<PAGE>   1

                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                    FORM 10-Q

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

For the quarterly period ended  June 30, 1998     Commission file number  0-784
                              ---------------                           --------

                               DETREX CORPORATION
                 ----------------------------------------------
             (Exact name of registrant as specified in its charter)


            Michigan                                    38-0480840
---------------------------------                  ---------------------   
 (State or other jurisdiction of                     (I.R.S. Employer
  incorporation or organization)                    Identification No.)

 24901 Northwestern Hwy., Ste. 500, Southfield,  MI                48075
--------------------------------------------------------------------------------
      (Address of principal executive offices)                   (Zip Code)

Registrant's telephone number, including area code            (248) 358-5800
                                                             -------------------

Securities registered pursuant to section 12(b) of the Act:

                                                       Name of each exchange on
   Title of each class                                     which registered
   -------------------                                 ------------------------ 
          None                                                  None

Securities registered pursuant to Section (g) of the Act:

                       Common Capital Stock, $2 Par Value
                       ----------------------------------  
                                (Title of Class)

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 and (2) has been subject to such filing requirements for
the past 90 days.

                                             YES  X       NO
                                                -----       -----
As of July 27, 1998 1,583,414 shares of the registrant's stock were outstanding.
      -------------


<PAGE>   2


DETREX CORPORATION
                                      INDEX

PART I               FINANCIAL INFORMATION                                 PAGE
------               ---------------------                                 ----
            Item 1   Condensed Consolidated Balance Sheets-
                     June 30, 1998 and December 31, 1997                     3

                     Condensed Consolidated Unaudited Statements
                     of Operations For the Three and Six Months
                     Ended June 30, 1998 and 1997                            4

                     Consolidated Unaudited Statements of Cash 
                     Flows-Six Months Ended June 30, 1998 and 1997           5

                     Notes to Condensed Consolidated Unaudited
                     Financial Statements                                    6

            Item 2   Management's Discussion and Analysis of
                     Interim Financial Information                           7-8


PART II              OTHER INFORMATION

            Item 4   Submission of Matters to Vote of Security Holders       9

            Item 6   Exhibits and Reports on Form 8-K                        9


SIGNATURES                                                                   10




                                                                              2
<PAGE>   3



DETREX CORPORATION
CONDENSED CONSOLIDATED BALANCE SHEETS

<TABLE>
<CAPTION>
                                                                               UNAUDITED              AUDITED
                                                                             June 30, 1998       December 31, 1997
                                                                             -------------       ----------------- 
<S>                                                                           <C>                   <C>        
ASSETS

Current Assets:
Cash and cash equivalents                                                     $   219,593           $   398,093
Accounts receivable (less allowance for uncollectible accounts
    of $263,000 in 1998 and $372,000 in 1997)                                  13,379,246            16,296,172
Buildings & equipment held for sale - current                                     --                  1,425,000
Inventories:
      Raw materials                                                             3,848,167             3,390,407
      Work in process                                                               4,952               355,459
      Finished goods                                                            6,287,030             5,996,243
                                                                              -----------           -----------
                              Total  Inventories                               10,140,149             9,742,109
Prepaid expenses and other                                                        302,937               692,543
Deferred income taxes                                                           1,349,842             1,349,842
                                                                              -----------           -----------
                              Total Current Assets                             25,391,767            29,903,759

Land, buildings, and equipment-net                                             22,619,346            21,348,429
Land, buildings, and equipment held for sale or lease                           1,350,239             1,350,239
Bond proceeds held for investment - restricted                                  2,973,046               --
Prepaid pensions                                                                1,444,454             1,338,951
Deferred income taxes                                                             879,237               693,406
Other assets                                                                      868,049               935,978
                                                                              -----------           -----------
                                                                              $55,526,138           $55,570,762
                                                                              ===========           ===========
LIABILITIES AND STOCKHOLDERS' EQUITY

Current Liabilities:
Loans payable                                                                 $ 5,830,236           $ 5,699,836
Current maturities of capital leases                                              280,801               303,464
Accounts payable                                                                7,815,744             9,843,411
Environmental reserve                                                           1,485,000             1,485,000
Accrued compensation                                                              321,495             1,184,740
Other accruals                                                                  1,537,782             2,113,776
                                                                              -----------           -----------
                               Total Current Liabilities                       17,271,058            20,630,227

Long term portion of capital lease obligations                                    522,702               569,396
Industrial development bonds                                                    4,000,000               --
Accrued postretirement benefits                                                 4,588,982             4,488,982
Environmental reserve                                                           7,481,694             8,090,952
Accrued pensions and other                                                        889,952             1,028,285
Minority interest                                                               2,052,080             1,941,147

