<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 March 31, 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 April 24, 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-
                            March 31, 1998 and December 31, 1997          3

                            Condensed Consolidated Unaudited Statements
                            of Operations For the Three Months
                            Ended March 31, 1998 and 1997                 4

                            Consolidated Unaudited Statements of Cash 
                            Flows- Three Months Ended March 31, 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 6   Exhibits and Reports on Form 8-K              9


SIGNATURES                                                                10


                                                                               2
<PAGE>   3



DETREX CORPORATION
CONDENSED CONSOLIDATED BALANCE SHEETS

<TABLE>
<CAPTION>
                                                                       UNAUDITED      AUDITED
                                                                    March 31, 1998 December 31, 1997
                                                                    -------------- -----------------
ASSETS
<S>                                                                  <C>           <C>        
Current Assets:
Cash and cash equivalents                                            $   440,899   $   398,093
Accounts receivable (less allowance for uncollectible accounts
  of $325,000 in 1998 and $372,000 in 1997)                           15,047,140    16,296,172
Buildings & equipment held for sale - current                                 --     1,425,000
Inventories:
     Raw materials                                                     3,431,922     3,390,407
     Work in process                                                     201,008       355,459
     Finished goods                                                    6,345,550     5,996,243
                                                                     -----------   -----------   
                Total  Inventories                                     9,978,480     9,742,109
Prepaid expenses and other                                               406,716       692,543
Deferred income taxes                                                  1,349,842     1,349,842
                                                                     -----------   -----------   
                Total Current Assets                                  27,223,077    29,903,759

Land, buildings, and equipment-net                                    21,875,111    21,348,429
Land, buildings, and equipment held for sale or lease                  1,350,239     1,350,239
Bond proceeds held for investment-restricted                           3,880,000            --
Prepaid pensions                                                       1,338,951     1,338,951
Deferred income taxes                                                    686,540       693,406
Other assets                                                           1,261,332       935,978
                                                                     -----------   -----------   
                                                                     $57,615,250   $55,570,762
                                                                     ===========   ===========
LIABILITIES AND STOCKHOLDERS' EQUITY

Current Liabilities:
Loans payable                                                          5,488,432     5,699,836
Current maturities of capital leases                                     280,544       303,464
Accounts payable                                                       9,347,959     9,843,411
Environmental reserve                                                  1,485,000     1,485,000
Accrued compensation                                                     315,705     1,184,740
Other accruals                                                         2,228,134     2,113,776
                                                                     -----------   -----------   
                Total Current Liabilities                             19,145,774    20,630,227

Long term portion of capital lease obligations                           504,587       569,396
Industrial development bonds                                           4,000,000            --
Accrued postretirement benefits                                        4,563,982     4,488,982
Environmental reserve                                                  7,528,431     8,090,952
Accrued pensions and other                                               895,240     1,028,285
Minority interest                                                      2,009,589     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                                                     15,778,799    15,632,925
                                                                     -----------   -----------   
                Total Stockholders' Equity                            18,967,647    18,821,773
                                                                     -----------   -----------   
                                                                     $57,615,250   $55,570,762
                                                                     ===========   ===========
</TABLE>


SEE NOTES TO CONDENSED CONSOLIDATED UNAUDITED FINANCIAL STATEMENTS

                                                                               3
<PAGE>   4





DETREX CORPORATION
CONDENSED CONSOLIDATED UNAUDITED STATEMENT OF OPERATIONS



<TABLE>
<CAPTION>
                                                   Three Months Ended
                                                        March 31
                                                   1998             1997
                                                -----------    ------------

<S>                                            <C>             <C>         
Net sales                                      $ 21,435,691    $ 23,161,212


Cost of sales                                    16,014,179      17,574,800
Selling, general and administrative expenses      4,207,315       4,240,546
Provision for depreciation and amortization         797,468         786,717
Other income and deductions                         (68,236)        (39,885)
Minority interest                                    68,441          68,332
Interest expense                                    181,244         193,472
                                               ------------    ------------

Income before income taxes                          235,280         337,230

Provision for income taxes                           89,406         201,242
                                               ------------    ------------

Net income                                     $    145,874    $    135,988
                                               ============    ============

Net income per common share:
       Basic                                   $        .09    $        .09
       Diluted                                 $        .09    $        .09

Weighted average shares outstanding:
       Basic                                      1,583,414       1,583,414
       Effects of dilutive stock options             67,001          13,289
                                               ------------    ------------
       Diluted                                    1,650,415       1,596,703
                                               ============    ============
</TABLE>












SEE NOTES TO CONDENSED CONSOLIDATED UNAUDITED FINANCIAL STATEMENTS




                                                                               4
<PAGE>   5


DETREX CORPORATION
CONSOLIDATED UNAUDITED STATEMENTS OF CASH FLOWS

<TABLE>
<CAPTION>
                                                                                   Three Months Ended         
                                                                                        March 31
                                                                                  1998            1997
                                                                                  ----            ---- 
<S>                                                                           <C>            <C>        
CASH FLOWS FROM OPERATING ACTIVITIES:
     Net income                                                               $   145,874    $   135,988
     Adjustments to reconcile net income to net cash provided by
     operating activities:
               Depreciation and amortization                                      797,468        786,717
               Gain on disposal of property                                            --         (2,161)
               Deferred income taxes                                                6,866        124,068
               Minority interest                                                   68,442         68,332
     Changes to operating assets and liabilities that provided (used) cash:
               Accounts receivable                                              1,249,032       (351,441)
               Refundable U.S. income taxes                                            --      1,003,827
               Note receivable                                                         --      1,562,665
               Inventories                                                       (236,371)      (917,027)
               Prepaid expenses and other                                         285,827        251,617
               Other assets                                                       (84,658)        25,821
               Accounts payable                                                  (495,452)    (1,633,077)
               Environmental reserve                                             (562,521)       (42,106)
               Accrued compensation                                              (869,035)      (190,735)
               Other accruals                                                     (18,687)       456,090
               Postretirement benefits                                             75,000         90,000
                                                                              -----------    -----------                 
                  Total adjustments                                               215,911      1,232,590
                                                                              -----------    -----------                 
                  Net cash provided by operating activities                       361,785      1,368,578
                                                                              -----------    -----------                 

