<PAGE>   1
                                  UNITED STATES

                       SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549


                                    FORM 10-Q

[X]      QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d)
            OF THE SECURITIES EXCHANGE ACT OF 1934


For the quarterly period ended:   May 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:   0-2572


                            STEEL CITY PRODUCTS, INC
              -----------------------------------------------------
             (Exact name of registrant as specified in its charter)


      DELAWARE                                                    55-0437067
------------------------                                      ------------------
(State of Incorporation)                                      (I.R.S. Employer
                                                             Identification No.)

               3513 CONCORD PIKE, SUITE 3527, WILMINGTON, DELAWARE
                                      19803
               ---------------------------------------------------
                    (Address of principal executive offices)
                                   (Zip Code)

                                 (302) 478-9170
              ----------------------------------------------------
              (Registrant's telephone number, including area code)


              -----------------------------------------------------
              (Former name, former address, and former fiscal year,
                         if changed since last report)

         Indicate by check mark whether the Registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
Registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days.  Yes  X  No
                                              ----   ----
         At July 1, 1998, 3,238,061 shares of the Registrant's Common Stock, 
$0.01 par value per share, were issued and outstanding.


                       DOCUMENTS INCORPORATED BY REFERENCE
                                      None


<PAGE>   2


                         PART I - FINANCIAL INFORMATION



ITEM 1.  FINANCIAL STATEMENTS



                          INDEX TO FINANCIAL STATEMENTS

                            STEEL CITY PRODUCTS, INC.

<TABLE>


<S>                                                                     <C>
Balance Sheets at May 31, 1998 (unaudited)
  and February 28, 1997 ..............................................   3


Statements of Operations for the three month periods ended
  May 31, 1998 and May 31, 1997 (unaudited) ..........................   4


Statement of Stockholders' Equity for the three months
  ended May 31, 1998 (unaudited) .....................................   5


Statements of Cash Flows for the three month periods ended
  May 31, 1998 and May 31, 1997 (unaudited)...........................   6


Notes to Financial Statements (unaudited) ............................   7
</TABLE>


                                      -2-

<PAGE>   3






                            STEEL CITY PRODUCTS, INC.
                                 BALANCE SHEETS
                (DOLLAR AMOUNTS IN THOUSANDS, EXCEPT SHARE DATA)


                                     ASSETS

<TABLE>
<CAPTION>


                                                                                        MAY 31,      FEBRUARY 28,
                                                                                         1998            1998
                                                                                     ------------    ------------
                                                                                     (Unaudited)
<S>                                                                                  <C>             <C>         
Current assets:
     Cash ........................................................................   $          2    $          1
     Trade accounts receivable, less allowance of $331 and $355, respectively ....          2,881           2,698
     Notes receivable - Oakhurst Company, Inc.....................................            300             293
     Inventories .................................................................          2,925           3,666
     Other .......................................................................             43              50
                                                                                     ------------    ------------
                       Total current assets ......................................          6,151           6,708
                                                                                     ------------    ------------

Property and equipment, at cost ..................................................            968             951
     Less accumulated depreciation ...............................................           (635)           (618)
                                                                                     ------------    ------------
                                                                                              333             333
                                                                                     ------------    ------------

Notes receivable - Oakhurst Company, Inc., long-term portion .....................            646             723
Advances to Oakhurst Company, Inc.................................................          6,842           5,706
Other assets .....................................................................            717             666
                                                                                     ------------    ------------
                                                                                            8,205           7,095
                                                                                     ------------    ------------

                                                                                     $     14,689    $     14,136
                                                                                     ============    ============

                                       LIABILITIES AND STOCKHOLDERS' EQUITY

Current liabilities:
     Accounts payable ............................................................   $      3,563    $      3,926
     Accrued compensation ........................................................            347             380
     Current maturities of long-term obligations .................................            540             543
     Due to affiliate ............................................................            511             462
     Other .......................................................................            120             150
                                                                                     ------------    ------------
                       Total current liabilities .................................          5,081           5,461
                                                                                     ------------    ------------

Long-term obligations:
     Long-term debt ..............................................................          2,978           2,070
     Other long-term obligations .................................................             58              62
                                                                                     ------------    ------------
                                                                                            3,036           2,132
                                                                                     ------------    ------------
Commitments and contingencies ....................................................