Stockholders' Equity:
Common capital stock, $2 par value, authorized 4,000,000 shares,
    outstanding 1,583,414 shares                                                3,166,828             3,166,828
Additional paid-in capital                                                         22,020                22,020
Retained earnings                                                              15,530,822            15,632,925
                                                                              -----------           -----------
                              Total Stockholders' Equity                       18,719,670            18,821,773
                                                                              -----------           -----------
                                                                              $55,526,138           $55,570,762
                                                                              ===========           ===========
</TABLE>

SEE NOTES TO CONDENSED CONSOLIDATED UNAUDITED FINANCIAL STATEMENTS


                                                                              3
<PAGE>   4

DETREX CORPORATION
CONDENSED CONSOLIDATED UNAUDITED STATEMENTS OF  
OPERATIONS

<TABLE>
<CAPTION>
                                                                     Three Months Ended              Six Months Ended
                                                                           June 30                        June 30
                                                                    1998            1997            1998           1997
                                                                    ----            ----            ----           ----

<S>                                                              <C>             <C>            <C>             <C>        
Net sales                                                        $21,292,432     $23,715,780    $42,728,123     $46,876,992


Cost of sales                                                     16,387,141      17,922,334     32,401,320      35,497,134
Selling, general and administrative expenses                       4,393,027       4,137,625      8,599,921       8,378,171
Provision for depreciation and amortization                          836,572         825,953      1,634,040       1,612,670
Other income and deductions                                        (168,437)         238,319      (236,252)         198,434
Minority interest                                                     72,491          95,864        140,932         164,196
Interest expense                                                     177,963         222,111        359,207         415,583
                                                                 -----------     -----------    -----------     -----------

Income before income taxes                                         (406,325)         273,574      (171,045)         610,804

Provision (credit) for income taxes                                (158,347)        (62,007)       (68,941)         139,235
                                                                 -----------     -----------    -----------     -----------

Net income (loss)                                                $ (247,978)     $   335,581    $ (102,104)     $   471,569
                                                                 ===========     ===========    ===========     ===========


Net income (loss) per common share:
       Basic                                                     $     (.15)     $       .21    $     (.06)     $       .30
       Diluted                                                   $     (.15)     $       .21    $     (.06)     $       .30

Weighted average shares outstanding:
       Basic                                                       1,583,414       1,583,414      1,583,414       1,583,414
       Effects of dilutive stock options                             --               26,289        --               26,289
                                                                 -----------     -----------    -----------     -----------
       Diluted                                                     1,583,414       1,609,703      1,583,414       1,609,703
                                                                 ===========     ===========    ===========     ===========
</TABLE>





SEE NOTES TO CONDENSED CONSOLIDATED UNAUDITED FINANCIAL STATEMENTS


                                                                              4

<PAGE>   5


DETREX CORPORATION
CONSOLIDATED UNAUDITED STATEMENTS OF CASH FLOWS
<TABLE>
<CAPTION>

                                                                                            Six Months Ended
                                                                                                June 30
                                                                                                -------
                                                                                         1998             1997
                                                                                         ----             ----
<S>                                                                                  <C>              <C>          
CASH FLOWS FROM OPERATING ACTIVITIES:
          Net income (loss)                                                          $  (102,104)     $     471,569
          Adjustments to reconcile net income to net cash provided by
          operating activities:
                    Depreciation and amortization                                       1,634,020         1,612,670
                    (Gain) Loss on disposal of property                                     (750)           247,810
                    Deferred income taxes                                               (185,831)            98,570
                    Minority interest                                                     110,933           134,194
          Changes to operating assets and liabilities that provided (used) cash:
                    Accounts receivable                                                 2,916,926         (971,213)
                    Refundable U.S. income taxes                                          --              1,003,827
                    Note receivable                                                       --              1,562,665
                    Inventories                                                         (398,040)            38,217
                    Prepaid expenses and other                                            284,104           221,340
                    Other assets                                                          345,693           (8,882)
                    Accounts payable                                                  (2,027,667)       (2,355,001)
                    Environmental reserve                                               (609,258)         (262,021)
                    Accrued compensation                                                (863,245)             7,741
                    Other accruals                                                      (714,327)           183,844
                    Postretirement benefits                                               100,000            87,000
                                                                                     ------------     -------------
                              Total adjustments                                           592,558         1,600,761
                                                                                     ------------     -------------
                              Net cash provided by operating activities                   490,454         2,072,330
                                                                                     ------------     -------------

CASH FLOWS FROM INVESTING ACTIVITIES:
          Capital expenditures                                                        (2,829,025)       (2,063,574)
          Proceeds from disposal of property                                            1,368,000             2,125
          Unused proceeds from bond issue - restricted for capital expenditures       (2,973,046)          --         
                                                                                     ------------     -------------
                              Net cash used in investing activities                   (4,434,071)       (2,061,449)
                                                                                     ------------     -------------

