<PAGE>   1


                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                    Form 10-Q


[X]      QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
         EXCHANGE ACT OF 1934 FOR THE QUARTERLY PERIOD ENDED SEPTEMBER 30, 1998

                                       or

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

         FOR THE TRANSITION PERIOD FROM _________________ TO _________________ 


                         Commission File Number: 0-15383


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

             North Carolina                             56-1019741 
--------------------------------------------------------------------------------
         (State of Incorporation)           (I.R.S. Employer Identification No.)

   3100 Smith Farm Road, Matthews, NC                      28105 
--------------------------------------------------------------------------------
(Address of principal executive offices)                (Zip Code)


               Post Office Box 200, Matthews, North Carolina 28106
--------------------------------------------------------------------------------
                (Mailing address of principal executive offices)


                                 (704) 821-7015
--------------------------------------------------------------------------------
              (Registrant's telephone number, including area code)


Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months (or for such shorter period that the registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days.

                             Yes [X]     No [ ]


3,082,543 shares of the issuer's $.05 par value common stock, its only class of
common stock, were outstanding as of October 26, 1998.


<PAGE>   2


PART I. FINANCIAL INFORMATION


ITEM 1. FINANCIAL STATEMENTS
CONDENSED CONSOLIDATED FINANCIAL STATEMENTS
For the Quarter Ended September 30, 1998
CEM Corporation
Matthews, North Carolina


The condensed financial statements included herein have been prepared by the
Company, without audit, pursuant to the rules and regulations of the Securities
and Exchange Commission. Certain information and footnote disclosures normally
included in financial statements prepared in accordance with generally accepted
accounting principles have been condensed or omitted pursuant to such rules and
regulations, although the Company believes that the disclosures are adequate to
make the information presented not misleading. It is suggested that these
condensed financial statements be read in conjunction with the financial
statements and the notes thereto included in the Company's Annual Report on Form
10-K for the fiscal year ended June 30, 1998.


                                       2

<PAGE>   3


                                 CEM Corporation
                      Condensed Consolidated Balance Sheets
                         September 30 and June 30, 1998
                                   (unaudited)

(in thousands)

<TABLE>
<CAPTION>
                                               September 30       June 30
                                               ------------       -------
<S>                                            <C>                <C>    
ASSETS

Current Assets:
   Cash and cash equivalents ............         $ 1,672         $ 2,963
   Short-term investments ...............           3,200           3,200
   Trade receivables ....................           6,025           6,616
   Inventories ..........................           6,285           5,675
   Deferred taxes and other .............             433             488
                                                  -------         -------

      Total current assets ..............          17,615          18,942

Long-term Investments ...................           3,532           3,442

Property, Plant and Equipment, Net ......           5,032           4,925

Other Assets ............................             953             989
                                                  -------         -------

                                                  $27,132         $28,298
                                                  =======         =======


LIABILITIES AND SHAREHOLDERS' EQUITY

Current Liabilities:
   Accounts payable and accrued expenses          $ 2,573         $ 3,488
   Deferred income ......................           1,278           1,280
   Income taxes payable .................             556             538
                                                  -------         -------

      Total current liabilities .........           4,407           5,306

Long-term Debt, Net of Current Maturities           1,265           1,177

Deferred Taxes ..........................              96              96

Shareholders' Equity ....................          21,364          21,719
                                                  -------         -------

                                                  $27,132         $28,298
                                                  =======         =======
</TABLE>


See accompanying notes to condensed consolidated financial statements.


                                       3

<PAGE>   4



                                 CEM Corporation
                   Condensed Consolidated Statements of Income
             For the three months ended September 30, 1998 and 1997
                                   (unaudited)

(in thousands, except per share data)

<TABLE>
<CAPTION>
                                                       1998             1997
                                                     -------          -------

<S>                                                  <C>              <C>    
Net sales ..................................         $ 7,152          $ 6,603
Cost of goods sold .........................           3,509            3,061
                                                     -------          -------
      Gross profit .........................           3,643            3,542

Selling, general and administrative expenses           2,593            2,631
Research and development expenses ..........             730              687
                                                     -------          -------
      Income from operations ...............             320              224