Stockholders' equity:
     Preferred stock, par value $0.01 per share; authorized
        5,000,000 shares, issued 1,938,526 shares;
        liquidation preference $10,135 ...........................................             19              19
     Common stock, par value $0.01 per share; authorized
        5,000,000 shares; issued 3,238,061 shares ................................             32              32
     Additional paid-in capital ..................................................         43,824          43,824
     Deficit (Reorganized on August 26, 1989) ....................................        (37,302)        (37,331)
     Treasury stock, at cost, 207 common shares ..................................             (1)             (1)
                                                                                     ------------    ------------
                       Total stockholders' equity ................................          6,572           6,543
                                                                                     ------------    ------------

                                                                                     $     14,689    $     14,136
                                                                                     ============    ============
</TABLE>


   The accompanying notes are an integral part of these financial statements.


                                       -3-


<PAGE>   4




                            STEEL CITY PRODUCTS, INC.
                            STATEMENTS OF OPERATIONS
              (DOLLAR AMOUNTS IN THOUSANDS, EXCEPT PER SHARE DATA)
                                   (Unaudited)


<TABLE>
<CAPTION>



                                                              THREE MONTHS   THREE MONTHS
                                                                 ENDED          ENDED
                                                                 MAY 31,       MAY 31,
                                                                  1998          1997
                                                              ------------   ------------


<S>                                                           <C>            <C>         
Sales .....................................................   $      4,855   $      5,151
Other income ..............................................            110            102
                                                              ------------   ------------
                                                                     4,965          5,253
                                                              ------------   ------------

Cost of goods sold, including occupancy and
   buying expenses ........................................          3,943          4,178
Operating, selling and administrative expenses ............            964            953
Provision for doubtful accounts ...........................             (5)            13
Interest expense ..........................................             81            111
                                                              ------------   ------------
                                                                     4,983          5,255
                                                              ------------   ------------

Net loss before undistributed earnings of
   investment in affiliate and income tax expense .........            (18)            (2)

Undistributed earnings of investment in affiliate .........             52             47
Income tax expense ........................................             (5)            --
                                                              ------------   ------------
Net income ................................................             29             45

Effect of Series A Preferred Stock dividends ..............           (253)          (253)
                                                              ------------   ------------

Net loss attributable to common stockholders ..............   $       (224)  $       (208)
                                                              ============   ============


Basic and diluted net loss per share attributable to common
   stockholders after preferred stock dividends ...........   $      (0.07)  $      (0.06)
                                                              ============   ============

Weighted average number of shares outstanding used in
   computing basic and diluted per share amounts ..........      3,238,061      3,238,061
                                                              ============   ============
</TABLE>







   The accompanying notes are an integral part of these financial statements.

                                       -4-



<PAGE>   5





                            STEEL CITY PRODUCTS, INC.
                        STATEMENT OF STOCKHOLDERS' EQUITY
                         THREE MONTHS ENDED MAY 31, 1998
                             (DOLLARS IN THOUSANDS)
                                   (Unaudited)




<TABLE>
<CAPTION>




                                                                                                       
                                        PREFERRED STOCK          COMMON STOCK        ADDITIONAL   RETAINED       TREASURY STOCK
                                     ---------------------   ---------------------    PAID-IN     EARNINGS    ---------------------
                                       SHARES    PAR VALUE    SHARES     PAR VALUE    CAPITAL    (DEFICIT)     SHARES       COST
                                     ---------   ---------   ---------   ---------   ---------   ---------    ---------   ---------


