<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                              Washington, DC 20549

                              ---------------------

                                    FORM 10-Q



[X]  Quarterly Report Pursuant to Section 13 or 15(d) of the Securities Exchange
     Act of 1934

[ ]  Transition Report Pursuant to Section 13 or 15(d) of the Securities
     Exchange Act of 1934



For Quarter Ended October 3, 1998                    Commission File No. 0-12640
---------------------------------                    ---------------------------


                               KAYDON CORPORATION


       A Delaware Corporation                IRS Employer ID No. 13-3186040
--------------------------------------------------------------------------------

19345 US 19 North, Clearwater, FL  33764                     Phone: 727/531-1101
--------------------------------------------------------------------------------




Kaydon Corporation:

         (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.

                                            Yes   X           No
                                                 ---             ---

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

                                            Yes   X           No
                                                 ---             ---

Common Stock Outstanding at November 12, 1998 - 32,162,025 shares, $0.10 par
value.


<PAGE>   2



                          KAYDON CORPORATION FORM 10-Q

                      FOR THE QUARTER ENDED OCTOBER 3, 1998


                                      INDEX
--------------------------------------------------------------------------------


<TABLE>
<CAPTION>
                                                                                              Page No.
                                                                                              --------
<S>      <C>                                                                                  <C>
Part I - Financial Information:

         Consolidated Condensed Balance Sheets -
         October 3, 1998 and December 31, 1997                                                   1

         Consolidated Condensed Statements of Income -
         Three Months and Nine Months Ended October 3, 1998
         and September 27, 1997                                                                  2

         Consolidated Condensed Statements of Cash Flows -
         Nine Months Ended October 3, 1998
         and September 27, 1997                                                                  3

         Notes to Consolidated Condensed Financial Statements                                  4 - 7

         Management's Discussion and Analysis of
         Financial Condition and Results of Operations                                         8 - 10



Part II - Other Information:

         Item 5. - Other Information                                                             11

         Item 6. - Exhibits and Reports on Form 8-K                                              11

         Signatures                                                                              12
</TABLE>





<PAGE>   3



                               KAYDON CORPORATION

                      CONSOLIDATED CONDENSED BALANCE SHEETS
--------------------------------------------------------------------------------



<TABLE>
<CAPTION>
                                              October 3, 1998   December 31, 1997
                                              ---------------   -----------------
                                                 (Unaudited)
<S>                                           <C>               <C>
Assets:
Cash and securities                            $ 75,314,000      $ 96,802,000
Accounts receivable, net                         53,684,000        42,690,000
Inventories, net                                 71,569,000        60,548,000
Other current assets                             12,972,000        14,738,000
                                               ------------      ------------

Total current assets                            213,539,000       214,778,000


Plant and equipment, net                         97,839,000        85,510,000
Cost in excess of net tangible
  assets of purchased businesses, net            65,775,000        66,687,000
Other assets                                     19,377,000        17,010,000
                                               ------------      ------------

Total assets                                   $396,530,000      $383,985,000
                                               ============      ============

Liabilities and Stockholders' Investment:
Accounts payable                               $ 14,751,000      $ 11,574,000
Accrued expenses                                 52,765,000        52,782,000
Federal income tax payable                        1,454,000         6,659,000
                                               ------------      ------------

Total current liabilities                        68,970,000        71,015,000

Other long-term liabilities                      30,490,000        29,374,000
Stockholders' investment                        297,070,000       283,596,000
                                               ------------      ------------
Total liabilities and
    stockholders' investment                   $396,530,000      $383,985,000
                                               ============      ============
</TABLE>


See accompanying notes to consolidated condensed financial statements.