CASH FLOWS FROM INVESTING ACTIVITIES:
     Capital expenditures                                                      (1,348,959)      (831,823)
     Proceeds from disposal of property                                         1,369,672             --
     Investment of bond proceeds - restricted                                  (3,880,000)            --      
                                                                              -----------    -----------                 
                  Net cash used in investing activities                        (3,859,287)      (831,823)
                                                                              -----------    -----------                 

CASH FLOWS FROM FINANCING ACTIVITIES:

     Repayment of short-term bank debt - net                                     (211,404)       (93,388)
     Principal payments under capital lease obligations                           (65,870)      (124,280)
     Proceeds from debt issued                                                  4,000,000             --
     Debt issuance costs                                                         (182,418)            --    
                                                                              -----------    -----------                 
                  Net cash provided by (used in) financing activities           3,540,308       (217,668)
                                                                              -----------    -----------                 
Net increase in cash and cash equivalents                                          42,806        319,087
Cash and cash equivalents at beginning of period                                  398,093      1,311,045
                                                                              -----------    -----------                 
Cash and cash equivalents at end of period                                    $   440,899    $ 1,630,132
                                                                              ===========    ===========

SUPPLEMENTAL DISCLOSURES OF CASH FLOW INFORMATION:
     Cash paid during the period for:
            Interest                                                          $   186,517    $   194,128
            Income taxes                                                      $    66,197    $    61,000
SUPPLEMENTAL SCHEDULE OF NONCASH INVESTING AND FINANCING ACTIVITIES:
     Capital lease obligations incurred with the acquisition of equipment     $    17,715    $   481,851
     Capital lease terminations                                               $    39,575    $    53,947
</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 three
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 properties owned by the
Company. The amount of the reserve at March 31, 1998 was $9.0 million. The
reserve includes a provision for the Company's anticipated share 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 other
sites. Some of these studies have been completed; others are ongoing. In some
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 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                                               
                                                                  March 31
                                                         1998               1997
                                                         ----               ----
                                                     $         %        $         %
<S>                                               <C>        <C>     <C>        <C>  
Sales                                             21,436     100.0   23,161     100.0
Gross margin                                       5,422      25.3    5,586      24.1
Selling, general and administrative expenses       4,207      19.6    4,241      18.3
Depreciation and amortization                        797       3.7      787       3.4
Net income                                           146        .7      136        .6

</TABLE>

Detrex Corporation and its consolidated subsidiaries (the Company) reported net
income of $145,874 for the first quarter of 1998 compared to $135,988 net income
for the first quarter of 1997. This is the ninth consecutive profitable quarter
for the Company.

Sales for the three months were $1.7 million less than the same period last
year, primarily a result of lower sales in the Company's Equipment Division. Two
subsidiaries, Harvel Plastics Inc. and The Elco Corporation, had increases in
sales.

The gross margin for the Company improved to 25.3% from the 24.1% level last
year. The major reason for the increase was improved margins at the Company's
Solvents and Environmental Services Division.

The decrease in selling, general and administrative expenses is primarily
attributable to a credit in pension expense, partially offset by small economic
increases at all of the Company's operating units.

The provision for depreciation and amortization is slightly higher than a year
ago since depreciation of the Company's new plant in Ashtabula, Ohio began in
the first quarter of 1998.

Interest expense is lower in 1998 than in 1997 due to the lower level of
borrowings in the first quarter of 1998.

Income tax expense in 1998 reflects an effective tax rate of 38% for federal,
state and local income taxes.




                                                                               7
<PAGE>   8


DETREX CORPORATION


Liquidity, Financial Condition, and Capital Resources

The Company utilized a combination of internally generated funds and the
proceeds from the sale of a closed plant to finance its activities during the
first three months of 1998.

In March 1998, $4.0 million of industrial development bonds were issued to
finance the expansion of Harvel Plastics in California. As of March 31, 1998,
$3.9 million of the proceeds were held for investment in a restricted trust.


On April 22, 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 March 31, 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 6                     EXHIBITS AND REPORTS ON FORM 8-K

(a)                        Exhibit 4 - Statement regarding Harvel Plastics, Inc.
                           financing instruments. 

                           Exhibit 10(o) - Third Amendment to Comerica Credit 
                           Agreement, dated as of April 22, 1998.

(b)                        No reports on Form 8-K have been filed for the 
                           quarter ended March 31, 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 5/5/98                                          S.J. Quinlan
    -------------                                    ---------------------------
                                                     S.J. Quinlan
                                                     Controller and Chief 
                                                     Accounting Officer



Date 5/5/98                                          G.J. Israel
    -------------                                    ---------------------------
                                                     G.J. Israel
                                                     Vice President - Finance 
                                                     and Chief Financial Officer








                                                                              10


<PAGE>   11
                                Exhibit Index

Exhibit No.                         Description
-----------                         -----------
4                              Statement regarding Harvel Plastics, Inc.
                               financing instruments.

10(o)                          Third amendment to Comerica Credit
                               Agreement dated as of April 22, 1998.

27                             Financial Data Schedule