<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  September 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  October 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-
                       September 30, 1998 (Unaudited) and
                       December 31, 1997                                  3

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

                       Consolidated Unaudited Statements of Cash Flows-
                       Nine Months Ended September 30, 1998 and 1997      5

                       Notes to Condensed Consolidated Unaudited
                       Financial Statements                               6

               Item 2  Management's Discussion and Analysis of
                       Interim Financial Information                      7-9


   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
                                                                                September 30,     December 31,
                                                                                -------------     ------------
                                                                                    1998              1997
                                                                                ------------       ------------                  

ASSETS

Current Assets:
<S>                                                                             <C>               <C>        
Cash and cash equivalents                                                       $   102,012       $   398,093
Accounts receivable (less allowance for uncollectible accounts
      of $360,971 in 1998 and $372,000 in 1997)                                  13,324,254        16,296,172
Buildings & equipment held for sale - current                                          --           1,425,000
Inventories:
           Raw materials                                                          3,383,618         3,390,407
           Work in process                                                          404,679           355,459
           Finished goods                                                         6,368,420         5,996,243
                                                                                -----------       -----------      
                              Total  Inventories                                 10,156,718         9,742,109
Prepaid expenses and other                                                          748,415           692,543
Deferred income taxes                                                             1,349,842         1,349,842
                                                                                -----------       -----------      
                              Total Current Assets                               25,681,241        29,903,759

Land, buildings, and equipment-net                                               23,423,411        21,348,429
Land, buildings, and equipment held for sale or lease                               100,239         1,350,239
Bond proceeds held for investment - restricted                                    2,010,227              --
Prepaid pensions                                                                  1,652,258         1,338,951
Deferred income taxes                                                             1,028,270           693,406
Other assets                                                                      1,258,240           935,978
                                                                                -----------       -----------      
                                                                                $55,153,886       $55,570,762
                                                                                ===========       ===========
LIABILITIES AND STOCKHOLDERS' EQUITY

Current Liabilities:
Loans payable                                                                   $ 4,890,227       $ 5,699,836
Current maturities of capital leases                                                246,576           303,464
Accounts payable                                                                  8,505,197         9,843,411
Environmental reserve                                                             1,485,000         1,485,000
Accrued compensation                                                                340,098         1,184,740
Other accruals                                                                    1,767,891         2,113,776
                                                                                -----------       -----------      
                               Total Current Liabilities                         17,234,989        20,630,227

Long term portion of capital lease obligations                                      463,223           569,396
Industrial development bonds                                                      4,000,000              --
Accrued postretirement benefits                                                   4,663,982         4,488,982
Environmental reserve                                                             7,344,895         8,090,952
Accrued pensions and other                                                          889,731         1,028,285
Minority interest                                                                 2,103,697         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                                                                15,264,521        15,632,925
                                                                                -----------       -----------      
                              Total Stockholders' Equity                         18,453,369        18,821,773
                                                                                -----------       -----------      
                                                                                $55,153,886       $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                       Nine Months Ended
                                                             September 30                            September 30
                                                       1998                1997                1998                 1997
                                                   ------------        ------------        ------------        ------------

<S>                                                <C>                 <C>                 <C>                 <C>         
Net sales                                          $ 22,112,737        $ 22,908,478        $ 64,840,860        $ 69,785,470


Cost of sales                                        16,540,226          17,117,851          48,998,792          52,614,985
Selling, general and administrative expenses          4,769,307           4,501,630          13,311,982          12,879,801
Provision for depreciation and amortization             835,597             849,161           2,469,637           2,461,831
Other income and deductions                             (45,992)                 98            (282,244)            198,532
Minority interest                                        81,617              73,359             222,549             237,555
Interest expense                                        228,315             189,260             587,522             604,843
                                                   ------------        ------------        ------------        ------------


Income (loss) before income taxes                      (296,333)            177,119            (467,378)            787,923

Provision (credit) for income taxes                     (30,033)              3,892             (98,974)            143,127
                                                   ------------        ------------        ------------        ------------

Net income (loss)                                  $   (266,300)       $    173,227        $   (368,404)       $    644,796
                                                   ============        ============        ============        ============