Investment income ..........................             105              151
Other expenses, net ........................             (10)             (16)
                                                     -------          -------
      Income before income taxes ...........             415              359

Provision for income taxes .................             132              118
                                                     -------          -------
      Net income ...........................             283              241
Foreign Currency Translation ...............              50             (177)
                                                     -------          -------
      Comprehensive Income .................         $   333          $    64
                                                     =======          =======

Net Income Per Share:

      Basic ................................         $   .09          $   .07
                                                     =======          =======

      Diluted ..............................         $   .09          $   .07
                                                     =======          =======

Average Shares Outstanding:

        Basic ..............................           3,163            3,486
                                                     =======          =======

        Diluted ............................           3,208            3,504
                                                     =======          =======
</TABLE>




See accompanying notes to condensed consolidated financial statements.



                                       4


<PAGE>   5

                                 CEM Corporation
                 Condensed Consolidated Statements of Cash Flows
             For the three months ended September 30, 1998 and 1997
                                   (unaudited)

(in thousands)

<TABLE>
<CAPTION>
                                                                     1998             1997
                                                                   -------          -------

<S>                                                                <C>              <C>    
Net cash provided by operating activities ................         $    61          $ 1,423
                                                                   -------          -------

Cash flows from investing activities:
      Purchase of available-for-sale investments .........            --               (700)
      Acquisition of intangibles .........................             (19)             (78)
      Capital expenditures, net ..........................            (313)            (187)
                                                                   -------          -------
                  Net cash used in investing activities ..            (332)            (965)
                                                                   -------          -------

Cash flows from financing activities:
      Payment of notes payable ...........................             (96)            --
      Proceeds from issuance of common stock .............              21               25
      Repurchase of common stock .........................            (948)             (47)
                                                                   -------          -------
              Net cash used in financing activities ......          (1,023)             (22)
                                                                   -------          -------

Effects of exchange rates on cash ........................               3                2
                                                                   -------          -------

      Net increase/(decrease) in cash and cash equivalents          (1,291)             438
      Cash and cash equivalents at beginning of period ...           2,963            5,833
                                                                   -------          -------

Cash and cash equivalents at end of period ...............         $ 1,672          $ 6,271
                                                                   =======          =======

</TABLE>



See accompanying notes to condensed consolidated financial statements.


                                       5

<PAGE>   6

                                 CEM Corporation
              Notes to Condensed Consolidated Financial Statements
                                   (unaudited)


1.  Basis of Presentation

The financial information included herein is unaudited; however, such
information reflects all adjustments (consisting of normal recurring
adjustments) which are, in the opinion of management, necessary for a fair
presentation of results for the interim periods. The results of operations for
the three months ended September 30, 1998 are not necessarily indicative of the
results that may be expected for the year ended June 30, 1999.


2.  Inventories

The components of inventories at current cost at September 30 and June 30, 1998
are as follows:

(in thousands)

<TABLE>
<CAPTION>
                                       September 30      June 30
                                       ------------      -------
<S>                                    <C>               <C>   
Parts and raw materials ..........         $3,729         $3,302
Work-in-process and finished goods          2,556          2,373
                                           ------         ------
                                           $6,285         $5,675
                                           ======         ======
</TABLE>


3.  Net Income Per Common Share

Basic Net Income Per Share Computation:

The computation of basic earnings per share is computed by dividing income
available to common shareholders by the weighted average number of common shares
outstanding during the period. Shares issued during the period and shares
repurchased by the Company during the period are weighted for the portion of the
period that they were outstanding. Income and share information for the three
months ended September 30, 1998 follows:

(in thousands, except per share data)

<TABLE>
<S>                                               <C>       <C>            <C> 
Net income....................................                             $      283
Less: preferred stock dividends...............                                      -
                                                                           ----------
Income available to common stockholders.......                             $      283
                                                                           ==========
                                                   
           Dates                                             Fraction          Weighted
        Outstanding                                Shares    of Period     Average Shares
        -----------                                ------    ---------     --------------
Shares outstanding, July 1, 1998..............                                  3,180
Shares repurchased during the period..........     (91)        17/92              (17)
Stock options exercised during the period.....       3           -                  -
                                                                           ----------
Weighted average shares.......................                                  3,163
                                                                           ==========
                                                   
