<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 July 4, 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 August 10, 1998 - 32,535,814 shares, $0.10 par
value.
<PAGE>   2
                          KAYDON CORPORATION FORM 10-Q

                       FOR THE QUARTER ENDED JULY 4, 1998


                                      INDEX


                                                                        Page No.

Part I - Financial Information:

      Consolidated Condensed Balance Sheets -
      July 4, 1998 and December 31, 1997                                       1

      Consolidated Condensed Statements of Income -
      Three Months and Six Months Ended July 4, 1998
      and June 28, 1997                                                        2

      Consolidated Condensed Statements of Cash Flows -
      Six Months Ended July 4, 1998 and June 28, 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
<PAGE>   3
                               KAYDON CORPORATION

                      CONSOLIDATED CONDENSED BALANCE SHEETS


<TABLE>
<CAPTION>
                                                 July 4, 1998     December 31, 1997
                                                 ------------       ------------
                                                  (Unaudited)
<S>                                              <C>              <C>
Assets:
Cash and cash equivalents                        $ 52,118,000       $ 74,735,000
Marketable securities                              44,572,000         22,067,000
Accounts receivable, net                           56,804,000         42,690,000
Inventories, net                                   68,266,000         60,548,000
Other current assets                               14,444,000         14,738,000
                                                 ------------       ------------

Total current assets                              236,204,000        214,778,000


Plant and equipment, net                           95,934,000         85,510,000
Cost in excess of net tangible
  assets of purchased businesses, net              65,838,000         66,687,000
Other assets                                       19,003,000         17,010,000
                                                 ------------       ------------

Total assets                                     $416,979,000       $383,985,000
                                                 ============       ============

Liabilities and Stockholders' Investment:
Accounts payable                                 $ 17,077,000       $ 11,574,000
Accrued expenses                                   62,665,000         52,782,000
Federal income tax payable                          4,928,000          6,659,000
                                                 ------------       ------------

Total current liabilities                          84,670,000         71,015,000

Other long-term liabilities                        30,180,000         29,374,000
Stockholders' investment                          302,129,000        283,596,000
                                                 ------------       ------------
Total liabilities and
    stockholders' investment                     $416,979,000       $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                     SIX MONTHS ENDED
                                      July 4, 1998       June 28, 1997      July 4, 1998       June 28, 1997
                                      ------------       ------------       ------------       ------------
<S>                                   <C>                <C>                <C>                <C>         
Net sales                             $ 99,548,000       $ 84,454,000       $198,657,000       $160,985,000

Gross profit                            40,614,000         35,574,000         81,082,000         67,397,000

Operating income                        29,190,000         24,769,000         57,450,000         46,315,000

Interest income, net                     1,198,000            884,000          2,447,000          1,763,000
                                      ------------       ------------       ------------       ------------


Income before income taxes              30,388,000         25,653,000         59,897,000         48,078,000

Provision for income taxes              11,547,000          9,749,000         22,761,000         18,293,000
                                      ------------       ------------       ------------       ------------


Net income                            $ 18,841,000       $ 15,904,000       $ 37,136,000       $ 29,785,000
                                      ============       ============       ============       ============


Weighted Average Common Shares:
  Basic                                 32,912,000         32,974,000         32,939,000         32,960,000
  Diluted                               33,169,000         33,124,000         33,195,000         33,106,000


Earnings Per Share:
  Basic                               $       0.57       $       0.48       $       1.13       $       0.90
  Diluted                             $       0.57       $       0.48       $       1.12       $       0.90
</TABLE>

See accompanying notes to consolidated condensed financial statements.