CASH FLOWS FROM FINANCING ACTIVITIES:

          Net change in short-term bank debt                                              130,400         (534,342)
          Principal payments under capital lease obligations                            (142,298)         (222,104)
          Proceeds from debt issued                                                     4,000,000          --
          Debt issuance costs                                                           (222,985)          -- 
                                                                                     ------------     -------------
                              Net cash provided by (used in) financing activities       3,765,117         (756,446)
                                                                                     ------------     -------------

Net decrease in cash and cash equivalents                                               (178,500)         (745,565)
Cash and cash equivalents at beginning of period                                          398,093         1,311,045
                                                                                     ------------     -------------
Cash and cash equivalents at end of period                                           $    219,593     $     565,480
                                                                                     ============     =============

SUPPLEMENTAL DISCLOSURES OF CASH FLOW INFORMATION:
          Cash paid during the period for:
                    Interest                                                         $    365,085     $     402,661
                    Income taxes                                                     $    138,012     $      90,544
SUPPLEMENTAL SCHEDULE OF NONCASH INVESTING AND FINANCING ACTIVITIES:
         Capital lease obligations incurred with the acquisition of equipment        $    119,373     $     556,665
         Capital lease terminations                                                  $     46,432     $      90,960

</TABLE>


SEE NOTES TO CONDENSED CONSOLIDATED UNAUDITED FINANCIAL STATEMENTS


                                                                             5
<PAGE>   6


DETREX CORPORATION

NOTES TO CONDENSED CONSOLIDATED UNAUDITED FINANCIAL STATEMENTS

1.        In the opinion of the Company, the accompanying condensed consolidated
unaudited financial statements reflect all adjustments (consisting of normal
recurring accruals) necessary to present fairly the results of operations for
the periods presented. Certain amounts for 1997 have been reclassified to
conform with 1998 classifications. The information furnished for the six months
may not be indicative of results to be expected for the full year.

2.        The Company and at least seventeen other companies are potentially
responsible for sharing the costs in a proceeding to clean up contaminated
sediments in the Fields Brook watershed in Ashtabula, Ohio. The Environmental
Protection Agency (`EPA') issued a Record of Decision in 1986 concerning the
methods it recommends using to accomplish this task. The Company and the other
potentially responsible parties have negotiated with the EPA as to how best to
effect the clean up operation. After negotiation, an agreement was reached with
the EPA on clean-up methodology. The Company's share of clean-up costs is
anticipated to be in the range of approximately $3.0 to $3.5 million.

          The Company maintains a reserve for anticipated expenditures over the
next several years in connection with remedial investigations, feasibility
studies, remedial design, and remediation relating to the clean up of
environmental contamination at several sites, including property owned by the
Company. The amount of the reserve at June 30, 1998 is $9.0 million. The reserve
includes a provision for the Company's anticipated share of remedial
investigation and studies to determine sources of contamination and methods of
remediation in the Fields Brook watershed referred to above, as well as a
provision for costs that are expected to be incurred in connection with
remediation of the Fields Brook watershed and other sites. Some of these studies
have been completed; others are ongoing. In many cases, the methods of
remediation remain to be agreed upon.

          The Company expects to continue to incur professional fees, expenses
and capital expenditures in connection with its environmental compliance
efforts. In addition to the above, there are several other claims and lawsuits
pending against the Company and its subsidiaries.

          The amount of liability to the Company with respect to costs of
remediation of contamination of the Fields Brook watershed and of other sites,
and the amount of liability with respect to several other claims and lawsuits
against the Company, was based on available data. The Company has established
its reserves in accordance with its interpretation of the principles outlined in
Statement of Financial Accounting Standards No. 5 and Securities and Exchange
Commission Staff Accounting Bulletin No. 92. In the event that any additional
accruals should be required in the future with respect to such matters, the
amounts of such additional accruals could have a material impact on the results
of operations to be reported for a specific accounting period but should not
have a material impact on the Company's consolidated financial position.




                                                                             6
<PAGE>   7

DETREX CORPORATION




                      MANAGEMENT'S DISCUSSION AND ANALYSIS
                        OF INTERIM FINANCIAL INFORMATION

Results of Operations

Summarized below is selected operating data for the current fiscal period and
the comparable data for the same period last year (in thousands):