Basic earnings per common share...............                             $      .09
                                                                           ==========
</TABLE>

                                       6


<PAGE>   7

3. Net Income Per Common Share (continued)

Income and share information for the three months ended September 30, 1997
follows:

(in thousands, except per share data)

<TABLE>
<S>                                                <C>       <C>         <C>    
Net income.......................................                          $   241
Less: preferred stock dividends..................                                -
                                                                           -------
Income available to common shareholders..........                          $   241
                                                                           =======

              Dates                                          Fraction        Weighted
           Outstanding                             Shares    of Period    Average Shares
           -----------                             ------    ---------    --------------
Shares outstanding, July 1, 1997.................                            3,487
Shares repurchased during the period.............   (5)        18/92            (1)
Stock options exercised during the period........    3             -             -
                                                                           -------
Weighted average shares..........................                            3,486
                                                                           =======

Basic earnings per common share..................                          $   .07
                                                                           =======
</TABLE>


Diluted Net Income Per Share Computation:

The computation of diluted earnings per common share is similar to the
computation of basic earnings per common share except that the denominator is
increased to include the number of additional common shares that would have been
outstanding if the dilutive potential common shares had been issued. Potential
common shares consist of dilutive stock options using the treasury stock method.

(in thousands, except per share data)

<TABLE>
<CAPTION>
                                                  For the three months  For the three months 
                                                          ended                ended
                                                   September 30, 1998    September 30, 1997
                                                   ------------------    ------------------
<S>                                               <C>                    <C>   
Net Income .....................................         $  283              $  241
Less: preferred stock dividends ................           --                  --
                                                         ------              ------
Income available to common shareholders ........         $  283              $  241
                                                         ======              ======
                                                                       
Weighted average shares ........................          3,163               3,486
Dilutive potential common shares (stock options)             45                  18
                                                         ------              ------
Adjusted weighted average shares ...............          3,208               3,504
                                                         ======              ======
Diluted earnings per share .....................         $  .09              $  .07
                                                         ======              ======
</TABLE>

Options to purchase 45,000 and 304,000 shares of common stock at a weighted
average price of $11.41 and $9.19 per share were outstanding during the three
months ended September 30, 1998 and 1997, respectively, which were not included
in the computation of diluted earnings per share because the option exercise
prices were greater than the average market price of the common shares during
the periods.


4.  New Pronouncement

There have been no new pronouncements issued which have not already been
implemented by the Company which management believes would have a material
impact on the financial statements.

                                       7


<PAGE>   8

ITEM 2.  Management's Discussion and Analysis of
Financial Condition and Results of Operations


The following table sets forth, for the three-month periods indicated, the
percentages which certain components of the condensed consolidated statements of
income bear to net sales and the percentage of change of such components from
the same period of the prior year.

<TABLE>
<CAPTION>
                                                            Three Months Ended
                                                   -------------------------------------
                                                    9/30/98       9/30/97      % Change
                                                    -------       -------      --------

<S>                                                <C>           <C>           <C>  
Net sales ..................................         100.0 %       100.0 %         8.3 %
Cost of goods sold .........................          49.1          46.4          14.6
                                                      ----          ----          
         Gross profit ......................          50.9          53.6           2.9

Selling, general and administrative expenses          36.2          39.9          (1.4)
Research and development expenses ..........          10.2          10.4           6.3
                                                      ----          ----          
         Income from operations ............           4.5           3.3          42.9

Investment income ..........................           1.5           2.3         (30.5)
Other expense, net .........................          (0.2)         (0.2)           nm
                                                      ----          ----          
         Income before income taxes ........           5.8           5.4          15.6

Provision for income taxes .................           1.8           1.8          11.9
                                                      ----          ----          
         Net income ........................           4.0 %         3.6 %        17.4
                                                      ====          ====          
</TABLE>


Results of Operations

Net sales for the first quarter of fiscal 1999 increased 8.3% primarily due to
the Company's Microwave Accelerated Reaction System (MARS), which accounted for
approximately 26% of net sales for the period. US sales increased 14% and
foreign sales increased 2%, despite continued declines in Asian sales. Foreign
sales as a percent of total sales decreased from 46% to 43%.