                                        1

<PAGE>   4



                               KAYDON CORPORATION

                   CONSOLIDATED CONDENSED STATEMENTS OF INCOME
                                   (UNAUDITED)
--------------------------------------------------------------------------------


<TABLE>
<CAPTION>
                                                      THREE MONTHS ENDED                NINE MONTHS ENDED
                                                Oct 3, 1998      Sep 27, 1997      Oct 3, 1998      Sep 27, 1997
                                                -----------      -----------      ------------      ------------
<S>                                             <C>              <C>              <C>               <C>
Net sales                                       $92,801,000      $83,380,000      $291,458,000      $244,365,000

Gross profit                                     37,165,000       34,356,000       118,247,000       101,753,000

Operating income                                 27,328,000       24,587,000        84,778,000        70,902,000

Interest income, net                                996,000          847,000         3,443,000         2,610,000
                                                -----------      -----------      ------------      ------------


Income before income taxes                       28,324,000       25,434,000        88,221,000        73,512,000

Provision for income taxes                       10,764,000        9,664,000        33,525,000        27,957,000
                                                -----------      -----------      ------------      ------------


Net income                                      $17,560,000      $15,770,000      $ 54,696,000      $ 45,555,000
                                                ===========      ===========      ============      ============


Weighted Average Common Shares:
  Basic                                          32,466,000       32,986,000        32,736,000        32,968,000
  Diluted                                        32,694,000       33,194,000        32,979,000        33,140,000


Earnings Per Share:
  Basic                                         $      0.54      $      0.48      $       1.67      $       1.38
  Diluted                                       $      0.54      $      0.47      $       1.66      $       1.37
</TABLE>




See accompanying notes to consolidated condensed financial statements.



                                        2

<PAGE>   5




                               KAYDON CORPORATION

                 CONSOLIDATED CONDENSED STATEMENTS OF CASH FLOWS
                                   (UNAUDITED)
--------------------------------------------------------------------------------


<TABLE>
<CAPTION>
                                                             NINE MONTHS ENDED
                                                       Oct 3, 1998        Sep 27, 1997
                                                      -------------     --------------
<S>                                                   <C>                <C>
Cash flows from operating activities                  $ 42,214,000       $ 44,251,000
                                                      ------------       ------------

Cash flows from investing activities:
 Purchases of marketable securities                    (44,956,000)       (86,025,000)
 Maturities of marketable securities                    67,023,000         89,122,000
 Capital expenditures, net                             (21,438,000)        (9,154,000)
 Acquisition of businesses, net of cash acquired            82,000        (27,027,000)
                                                      ------------       ------------

 Cash provided by (used in) investing activities           711,000        (33,084,000)
                                                      ------------       ------------


Cash flows from financing activities:
 Proceeds from issuance of common stock                  4,148,000          1,094,000
 Dividends paid                                         (8,916,000)        (6,921,000)
 Purchase of treasury stock                            (38,601,000)          (832,000)
 Payment of debt                                                 0         (8,031,000)
                                                      ------------       ------------

 Cash used in financing activities                     (43,369,000)       (14,690,000)
                                                      ------------       ------------

Effect of exchange rate changes on cash
 and cash equivalents                                    1,023,000           (197,000)
                                                      ------------       ------------

Net decrease in cash and cash equivalents                  579,000         (3,720,000)

Cash and cash equivalents - Beginning of period         74,735,000         54,443,000
                                                      ------------       ------------

Cash and cash equivalents - End of period             $ 75,314,000       $ 50,723,000
                                                      ============       ============

Cash expended for income taxes                        $ 35,016,000       $ 29,030,000
                                                      ============       ============

Cash expended for interest                            $     35,000       $    210,000
                                                      ============       ============
</TABLE>


See accompanying notes to consolidated condensed financial statements.

                                        3

<PAGE>   6




                               KAYDON CORPORATION

              NOTES TO CONSOLIDATED CONDENSED FINANCIAL STATEMENTS
--------------------------------------------------------------------------------

(1)      The consolidated condensed financial statements included herein have
         been prepared by Kaydon Corporation and subsidiaries (the "Company"),
         without audit, pursuant to the rules and regulations of the Securities
         and Exchange Commission. Certain information and footnote disclosures
         normally included in annual 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 made in this document are adequate to
         make the information presented not misleading. It is suggested that
         these consolidated condensed financial statements be read in
         conjunction with the consolidated financial statements and notes
         thereto in the Company's 1997 Annual Report on Form 10-K.

