
fiscal year 1997. The decrease is attributable to the fact that 1997 sales were
favorably impacted by one-time significant equipment sales to Treadco, Inc.
related to the start-up of business with that customer. This decline was
partially offset by general volume increases in the segment's precure, moldcure
and custom mix product lines.

         Gross income for the Company's third quarter of fiscal 1998 increased
$7.3 million to $46.1 million, or 16.6% of net sales, from $38.8 million, or
13.8% of net sales for the same period in fiscal 1997. Principal factors
affecting the improvement were enhanced operating results in Brazil and at Holm
Industries, process improvements in North America resulting in lower scrap
rates, and favorable raw material pricing resulting from coordination of
worldwide procurement. These improvements brought year-to-date gross income to
14.0% of sales as compared to 11.8% for the same period last year. Operating
results were adversely impacted by $2.7 million in charges in launching a
substantial number of new products at the Company's U.K. subsidiary during the
current year. These new product launches in the U.K. are proving to be difficult
for the Company. While management believes the Company's performance for this
year's fourth quarter can match last year's record earnings, the costs
associated with the new product launches will prevent it from improving upon
that achievement by any meaningful amount.



                                       8

<PAGE>   9

         Research, engineering and development expenses for the third quarter
remained flat at $11.4 million when compared to the same period in fiscal 1997.
Year-to-date, such expenses are slightly lower than in the prior year, at $32.9
million, or 4.1% of net sales.

         Selling, general and administrative expenses for the third quarter
increased $2.2 million to $19.7 million when compared with the prior year. The
increase is attributable to additional personnel costs of $1.4 million, facility
costs of $0.5 million, and professional fees of $0.4 million. Year-to-date costs
increased $5.1 million, to $56.9 million due principally to personnel cost
increases of $2.5 million and facility cost increases of $1.1 million. The
increases are associated with concerted efforts to upgrade the organization and
develop new business.

         In fiscal 1997, the Company made a provision for $17.7 million for the
closure of two manufacturing facilities in North America. The closings were
deemed necessary by management to reduce overcapacity. Operations at these
plants were redistributed to other existing locations. The closures were
completed in the third quarter of fiscal 1998.

         Other income and expense totaled $15.0 million in expense for the first
nine months of fiscal 1998, an increase of $6.2 million over the same period a
year ago. Approximately $5.1 million of this increased expense is attributable
to a reduction in earnings at NISCO, the Company's joint venture with Nishikawa
Rubber Company of Japan. The losses at NISCO in fiscal 1998 have resulted
primarily from issues associated with the launch of the new Honda Accord. The
losses improved from $1.3 million in the second quarter of fiscal 1998 to $0.8
million in the third quarter as management addressed these operational issues.
Management expects that NISCO will continue to report improved operating
results. Interest expense for fiscal year 1998 has decreased by $0.4 million
from the same period last year due to lower borrowing levels and more favorable
short-term financing rates.

         The Company's tax provision for the third quarter of fiscal 1998
reflects a tax rate of 36.5% which reflects a favorable rate reduction from the
prior year. This is primarily attributable to the profitability of Brazilian
operations which will allow for the use of previously generated tax loss
carryforwards and the utilization of previously unbenefited tax credits. The
year-to-date effective tax rate is 38.4%.

(2)      FINANCIAL CONDITION

         Cash provided by operations for the first nine months of fiscal 1998
was $76.9 million. This represents an increase from the same period in fiscal
1997 of $27.6 million. This increase was primarily caused by improved net income
in the current fiscal year. Other significant factors included a reduction in
inventory during the first nine months of fiscal 1998 compared to a large
buildup during the same period of fiscal 1997, a larger reduction in accrued
liabilities during 1998 than occurred in 1997 and a decrease in trade
receivables outstanding. The major inventory reduction occurred in Brazil and
the United States. In Brazil, the Company has gone from a ramp-up environment to
expected production levels. This has consequently taken inventory from an
increasing to a slightly decreasing mode. In the United States, the closure of
two plants in Lexington, Kentucky and Schenectady, New York resulted in lower
inventory balances. The reduction in accrued liabilities is directly related to
the closure of the previously mentioned plants announced in the third quarter of
fiscal 1997. The trade receivables reduction is attributable to the receipt of
customer payments prior to the end of the quarter.