Gross profit margins declined from 53.6% to 50.9% primarily due to competitive
pricing pressure in Europe resulting from the MARS market share gain (MARS
currently carries lower profit margins), inventory adjustments, instrument
trade-in discounts and product mix. During the later half of fiscal 1999,
management expects some margin pressure resulting from new product
introductions. This pressure should be mitigated by MARS platform costs
reductions.

Selling, general and administrative expenses decreased slightly compared to the
prior year primarily due to the settlement of the litigation that the Company
initiated to establish the validity of a patent for microwave digestion vessels.
The 6.3% increase in research and development expense from the prior year
reflects the Company's continued commitment to new product development and
enhancements. Management expects research and development expense to remain
between 8% and 10% of sales for the foreseeable future.

Investment income decreased 30.5% due to a decrease in average cash and
investment balances during the period.

The Company's effective tax rate decreased slightly to 32% which approximates
the fiscal 1998 tax rate.


                                       8

<PAGE>   9

ITEM 2.  Management's Discussion and Analysis of
Financial Condition and Results of Operations


Financial Condition

In the first quarter of fiscal 1999, the Company generated cash from operations
of $61,000. Cash generated through accounts receivable collections since June
30, 1998 was offset by an increase in inventories and routine payments of fiscal
1998 accruals, including incentive compensation and employee profit sharing. The
increase in inventory resulted from high MARS raw material inventory levels
which management expects to decrease by the end of the second fiscal quarter
with the seasonal increase in sales.

During the three months ended September 30, 1998, the Company invested $948,000
to acquire 85,000 shares of its common stock. Another $181K was committed to
acquire 15,600 shares of common stock during the quarter; however, the trades
had not been settled by September 30, 1998. This exhausted the amount remaining
under the funds authorized by the Board of Directors for this purpose. On
November 5, 1998, the Company's Board of Directors authorized an additional $2
million to repurchase common stock. One of the benefits of any shares
repurchased as a result of this program will be to minimize the dilutive effect
to existing shareholders from the issuance of shares under the Company's
Management Equity Plan and Nonqualified Stock Option Plan for Non-Employee
Directors. The stock repurchase program had the effect of increasing net income
per diluted share by $.01 for the quarter as compared to the same quarter last
year.

Management believes that working capital, planned capital expenditures, debt
servicing and stock repurchases can be funded currently with cash on hand and
cash generated from operations. The Company has never paid, and does not
anticipate paying, cash dividends in the foreseeable future.


Year 2000 Issues

The Company expects to complete its plan for addressing the Year 2000 Issue by
the end of its second fiscal quarter. Plans for addressing IT systems in the
United States are substantially complete and involve primarily software upgrades
and/or hardware upgrades. The Company believes that it will be able to identify
similar ways to address IT systems located outside of the United States. For
non-IT systems, the Company does not expect to identify any areas that are not
capable of being repaired at a fairly low cost or where Year 2000 problems would
have a material impact on the Company.

The Company expects to complete the implementation of its plans to address the
Year 2000 Issue sometime during late calendar 1999, in time to allow testing to
ensure that the steps taken will be adequate to address the problems identified.
If the Company's plans to address these issues are not successful, the Company
would attempt to identify and purchase replacement systems that do not have
problems associated with the Year 2000 Issue. The cost of such replacement
systems has not been estimated by the Company.


Cautionary Statement

The following cautionary statement identifies important factors that could cause
the Company's actual results to differ materially from those projected in
forward-looking statements made by or on behalf of the Company. Except for
factual statements and historical information contained here, the matters
discussed in the foregoing discussion may be deemed forward-looking statements
within the meaning of the Private Securities Litigation Reform Act of 1995.
Forward-looking statements are statements that include projections, predictions,
expectations or beliefs about future events or results or otherwise are not
statements of historical fact. Such statements are often characterized by the
use of qualifying words (and their derivatives) such as "expect," "believe,"
"plan," "project," or other statements concerning opinions or judgment of the
Company and its management about future events.

The industry in which the Company competes, as well as the markets that it
serves, is characterized by cyclical market patterns as a consequence of, among
other things, business cycles, foreign exchange fluctuations, regulatory
changes, government spending levels and general economic conditions. These
factors affect the timing of orders from the Company's customers and cause
substantial variations in sales and profitability from quarter to quarter.
Likewise, supplier-related delays and the timing of the release of orders by the
Company's customers may affect quarter-to-quarter sales and profitability. 