(2)      In the opinion of management, the accompanying unaudited consolidated
         condensed financial statements contain all adjustments, of a normal and
         recurring nature, necessary to present fairly the financial position of
         the Company as of October 3, 1998 and the results of its operations and
         its cash flows for the nine months then ended. However, interim results
         are not necessarily indicative of results of a full year.

(3)      Inventories are valued at the lower of cost or market and include
         material, labor and overhead. Cost is determined under the first-in,
         first-out ("FIFO") method.
         Inventories are summarized as follows:

<TABLE>
<CAPTION>
                                      Oct 3, 1998             Dec 31, 1997
                                     ------------             ------------
         <S>                         <C>                      <C>
         Raw Material                 $26,194,000              $20,282,000
         Work in Process               25,160,000               19,424,000
         Finished Goods                20,215,000               20,842,000
                                      -----------              -----------
                                      $71,569,000              $60,548,000
                                      ===========              ===========
</TABLE>

(4)      Effective January 1, 1998, the Company adopted Statement of Financial
         Accounting Standards No. 130, "Reporting Comprehensive Income". This
         statement establishes standards for reporting and display of
         comprehensive income and its components. Comprehensive income reflects
         the change in equity of a business enterprise during a period from
         transactions and other events and circumstances from nonowner sources.
         For the Company, the comprehensive income represents net income
         adjusted for unrealized gains and losses on foreign currency
         translation adjustments. Other comprehensive income, net of tax, was
         approximately $1,026,000 and $(935,000), resulting in comprehensive
         income of $18,586,000 and $14,835,000 for the quarters

                                        4

<PAGE>   7



         ended October 3, 1998 and September 27, 1997, respectively. On a nine
         month basis, other comprehensive income, net of tax, was approximately
         $2,118,000 for 1998 versus a net loss of $1,746,000 for 1997, resulting
         in year to date comprehensive income of $56,814,000 and $43,809,000 for
         the quarters ended October 3, 1998 and September 27, 1997,
         respectively.

(5)      Effective December 31, 1997, the Company adopted the provisions of
         Statement of Financial Accounting Standards No. 128, "Earnings Per
         Share". This statement establishes standards for computing and
         presenting earnings per share ("EPS"). Under these standards, basic
         earnings per share excludes dilution and is computed by dividing net
         income by the weighted average number of common shares outstanding for
         the period. Diluted earnings per share is computed by dividing net
         income by the weighted average number of common shares outstanding plus
         all potential common shares. Dilutive potential common shares include
         all shares which may become contractually issuable. For the Company,
         dilutive potential common shares are primarily comprised of shares
         issuable under stock option plans. All prior period earnings per share
         data presented has been restated to conform to this statement.

         The following table reconciles the numerators and denominators used in
         the calculation of basic and diluted earnings per share for the
         quarters presented.

<TABLE>
<CAPTION>
                                                  Quarter Ending   Quarter Ending
                                                    Oct 3, 1998     Sep 27, 1997
                                                    -----------     ------------
         <S>                                      <C>              <C>
         Numerators:
           Numerators for both basic
           and diluted earnings per share,
           net income                             $17,560,000      $15,770,000
                                                  ===========      ===========

         Denominators:
           Denominators for basic earnings
           per share, weighted average
           common shares outstanding               32,466,000       32,986,000

         Potential dilutive shares resulting
         from stock option plans                      228,000          208,000
                                                  -----------      -----------

         Denominator for dilutive
         earnings per share                        32,694,000       33,194,000
                                                  ===========      ===========

         Earnings Per Share:
         Basic                                    $       .54      $       .48
         Diluted                                  $       .54      $       .47
                                                  ===========      ===========
</TABLE>