Net income (loss) per common share:
       Basic                                       $       (.17)       $        .11        $       (.23)       $        .41
       Diluted                                     $       (.17)       $        .11        $       (.23)       $        .41


Weighted average shares outstanding:
       Basic                                          1,583,414           1,583,414           1,583,414           1,583,414
       Effects of dilutive stock options                   --                28,925                --                28,925
                                                   ------------        ------------        ------------        ------------
       Diluted                                        1,583,414           1,612,339           1,583,414           1,612,339
                                                   ============        ============        ============        ============

</TABLE>


SEE NOTES TO CONDENSED CONSOLIDATED UNAUDITED FINANCIAL STATEMENTS

                                                                               4
<PAGE>   5


<TABLE>
<CAPTION>
DETREX CORPORATION
CONSOLIDATED UNAUDITED STATEMENTS OF CASH FLOWS                                               Nine Months Ended
                                                                                                September 30
                                                                                                ------------
                                                                                           1998               1997
                                                                                       -----------        -----------
CASH FLOWS FROM OPERATING ACTIVITIES:
<S>                                                                                    <C>                <C>        
          Net income (loss)                                                            $  (368,404)       $   644,796
          Adjustments to reconcile net income to net cash provided by
          operating activities:
                    Depreciation and amortization                                        2,469,637          2,461,831
                    (Gain) loss on disposal of assets                                         (750)           250,459
                    Deferred income taxes                                                 (334,864)            86,271
                    Minority interest                                                      162,550            177,553
          Changes to operating assets and liabilities that provided (used) cash:
                    Accounts receivable                                                  2,971,918           (832,308)
                    Refundable U.S. income taxes                                              --            1,003,827
                    Note receivable                                                           --            1,562,665
                    Inventories                                                           (414,609)          (174,464)
                    Prepaid expenses and other                                            (369,179)            71,938
                    Other assets                                                           (47,996)            16,666
                    Accounts payable                                                    (1,338,214)        (1,406,136)
                    Environmental reserve                                                 (746,057)          (353,513)
                    Accrued compensation                                                  (844,642)           (74,260)
                    Other accruals                                                        (484,439)          (192,502)
                    Postretirement benefits                                                175,000            130,262
                                                                                       -----------        -----------
                              Total adjustments                                          1,198,355          2,728,289
                                                                                       -----------        -----------
                              Net cash provided by operating activities                    829,951          3,373,085
                                                                                       -----------        -----------

CASH FLOWS FROM INVESTING ACTIVITIES:
          Capital expenditures                                                          (4,492,286)        (3,548,079)
          Proceeds from disposal of property                                             1,368,000              2,125
          Unused proceeds from bond issue-restricted for capital expenditures           (2,010,227)              --
          Proceeds from insurance settlement                                             1,250,000               --
                                                                                       -----------        -----------
                               Net cash used in investing activities                    (3,884,513)        (3,545,954)
                                                                                       -----------        -----------

CASH FLOWS FROM FINANCING ACTIVITIES:

          Repayment of short-term bank debt - net                                         (809,609)          (191,735)
          Principal payments under capital lease obligations                              (208,925)          (317,779)
          Proceeds from debt issued                                                      4,000,000               --
          Debt issuance costs                                                             (222,985)              --
                                                                                       -----------        -----------

                               Net cash provided by (used in) financing activities       2,758,481           (509,514)
                                                                                       -----------        -----------
Net decrease in cash and cash equivalents                                                 (296,081)          (682,383)
Cash and cash equivalents at beginning of period                                           398,093          1,311,045
                                                                                       -----------        -----------
Cash and cash equivalents at end of period                                             $   102,012        $   628,662
                                                                                       ===========        ===========