<TABLE>
<CAPTION>
                                                        THREE MONTHS ENDED                      SIX MONTHS ENDED
                                                              June 30                                 June 30
                                                  -----------------------------------     --------------------------------
                                                         1998               1997                1998              1997
                                                  ----------------   ----------------     ---------------    -------------
                                                     $         %        $         %         $         %         $      %
                                                  ------     -----   ------     -----     ------    -----    ------  ----- 
<S>                                               <C>        <C>     <C>        <C>       <C>       <C>      <C>     <C>  
Sales                                             21,292     100.0   23,716     100.0     42,728    100.0    46,877  100.0
Gross margin                                       4,905      23.0    5,793      24.4     10,327     24.2    11,380   24.3
Selling, general and administrative expenses       4,393      20.6    4,138      17.4      8,600     20.1     8,378   17.9
Depreciation and amortization                        837       3.9      826       3.5      1,634      3.8     1,613    3.4
Net income (loss)                                  (248)     (1.2)      336       1.4      (102)    (0.2)       472    1.0
</TABLE>

Detrex Corporation and its consolidated subsidiaries (the Company) incurred a
net loss of $247,978 for the second quarter of 1998 compared with net income of
$335,581 for the second quarter of 1997. For the first half of 1998, the Company
incurred a net loss of $102,104 compared with net income of $471,569 for the
first half of 1997.

Sales for the six month period were down $4.1 million as all of the Company's
business units recorded declines in sales except its plastic pipe subsidiary,
Harvel Plastics, and its research laboratory, RTI. The current economic
situation in Asia, the slowdown in computer chip manufacturing, the strong U.S.
dollar, and the effects of the General Motors strike all contributed to the
decline in volume.

The gross margin for the Company remained approximately the same for the six
month period, 24.2% versus 24.3% a year ago. However, there was a decline in
gross margin for the second quarter, 23.0% in the second quarter of 1998,
compared to 24.4% for the same period in 1997 as we experienced a drop in volume
and pricing pressure from the external factors referred to above.

The increase in selling, general and administrative expenses is attributable to
economic increases in all of the Company's operating units and additional
marketing and technical support personnel in some of our business units. These
increases more than offset a credit in pension expense.

The provision for depreciation and amortization is slightly higher than a year
ago since depreciation of plant additions in Ashtabula, Ohio began in 1998.

Interest expense is lower than in 1997 due to lower interest rates which
resulted from the renegotiation of the Company's credit agreement.

The income tax credit in 1998 reflects a credit for federal income tax,
partially offset by state and local income tax expense.


                                                                             7


<PAGE>   8

DETREX CORPORATION


Liquidity, Financial Condition, and Capital Resources

The Company utilized internally generated funds and the proceeds from the sale
of a closed plant to finance its activities during the first half of 1998. In
addition, Harvel Plastics is financing its expansion in California with
industrial development bonds.

In April 1998, the Company and Comerica Bank amended the Company's credit
agreement and extended the facility to May 1, 2000. The major change in the new
agreement is a reduction in the interest rate from prime plus one percent to
prime.

Working capital was $8.1 million at June 30, 1998 compared to $9.3 million at
December 31, 1997. The Company has paid no dividends since the second quarter of
1991 and cannot forecast when the dividend will be restored.


Other

The Company will be implementing Statement of Financial Accounting Standards No.
131, Disclosures about Segments of an Enterprise and Related Information in the
fourth quarter of 1998. At the current time the Company cannot determine how
many segments it will be reporting.

                                                                             8

<PAGE>   9


DETREX CORPORATION

                           PART II - OTHER INFORMATION

Item 4     SUBMISSION OF MATTERS TO VOTE OF SECURITY HOLDERS

(a)        The 73rd Annual Meeting of the Stockholders of Detrex
           Corporation was held in Southfield, Michigan on the
           23rd day of April 1998.

(b)        Election of Messrs. Cox, Mark and Withrow as
           Directors of the Third Class to hold office for three
           year terms and until their successors have been
           elected and qualify:

                                Mr. Cox           Mr. Mark        Mr. Withrow

           For                 1,378,137         1,378,137         1,378,137
           Against                --                --                --
           Abstain                10,121            10,121            10,121


           Messrs. Emmett, King, Mangold, McCleary, and Thalacker continue 
           as directors.


Item 6     EXHIBITS AND REPORTS ON FORM 8-K

(a)        None

(b)        No reports on Form 8-K have been filed for the quarter ended 
           June 30, 1998.


                                                                              9

<PAGE>   10


DETREX CORPORATION



                                   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.


                               DETREX CORPORATION

Date     8/6/98                S.J. Quinlan
    --------------             ---------------------------------------------
                               S.J. Quinlan
                               Controller and Chief Accounting Officer



Date     8/6/98                G.J. Israel
    --------------             ---------------------------------------------
                               G.J. Israel
                               Vice President - Finance and Chief Financial 
                               Officer

                                                                            10
<PAGE>   11

                                Exhibit Index
                                -------------


<TABLE>
<CAPTION>
Exhibit No.                  Description
-----------                  -----------
<S>                          <C>
     27                       Financial Data Schedule

</TABLE>