                                        5

<PAGE>   8



(6)      The Company, together with other companies, certain former officers and
         directors, has been named as a co-defendant in lawsuits filed in
         federal court in New York in 1993. The suits purport to be class
         actions on behalf of all persons who have unsatisfied personal injury
         and property damage claims against Keene Corporation which filed for
         bankruptcy under Chapter 11. The premise of the suits is that assets of
         Keene were transferred to Bairnco subsidiaries, of which Kaydon was one
         in 1983, at less than fair value. The suits also allege that the
         Company, among other named defendants, was a successor to Keene. The
         Keene Creditors' Trust is seeking from the defendants, collectively,
         damages approximating $700 million. The complaint fails to specify the
         amount of damages sought against Kaydon individually. In 1994, an
         examiner was appointed by a bankruptcy court to examine the issues at
         stake. On September 23, 1994, the "Preliminary Report of the Examiner"
         was made public. In the report, the examiner stated that the alleged
         fraudulent conveyance claims against the Company appear to be
         time-barred by the statute of limitations, subject to certain possible
         exceptions which the Company does not believe are significant or
         factual. In June 1995, the creditors' committee filed a complaint in
         the same bankruptcy court asserting claims against the Company similar
         to those previously filed. On June 12, 1996, the District and
         Bankruptcy Courts for the Southern District of New York entered an
         order confirming the plan of reorganization for Keene Corporation. As a
         result, the so-called transactions lawsuit was transferred in April
         1997 from the Bankruptcy Court for the Southern District of New York to
         the District Court for that district and the stay of the transactions
         lawsuit was lifted. On September 15, 1997, the Company submitted a
         motion to dismiss the complaint based on the statute of limitations.
         All motions, supporting documents and rebuttal were filed on December
         15, 1997. On October 13, 1998, the U.S. District Court, Southern
         District of New York, issued an Opinion which dismissed many of the
         charges against Kaydon and the other defendants. At the same time, the
         Opinion denied Kaydon's motion for summary judgement and dismissal on
         the statute of limitation. The Opinion stated that the suit may go
         forward and the stay of discovery is lifted. Management believes it has
         meritorious defenses against any claims. Accordingly, no provision has
         been reflected in the consolidated financial statements for any alleged
         damages. Management further believes that the outcome of this
         litigation will not have a material adverse effect on the Company's
         financial position.

         In June 1996, the Company received a subpoena issued by the U.S.
         District Court in Bridgeport, Connecticut on behalf of a grand jury
         investigating a May 9, 1996 accident involving a Sikorsky helicopter
         (CH-53E) in which four persons died. The grand jury requested and
         received documents and records relating to bearings manufactured by
         Kaydon and used in the Sikorsky helicopter. In addition, a "Mishap
         Board" led by Sikorsky Aircraft Corporation alleged that

                                        6

<PAGE>   9



         product quality problems or deficiencies existed with respect to the
         Kaydon bearing used in the Sikorsky helicopter described above. Kaydon
         was excluded from participation on this "Mishap Board". However, it has
         independently evaluated the available evidence and refuted the "Mishap
         Board" findings in reports submitted to the Navy. Subsequent incidents
         have occurred in the helicopter fleet even though the bearings used
         were newly manufactured, inspected and approved by Sikorsky and Navy
         personnel, reinforcing the Company's position that the bearing quality
         was not the causative action in the May 9, 1996 accident. During the
         first half of 1997, the estates of the four deceased individuals filed
         civil suits against the Company. On July 6, 1998, Sikorsky filed a
         claim against the Company in those same civil cases claiming damages
         which they are alleged to have incurred following the May 9, 1996
         accident. In October 1998, Kaydon reached settlement agreements with
         the estates of each plaintiff in the four civil suits. All settlement
         amounts were fully covered under Company insurance. In September 1998,
         Kaydon received the Judge Advocate General's (the "JAG Report") and the
         Naval Air Systems Command "First Endorsement" to the JAG Report dated
         28 July 1998 wherein the U.S. Navy reviewed the crash of the Sikorsky
         CH-53E on 9 May 1996. The findings contained in the JAG Report,
         management believes, reaffirms the position that the bearing was not
         the causative action in the May 9, 1996 accident. Management believes
         it has meritorious defenses against any claims.