SUPPLEMENTAL DISCLOSURES OF CASH FLOW INFORMATION:
          Cash paid during the period for:
                    Interest                                                           $   596,628        $   584,989
                    Income taxes                                                       $   282,413        $   182,429
SUPPLEMENTAL SCHEDULE OF NONCASH INVESTING AND FINANCING ACTIVITIES:
         Capital lease obligations incurred with the acquisition of equipment          $   119,373        $   556,665
         Capital lease terminations                                                    $   (73,530)       $  (124,147)
</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 nine 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 September 30, 1998 is $8.8 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                      Nine Months Ended       
---------------------------------------------------------------------------------------------------------------------------
                                                              September 30                            September 30
                                                              ------------                            ------------
                                                        1998               1997                 1998              1997
                                                        ----               ----                 ----              ----
                                                     $         %        $         %          $        %         $       %
---------------------------------------------------------------------------------------------------------------------------
<S>                                               <C>        <C>     <C>        <C>       <C>       <C>      <C>     <C>  
Sales                                             22,113     100.0   22,908     100.0     64,841    100.0    69,785  100.0
---------------------------------------------------------------------------------------------------------------------------
Gross margin                                       5,573      25.2    5,791      25.3     15,842     24.4    17,170   24.6
---------------------------------------------------------------------------------------------------------------------------
Selling, general and administrative expenses       4,769      21.6    4,502      19.7     13,312     20.5    12,880   18.5
---------------------------------------------------------------------------------------------------------------------------
Depreciation and amortization                        836       3.8      849       3.7      2,470      3.8     2,462    3.5
---------------------------------------------------------------------------------------------------------------------------
Net income (loss)                                  (266)     (1.2)      173        .8      (368)     (.6)       645     .9
---------------------------------------------------------------------------------------------------------------------------
</TABLE>

Detrex Corporation and its consolidated subsidiaries (the Company) incurred a
net loss of $266,300 for the third quarter of 1998 compared to net income of
$173,227 for the third quarter of 1997. For the first nine months of 1998 the
Company incurred a net loss of $368,404 compared to net income of $644,796 for
the first nine months of 1997.

Sales for the nine month period were down $4.9 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 Company continues to be
adversely affected by the economic situation in Asia, the slowdown in computer
chip manufacturing, and the reduction in capital spending for parts cleaning
equipment. Also, sales of the Company's paint subsidiary , Seibert-Oxidermo,
declined during the second and third quarters as a result of the General Motors
strike.

The Company's gross margin remained relatively constant on a year-to-year basis
with the margins in 1998 being 24.4% versus 24.6% for 1997. Margins for the
quarter were 25.2%, reflecting some margin improvement from the preceding
quarter.

The year-to-date increase in selling, general and administrative expenses is due
to economic increases in all of the Company's operating units, termination and
severance costs accrued in the third quarter, and additional marketing and
technical support personnel in some of the Company's 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, primarily a result of depreciation of plant additions in Ashtabula, Ohio
beginning in 1998.

Interest expense for the nine months is lower than last year due to lower rates
being negotiated when the Company's credit agreement was extended. Interest
expense in the third quarter increased due to interest paid to the Internal
Revenue Service from the tax deferral of income from certain export sales.

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 1998. In late September,
insurance proceeds were received in conjunction with storm damage to a plant
being held for sale. It is anticipated that the plant will be sold in the fourth
quarter. Also, financing for Harvel Plastics' expansion in California is being
accomplished with industrial development bonds.

Working capital was $8.4 million at September 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.


Year 2000 Compliance
---------------------------

The Company currently is working to resolve the potential impact of the Year
2000 on the processing of information by its computerized information systems.
Year 2000 ("Y2K") issues may arise if computer programs have been written using
two digits, instead of four, to define the applicable year. In such case, a
program that utilizes time-sensitive logic may recognize a date using "00" as
the Year 1900 rather than the Year 2000, which could result in miscalculations
or system failures.

In 1997, the Company undertook a study to determine its future computer hardware
and software requirements, including Y2K compliance considerations. Since then
the Company has implemented a program, consisting of two phases, for achieving
upgraded systems and Y2K compliance. The first phase of the program consists of
replacing the Company's computerized information systems with new systems and
programs that are Y2K compliant. As of September 30, 1998, the Company had
substantially completed the first phase. As a result, the Company's accounts
payable, accounts receivable and general ledger were upgraded to new, Y2K
compliant systems and programs, effective with October transactions. The Company
expects to convert its fixed asset records to new, Y2K compliant programs as
part of its 1998 year-end financial closing.