                                       9

<PAGE>   10

The Company's sales may also be adversely affected by direct and indirect
competition from third parties including, but not limited to, legal challenges
to existing patents or pending patent applications.

Demand for the Company's instrumentation is substantially affected by the
enactment, timing, extent and severity of state, federal and foreign laws
governing environmental testing standards as well as product labeling
requirements including foods and pharmaceuticals. The Company has and may
experience fluctuations in sales of such products as well as in demand for
particular product enhancements as a result of actual or perceived changes in
regulatory requirements. Legislation or regulations resulting in the development
or expansion of acceptance standards for specific testing methods has and may
result in periodic delays in sales, especially in the United States. Conversely,
increases in international sales have resulted, and may result in the future,
from less stringent or nonexistent acceptance standards in a given country.

Moreover, the Company's success is dependent on its ability to continue to
develop and engineer high-quality, high-performance products that are
commercially acceptable. Risks associated with new product development include
market acceptance, competition from other products and the Company's ability to
manufacture and market products on an efficient and timely basis at a reasonable
cost and in sufficient volume.




PART II. OTHER INFORMATION


ITEMS 1, 2, 3, 4 and 5 are not applicable and are omitted.


ITEM 6. Exhibits and Reports on Form 8-K

         (a) Exhibits:

              3.1      Restated Charter of the Company, as amended.(1)

              3.2      Bylaws of the Company.(1)

             10.1   *  CEM Corporation 1986 Nonqualified Stock Option
                       Plan, as amended, incorporated herein by reference to
                       the Company's Registration Statement on Form S-8
                       (File No. 33-53694).

             10.2   *  CEM Corporation Employee Stock Purchase Plan, as
                       amended, incorporated herein by reference to the
                       Company's Registration Statement on Form S-8 (File
                       No. 33-80136).

             10.3   *  CEM Corporation 1987 Stock Option Plan, as
                       amended.(1)

             10.4   *  CEM Corporation 1993 Management Equity Plan,
                       incorporated herein by reference to the Company's
                       Registration Statement on Form S-8 (File No.
                       33-75368).

             10.5   *  CEM Corporation Management Incentive Compensation
                       Plan(2).

             10.6      CEM Corporation 1993 Nonqualified Stock Option Plan
                       for Non-Employee Directors, incorporated herein by
                       reference to the Company's Registration Statement on
                       Form S-8 (File No. 33-75366).

              27       Financial Data Schedule (filed in electronic format
                       only). This schedule shall not be deemed "filed" for
                       purposes of Section 11 of the Securities Act of 1933
                       or Section 18 of the Securities Exchange Act of 1934
                       or otherwise be subject to the liabilities of such
                       sections, nor shall it be deemed a part of any
                       registration statement to which it relates.


                    *  This exhibit is one of the Company's management
                       contracts and compensatory plans and arrangements.
                      
                   (1) Incorporated herein by reference to the Company's
                       Form 10-K for the year ended June 30, 1994.
                      
                   (2) Incorporated herein by reference to the Company's
                       Form 10-K for the year ended June 30, 1997.


         (b) Reports on Form 8-K:

                  No Reports on Form 8-K were filed during the quarter ended
September 30, 1998.

                                       10

<PAGE>   11


                                 CEM CORPORATION
                                    SIGNATURE


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.



Date: November 9, 1998                  CEM CORPORATION

                                        BY:  \s\ Richard N. Decker
                                             ---------------------------------
                                             Richard N. Decker
                                               Secretary, Treasurer and
                                               Chief Financial Officer



                                       11

<PAGE>   12


                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                                Washington, D.C.

                                    EXHIBITS

                                    ITEM 6(a)

                          Quarterly Report on Form 10-Q


For the quarter ended September 30, 1998        Commission File Number: 0-15383


                                 CEM CORPORATION
                                  EXHIBIT INDEX

Exhibit Number:       Exhibit Description                                      
---------------       -------------------                                      

      27              Financial Data Schedule (filed in electronic format only)




                                       12