         Various other claims, lawsuits and environmental matters arising in the
         normal course of business are pending against the Company. Management
         believes that the outcome of these matters, including the Sikorsky
         matter referred to above, will not have a material adverse effect on
         the Company's financial position or results of operations.



                                        7

<PAGE>   10



                      MANAGEMENT'S DISCUSSION AND ANALYSIS

                OF FINANCIAL CONDITION AND RESULTS OF OPERATIONS

--------------------------------------------------------------------------------


Results of Operations

Kaydon Corporation and subsidiaries (the "Company") reported record third
quarter 1998 sales of $92,801,000, up 11.3% from $83,380,000 in the third
quarter of last year. The growth was driven primarily by continued strength in
heavy industrial equipment markets for fluid power products and specialty
bearings. Growth in slip rings continued, while filtration products posted
strong improvement reflecting increased market demand and a slower comparable
period in 1997.

Gross profit for the quarter was 40.0% compared to 40.8% last quarter and 41.2%
in the third quarter last year. The rate of gross margin as compared to 1997
reflects the proportional increase of sales into heavy industrial equipment
markets relative to total corporation sales. In general, gross margins from such
sales have been at a lower rate. As compared to the second quarter of 1998,
gross margins were down slightly as expected, reflecting traditional third
quarter shutdowns.

Selling and administrative expenses were $ 9,837,000 as compared to $9,769,000
last year. Expenses as a percent of sales were 10.6% versus 11.7% last year and
11.5% last quarter. The percentage decrease is attributed to emphasis on
spending controls and slower expense growth to support the larger sales base.

Net interest income was $996,000 up $149,000 from last year. This was due to
higher average cash balances for the quarter over the third quarter last year.

Net income was $17,560,000, with return on sales at 18.9% and earnings per share
on a diluted basis at $.54. Relative to the third quarter 1997, net income and
EPS increased 11.4% and 14.9%, respectively.

The effective tax rate of 38.0% was flat with the third quarter of 1997.


Nine Months 1998 to 1997:

Sales for the nine months of 1998 were $291,458,000, an increase of 19.3% over
$244,365,000 for the comparable period in 1997. Year to date net income was
$54,696,000, a gain of 20.1% over the 1997 earnings of $45,555,000. Earnings per
share were up 21.2% on a diluted basis at $1.66 versus $1.37 last year.


                                        8

<PAGE>   11



Gross margins for the nine month period were 40.6% versus 41.6% in 1997. The
lower rate as compared to the same period in 1997 primarily reflects the
proportional increase in sales to heavy industrial equipment markets versus
total company sales.

Selling and administrative expenses were $33,469,000, up $2,618,000 from
$30,851,000 in 1997. Although up in absolute dollar terms, expenses declined
relative to sales at 11.5% versus 12.6% for the nine month period in 1997. The
decrease reflects emphasis on spending controls and slower expense growth in
support of increased sales.

Liquidity and Capital Resources:

Working capital at the end of the third quarter 1998 totaled $144,569,000
compared to $143,763,000 at the end of 1997. Corresponding current ratios were
3.1 for the third quarter 1998 and 3.0 at the end of 1997. The modest increase
in working capital reflects higher levels of inventory and receivables to
support increased sales, primarily offset by lower levels of cash and marketable
securities.