         Capital spending for all of fiscal 1997 totaled $59.0 million, while
management believes fiscal 1998 capital spending will total approximately $65.0
million. For the first nine months of fiscal 1998, capital spending is $10.1
million higher than in the same period of fiscal 1997. Approximately $6.9
million of this increase relates to new programs in the U.K., $1.5 million is
attributable to construction of a new plant in Baclair, France, while the
remainder represents timing factors between periods.

         Cash utilized by financing activities resulted in a net outflow of
$21.3 million for the first nine months of the fiscal year. The payment of
regular quarterly dividends and repayment of borrowings on the Company's
revolving line of credit accounted for the majority of this fund utilization. At
March 31, 1998, debt represented 31.3% of total capitalization compared with
34.7% at June 30, 1997.


                                       9


<PAGE>   10

         As mentioned in Footnote 3, on September 26, 1997 the Company signed
an unsecured five-year, $225 million revolving credit agreement with a 
syndicate of U.S. banks. This agreement replaces the Company's $125 million 
credit agreement that was to mature in January, 1999. The new agreement 
provides improved capital and pricing terms compared with the previous
agreement. This will be utilized by the Company to fund working capital
requirements and as a source for possible acquisition financing. To date, only a
small portion of this line of credit has been utilized. The agreement requires
the Company to maintain certain financial ratios and covenants as to net worth
and leverage.

         The Company has considered its Brazilian subsidiaries to operate in a
"highly inflationary economy" under Statement of Financial Accounting Standard
("SFAS") No. 52, and that its functional currency is the U.S. dollar.
Accordingly, the results for these operations have been translated utilizing a
remeasurement process prescribed by SFAS No. 52. The criteria for determining
highly inflationary status and the functional currency of an operation are
detailed in SFAS No. 52. Although Brazil may soon fail to meet the highly
inflationary criteria, 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 Company recognizes the need to ensure that its operations will not
be adversely impacted by Year 2000 software or hardware failures. Failures due
to processing errors potentially arising from calculations using the Year 2000
date are a known risk.

         The Company's effort to address Year 2000 compliance issues is under
way. The effort consists of evaluating internal computing infrastructure,
business applications and shop-floor systems for Year 2000 compliance and
replacing or renovating systems and applications as necessary to assure such
compliance. The Company intends to complete its plan for resolving Year 2000
compliance issues late in calendar 1998 or early 1999.

         In addition to internal Year 2000 software and equipment implementation
activities, the Company is in contact with its key suppliers to assess their
compliance and is a participant in the automotive industry's group efforts to
deal with these problems through its trade group, the Automotive Industry Action
Group. However, there can be no absolute assurance that there will not be a
material adverse effect on the Company if third parties do not convert their
systems in a timely manner and in a way that is compatible with the Company's
systems. The Company believes that its actions with suppliers will minimize
these risks.

         The Company estimates that the cost of Year 2000 compliance for its
information systems will not have a material adverse effect on the future
consolidated results of operations of the Company. The Company is not yet able
to estimate the cost for Year 2000 compliance with respect to production
systems, products, customers and suppliers; however, based on a preliminary
review, management does not expect that such costs will have a material adverse
effect on the future consolidated results of operations of the Company.

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

         This document may include projections, forecasts and other
forward-looking statements about the Company, the industry in which it competes
and the markets it serves. The achievement of such projections, forecasts and
other forward-looking statements is subject to certain risks and uncertainties,
fully detailed in the "Cautionary Statements for Purposes of "Safe Harbor" Under
the Private Securities Reform Act of 1995" in the Company's Annual Report on
Form 10-K for the year ended June 30, 1997, which is on file with the Securities
and Exchange Commission.



                                       10

<PAGE>   11


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

              None.

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.



                                       11

<PAGE>   12


                                   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:   May 15, 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


                                       12
<PAGE>   13


             
                                  EXHIBIT INDEX


Exhibit
Number                       Description
--------                     ------------
  27                         Financial Data Schedule