The second phase of becoming Y2K compliant is the implementation of computerized
information systems and programs that perform job costing for the Company's
Equipment Division and sales invoicing for the Company's Solvents Division. The
Company expects to complete the second phase of its Y2K compliance program by
mid-year 1999.

All of the parent Company's operational systems have been reviewed and work
plans have been established to develop Y2K compliance by mid-year 1999. Two of
the Company's subsidiaries, Seibert-Oxidermo, Inc. and Harvel Plastics, Inc.,
are substantially Y2K compliant at the present time. A third subsidiary, The
Elco Corporation, has developed a work plan and has an approved capital
expenditure of approximately $75,000 for its Y2K compliance program which is
scheduled to be completed by mid-year 1999.

Since the Company relies on electronic data from certain of its vendors,
financial institutions and customers, the Company has conducted surveys to
determine if these entities are Y2K compliant or are on schedule to become Y2K
compliant before the end of 1999. The Company has sent detailed questionnaires
to approximately 450 vendors, financial institutions and customers to determine
if they are on schedule to become Y2K compliant. Approximately 250 entities have
responded to the questionnaires in varying degrees of detail. All of these
entities have indicated that they are or will become Y2K compliant. However, the
Company has not yet conducted any testing with third parties and therefore has
no assurance that these entities, or others that have not responded, will become
Y2K compliant on a timely basis. If the Company's most significant vendors,
financial institutions and customers fail to become Y2K compliant on a timely
basis, such failure could have a material adverse effect on the Company's
business and operations.


                                                                               8

<PAGE>   9

DETREX CORPORATION


To become Y2K compliant, the Company has appointed an officer as project
coordinator for its Y2K program and has engaged the services of information
services consultants. As of September 30, 1998, the Company had spent
approximately $400,000 to upgrade its information systems and programs, most of
which were capital expenditures. Although the Company cannot predict with
certainty the remaining expenditures that it will make during 1998 and 1999 for
such upgrades, the Company's current estimates are in the range of $500,000,
most of which will also be capital expenditures. The Company cannot accurately
allocate the portion of such expenditures for information systems and programs
that relate solely to Y2K compliance.

In the last eighteen months, the Company has dedicated significant management
attention to the Y2K issue. Management updates the Board of Directors on a
regular basis concerning the Company's progress in achieving Y2K compliance.
Because it expects to become Y2K compliant, the Company has not developed a
contingency plan in the event that it should fail to become Y2K compliant. The
Company will continue to monitor its progress in becoming Y2K compliant and will
develop a contingency plan, probably involving the use of an outside service
bureau, if it determines that there will be a shortfall in its Y2K efforts or
those of its vendors, financial institutions and customers. The Company
currently cannot determine the cost of a contingency plan, should one be
necessary.

The cost of the Company's Y2K program and the dates by which the Company
believes it will become Y2K compliant are based upon management's best
estimates. The Company cannot assure that it will achieve Y2K compliance
according to this program and actual results could differ from those outlined.
Various factors, including numerous assumptions as to future events, the timely
availability of experienced personnel, the complexity of the transition from its
old systems to the new systems and the compliance efforts of third parties,
which the Company does not control, may adversely affect its Y2K compliance
progress. Any failure to become Y2K compliant on a timely basis could have a
material adverse effect on the Company, including the inability to properly bill
and collect payments from customers, as well as errors and omissions in
accounting and financial data.

                           PART II - OTHER INFORMATION
                           ---------------------------

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 
              September 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    11/12/98             /s/ S. J. Quinlan
     -----------------      ---------------------------------------------- 
                            S. J. Quinlan
                            Controller and Chief Accounting Officer



Date     11/12/98            /s/  G. J. Israel                 
     -----------------      ---------------------------------------------- 
                            G. J. Israel
                            Vice President - Finance and Chief Financial Officer






                                                                              10


<PAGE>   11




                               INDEX TO EXHIBITS



EXHIBIT NO.                   DESCRIPTION
-----------                   -----------

    27                        Financial Data Schedule