Cash and securities totaled $75,314,000 at the end of the third quarter 1998
versus $96,802,000 at the end of 1997. Cash flow from operations for the nine
months of 1998 totaled $42,214,000 offset by net capital expenditures of
$21,438,000 and repurchases of common stock of $38,601,000. Capital expenditures
for the year include $12,285,000 of non-routine spending for the purchase of a
new manufacturing facility and equipment in Mocksville, North Carolina and plant
expansions of existing facilities in Monterey, Mexico and Blacksburg, Virginia.
Purchases of common stock for the nine months 1998 totaled 1,113,131 shares,
with 1,010,800 shares purchased on the open market. Of the total Board
authorized share repurchase of 6,000,000, there remains 1,863,186 shares
available.

Depreciation and amortization totaled $3,603,000 for the third quarter 1998
versus $2,877,000 in 1997. For the nine month period, depreciation and
amortization was $11,030,000 as compared to $9,415,000 for the same period in
1997.

Management expects that the Company's planned capital requirements for the
remainder of 1998, which consist primarily of capital expenditures and dividend
payments will be financed by operations. The Company has $100,000,000 available
under it multi-bank revolving credit agreements that could be utilized to meet
liquidity needs. The Company is currently debt free.

Year 2000

The Company's plan to address its computer systems' compliance with the year
2000 continues. The Company expects that all internal remediation activities and
all internal acceptance testing will be completed by mid-1999. The Company is in
the process of ascertaining the status of its suppliers' year 2000 compliance
efforts, and plans to


                                        9

<PAGE>   12



develop contingency plans by mid-1999 for any key suppliers that will not be
compliant on a timely basis. The Company currently believes that the cost of
addressing the year 2000 issue will not be material to the Company's business,
operations or financial condition.

While the Company believes all necessary work will be completed, there can be no
guarantee that all systems will be in compliance by the year 2000 or that the
systems of other companies on which the Company relies will be converted in a
timely manner. Such failure to complete the necessary work by the year 2000
could cause delays in the Company's ability to produce or ship its products,
process transactions or otherwise conduct business in its markets, resulting in
material financial risk.


Outlook

The backlog of unshipped orders at the end of the third quarter 1998 was
$153,314,000 compared to $143,037,000 at the end of the same period in 1997.
However, management views backlog as only one of many indicators of future
operating performance due to continuing shortening of lead times and variability
of order release dates. Based on the Company's expectation of continued modest
economic improvement, ongoing operating efficiencies and market share
initiatives, as well as contributions from companies acquired in 1997,
management believes that the Company should achieve record sales and earnings in
1998.

Under the safe harbor provisions of the Private Securities Litigation Reform Act
of 1995, the Company cautions investors that any forward-looking statements or
projections made by the Company, including those made in this document, are
subject to risks and uncertainties that may cause results to differ materially
from those projected.



                                       10

<PAGE>   13




Part II                         OTHER INFORMATION

Item 5.           Other Information

                  At its September 23, 1998 meeting, the Board of Directors
                  elected Brian P. Campbell as President and Chief Executive
                  Officer of the Company. Lawrence J. Cawley will continue as
                  Chairman of the Board until the Annual Meeting in April 1999.

                  At the same meeting, the Board appointed Thomas C. Sullivan to
                  the Board of Directors of the Company to fill a vacancy. Mr.
                  Sullivan is Chairman and Chief Executive Officer of RPM, Inc.


Item 6.           Exhibits and Reports on Form 8-K

       A.         Exhibit No.      Description

                      (27)         Financial Data Schedule (for SEC use only)


       B.         Reports on Form 8-K

                                   No reports on Form 8-K were filed during the
                                   quarter ended October 3, 1998.


                                       11

<PAGE>   14



                                   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.


                                   KAYDON CORPORATION



November 17, 1998                   /s/ Brian P. Campbell
                                   ---------------------------------------------
                                   Brian P. Campbell
                                   (President and Chief Executive Officer)



November 17, 1998                   /s/ Joseph P. Port
                                   ---------------------------------------------
                                   Joseph P. Port
                                   (Vice President Finance and
                                   Corporate Controller)


                                       12