<S>                                  <C>         <C>         <C>         <C>         <C>         <C>          <C>          <C>  
Balances, February 28, 1998 ......   1,938,526   $      19   3,238,061   $      32   $  43,824   $ (37,331)         207    $     (1)




Net income for the period ........                                                                      29




                                     ---------   ---------   ---------   ---------   ---------   ---------    ---------   ---------
Balances, May 31, 1998 ...........   1,938,526   $      19   3,238,061   $      32   $  43,824   $ (37,302)         207   $      (1)
                                     =========   =========   =========   =========   =========   =========    =========   =========
</TABLE>





   The accompanying notes are an integral part of these financial statements.

                                       -5-


<PAGE>   6


                            STEEL CITY PRODUCTS, INC.
                            STATEMENTS OF CASH FLOWS
                          (DOLLAR AMOUNTS IN THOUSANDS)
                                   (Unaudited)


<TABLE>
<CAPTION>



                                                                              THREE MONTHS    THREE MONTHS
                                                                                 ENDED           ENDED
                                                                                 MAY 31,        MAY 31,
                                                                                  1998           1997
                                                                              ------------    ------------
<S>                                                                           <C>             <C>         
Cash flows from operating activities:
     Net income ...........................................................   $         29    $         45
     Adjustments to reconcile net income
         to net cash provided by (used in) operating activities:
              Depreciation and amortization ...............................             27              50
              Undistributed earnings of investment in affiliate ...........            (52)            (47)
     Other changes in operating assets and liabilities:
              Accounts receivable .........................................           (183)           (668)
              Inventories .................................................            741             286
              Accounts payable ............................................           (363)            301
              Other .......................................................             (1)           (126)
                                                                              ------------    ------------
Net cash provided by (used in) operating activities of:
     Continuing operations ................................................            198            (159)
     Discontinued operations ..............................................              6              10
                                                                              ------------    ------------
Net cash provided by (used in) operating activities .......................            204            (149)
                                                                              ------------    ------------

Cash flows from investing activities:
     Advances to Oakhurst Company, Inc. ...................................         (1,136)           (602)
     Collection of note receivable, Oakhurst Company, Inc. ................             70              67
     Additions to property and equipment ..................................            (17)             --
     Other ................................................................             (1)             --
                                                                              ------------    ------------
Net cash used in investing activities .....................................         (1,084)           (535)
                                                                              ------------    ------------

Cash flows from financing activities:
     Net borrowings under revolving credit agreement ......................            908             753
     Principal payments on long-term obligations ..........................             (7)            (69)
     Deferred loan costs ..................................................            (20)             --
                                                                              ------------    ------------
Net cash provided by financing activities .................................            881             684
                                                                              ------------    ------------

Net increase in cash ......................................................              1              --
Cash at beginning of period ...............................................              1               2
                                                                              ------------    ------------
Cash at end of period .....................................................   $          2    $          2
                                                                              ============    ============
</TABLE>









   The accompanying notes are an integral part of these financial statements.

                                       -6-






<PAGE>   7




                            STEEL CITY PRODUCTS, INC.
                          NOTES TO FINANCIAL STATEMENTS
                         THREE MONTHS ENDED MAY 31, 1998

1.  INTERIM FINANCIAL STATEMENTS

         In the opinion of management, the accompanying unaudited financial
statements contain all adjustments necessary to present fairly the financial
position, results of operations and cash flows for the interim periods
presented. All adjustments made are of a normal recurring nature.

         While the Company believes that the disclosures presented herein are
adequate to make the information not misleading, it is suggested that these
unaudited financial statements be read in conjunction with the audited financial
statements for the fiscal year ended February 28, 1998 ("fiscal 1998") as filed
in the Company's Annual Report on Form 10-K.


2.  RECENTLY ISSUED ACCOUNTING STANDARDS

         In June 1997, the Financial Accounting Standards Board ("FASB") issued
Statement of Financial Accounting Standards ("SFAS") No. 130, "Reporting
Comprehensive Income". SFAS No. 130 establishes standards for reporting
comprehensive income and its components. SFAS No. 130 also requires that the
cumulative balance of these items of other comprehensive income be reported
separately from retained earnings and additional paid-in capital in the equity
section of a statement of financial position. SFAS No. 130 is effective for
fiscal years beginning after December 15, 1997. The Company has adopted SFAS No.
130 in the first quarter ended May 31, 1998 (unaudited) and the adoption did not
have a material impact on the Company's disclosures in its financial statements.

         In June 1997, the FASB issued SFAS No. 131, "Disclosure about Segments
of an Enterprise and Related Information". SFAS No. 131 establishes standards
for the way public companies report selected information about operating
segments in both quarterly and annual financial statements to their
shareholders. It also establishes standards for related disclosures about
products and services, geographic areas and major customers. SFAS No. 131 is
effective for fiscal years beginning after December 15, 1997. This statement is
not required to be applied to interim financial statements in the initial year
of its application. The Company has not yet determined the effects, if any, that
SFAS No. 131 will have on the disclosures in its financial statements.

                                      -7-

<PAGE>   8






ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
OF OPERATIONS

OVERVIEW

         Steel City Products, Inc. ("SCPI") is a special, limited purpose,
majority-owned subsidiary of Oakhurst Company, Inc. ("Oakhurst"). SCPI is
expected to concentrate on its historical line of business, while any future
growth and expansion opportunities are expected to be pursued by one or more
subsidiaries of Oakhurst. Through Oakhurst's ownership of SCPI, primarily in the
form of preferred stock, Oakhurst retains substantially all the value of SCPI,
and receives substantially all of the benefit of operations through dividends on
the preferred stock. Oakhurst's ownership of SCPI is designed to facilitate the
preservation and utilization of SCPI's and Oakhurst's net operating tax loss
carry-forwards which amount to approximately $154 million.

         In addition to cash derived from operations, SCPI's liquidity and
financing requirements are determined principally by the working capital needed
to support its level of business, together with the need for capital
expenditures and the cash required to repay its debt. SCPI also receives cash
payments pursuant to a note receivable from Oakhurst, and from time to time,
repayments of advances to Oakhurst. SCPI's working capital needs fluctuate
primarily due to the amounts of inventory it carries which can change
seasonally, the size and timeliness of payment of receivables from its customers
to which from time to time SCPI grants extended payment terms for their seasonal
inventory builds, and the amount of credit extended to SCPI by its suppliers.
SCPI participates in a cash concentration system together with all the
subsidiaries of Oakhurst. Available cash that is transferred to Oakhurst is
reflected as an addition to the advances to Oakhurst.

         At May 31, 1998, SCPI's debt primarily consisted of notes payable with
outstanding principal balances aggregating approximately $522,000 that were
issued in connection with the settlement of certain contingent liabilities
related to SCPI's former retail division. SCPI also has revolving debt of
approximately $3 million which is offset entirely by advances receivable from
Oakhurst that bear interest at the same rate as the revolving debt.

         Oakhurst and its subsidiaries, including SCPI, have available financing
under a revolving credit facility (the "Revolver") from an institutional lender
up to a maximum of $7 million, subject to a borrowing base that is calculated
according to defined levels of the subsidiaries' accounts receivable and
inventories. At May 31, 1998, the borrowing base under the Revolver was $5.5
million. In fiscal 1998, the Revolver was extended to April 1999, and provides
for subsequent renewal terms of one year each upon payment of a renewal fee of
0.5% of the entire line, unless earlier terminated as provided for in the
agreement. Management believes that the Revolver will provide adequate funding
for SCPI's working capital requirements for at least the next twelve months,
assuming no material deterioration in current sales levels or gross profit
margins.

         From time to time the information provided by the Company or statements
made by its employees may contain so-called "forward looking" information that
involves risks and uncertainties. In particular, statements contained in this
Item 2 - "Management's Discussion and Analysis of Financial Condition and
Results of Operations," which are not historical facts (including, but not
limited to statements concerning anticipated sales, profit levels, customers and
cash flows) are forward looking statements. The Company's actual future results
may differ significantly from those stated in any forward looking statements.
Factors that may cause such differences include, but are not limited to the
factors discussed above as well as the accuracy of the Company's internal
estimates of revenue and operating expense levels. Each of these factors 


                                      -8-

<PAGE>   9


and others are discussed from time to time in the Company's Securities and
Exchange Commission filings.


MATERIAL CHANGES IN FINANCIAL CONDITION

         As of May 31, 1998, there had been no material changes in the Company's
financial condition from February 28, 1998, discussed in Item 7 of the Company's
Annual Report on Form 10-K for fiscal 1998.


MATERIAL CHANGES IN RESULTS OF OPERATIONS

         Operations include the results of SCPI's operating division, Steel City
Products, a distributor of automotive parts and accessories and of non-food pet
supplies based in Pittsburgh, Pennsylvania.

THREE MONTHS ENDED MAY 31, 1998 COMPARED WITH THREE MONTHS ENDED MAY 31, 1997

         Sales in the first quarter of the current year decreased by $296,000
compared to the prior year. Sales to existing automotive customers decreased by
approximately $580,000, primarily as a result of competitive pressures
encountered by certain of SCPI's customers, and because some customers have
changed their buying practices to obtain certain product lines direct from the
manufacturer. The prior year first quarter also included sales of approximately
$117,000 relating to the "Wing-tech" division that was sold in such quarter.
Partially offsetting these decreases were sales to new automotive customers of
approximately $210,000.

         Sales of non-food pet supplies were $407,000 in the current year,
compared with $218,000 in the prior year. The increase in sales of $189,000
resulted from expanded sales to existing pet supply customers, together with
sales of $90,000 to new pet supply customers recently added.

         Gross profits decreased by $61,000 in the first quarter compared with
the first quarter of the prior year, due primarily to the net decrease in sales.

         Operating, selling and administrative increased by $11,000 when
compared to the prior year first quarter. Lower expenses of approximately
$30,000 resulting from the sale of the Wing-tech division were offset by higher
selling expenses which primarily related to higher broker's commissions that are
paid in connection with the pet supply business.

         There was an decrease in the provision for doubtful accounts of $18,000
in the current year. The prior year provision reflected the bankruptcy of a
customer.

         Interest expense decreased by $30,000, due to SCPI's repayment of a
term loan in December 1997.



                                      -9-


<PAGE>   10



                           PART II - OTHER INFORMATION



ITEM 1.  LEGAL PROCEEDINGS

         There are no material legal proceedings pending against the Company.



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

         No matters were submitted to a vote of security holders during the
quarter for which this report is filed.



ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K

         (a)   Exhibits

               27.   Financial Data Schedule (EDGAR transmission only)


         (b)   No reports on Form 8-K were filed during the quarter for which
               this report is filed.



                                      -10-

<PAGE>   11



                                   SIGNATURES


         Pursuant to the requirements of the Securities and Exchange Act of
1934, the registrant has duly caused this report to be signed on its behalf by
the undersigned thereunto duly authorized.


                                            STEEL CITY PRODUCTS, INC.


Date: July 10, 1998                         By:  /s/ Bernard H. Frank
                                                 -------------------------------
                                                 Bernard H. Frank
                                                 Chief Executive Officer


Date: July 10, 1998                         By:  /s/ Mark Auerbach
                                                 -------------------------------
                                                 Mark Auerbach
                                                 Chief Financial Officer




                                      -11-

<PAGE>   12

                               INDEX TO EXHIBITS

<TABLE>
<CAPTION>



            EXHIBITS               DESCRIPTION
            --------               -----------
<S>                  <C>
               27.   Financial Data Schedule (EDGAR transmission only)
</TABLE>