                                        2
<PAGE>   5
                               KAYDON CORPORATION

                 CONSOLIDATED CONDENSED STATEMENTS OF CASH FLOWS
                                   (UNAUDITED)


<TABLE>
<CAPTION>
                                                              SIX MONTHS ENDED

                                                       July 4, 1998        June 28, 1997
                                                       ------------        ------------
<S>                                                    <C>                 <C>         
Cash flows from operating activities                   $ 24,161,000        $ 22,335,000
                                                       ------------        ------------

Cash flows from investing activities:
 Purchases of marketable securities                     (44,956,000)        (60,286,000)
 Maturities of marketable securities                     22,451,000          68,947,000
 Capital expenditures, net                              (16,725,000)         (5,514,000)
 Acquisition of businesses, net of cash acquired             82,000         (27,165,000)
                                                       ------------        ------------

 Cash used in investing activities                      (39,148,000)        (24,018,000)
                                                       ------------        ------------

Cash flows from financing activities:
 Proceeds from issuance of common stock                   4,110,000             884,000
 Dividends paid                                          (5,941,000)         (6,921,000)
 Purchase of treasury stock                              (6,667,000)           (645,000)
 Payment of debt                                                  0          (8,031,000)
                                                       ------------        ------------

 Cash used in financing activities                       (8,498,000)        (14,713,000)
                                                       ------------        ------------

Effect of exchange rate changes on cash
 and cash equivalents                                       868,000             (13,000)
                                                       ------------        ------------

Net decrease in cash and cash equivalents               (22,617,000)        (16,409,000)

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

Cash and cash equivalents - End of period              $ 52,118,000        $ 38,034,000
                                                       ============        ============

Cash expended for income taxes                         $ 23,388,000        $ 19,450,000
                                                       ============        ============

Cash expended for interest                             $     24,000        $    139,000
                                                       ============        ============
</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 July 4, 1998 and the results of its operations and its
      cash flows for the six 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>
                                             July 4, 1998           Dec 31, 1997
                                             -----------             -----------
<S>                                          <C>                    <C>        
Raw Material                                 $25,182,000             $20,282,000
Work in Process                               23,942,000              19,424,000
Finished Goods                                19,142,000              20,842,000
                                             -----------             -----------
                                             $68,266,000             $60,548,000
                                             ===========             ===========
</TABLE>


                                        4
<PAGE>   7
(4)   On March 5, 1998, the Company purchased a manufacturing facility and
      adjacent property in Mocksville, North Carolina for $4,630,500. Year to
      date, with equipment, a total of $8,077,000 has been invested. This
      facility will produce custom bearings for various commercial applications
      and represents additional capacity for the continuing growth of the
      Bearings Division. Limited production started late in the second quarter.


(5)   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 $118,000 and $661,000,
      resulting in comprehensive income of $18,565,000 and $16,565,000 for the
      quarters ended July 4, 1998 and June 28, 1997, respectively. On a six
      month basis, other comprehensive income, net of tax, was approximately
      $1,092,000 for 1998 versus a net loss of $811,000 for 1997, resulting in
      year to date comprehensive income of $38,228,000 and $28,974,000 for the
      quarters ended July 4, 1998 and June 28, 1997, respectively.


(6)   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.


                                        5
<PAGE>   8
      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
                                                July 4, 1998        June 28, 1997
                                                 -----------         -----------
<S>                                            <C>                 <C>
Numerators:
  Numerators for both basic
  and diluted earnings per share,
  net income                                     $18,841,000         $15,904,000
                                                 ===========         ===========
Denominators:
  Denominators for basic earnings
  per share, weighted average
  common shares outstanding                       32,912,000          32,974,000

Potential dilutive shares resulting
from stock option plans                              257,000             150,000
                                                 -----------         -----------
Denominator for dilutive
earnings per share                                33,169,000          33,124,000
                                                 ===========         ===========
Earnings Per Share:
Basic                                            $       .57         $       .48
Diluted                                          $       .57         $       .48
                                                 ===========         ===========
</TABLE>

      All options were included in second quarter 1998 and 1997 because the
      options' exercise price was less than the average market price of common
      shares.


(7)   The Company, together with other companies, certain former officers, and
      certain former 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 and alter ego of Keene.
      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.
      Although the examiner has made certain recommendations regarding a
      mechanism to resolve the claims against the Company, the Court has not
      taken any action related to the report. Nevertheless, in the Company's
      opinion,


                                        6
<PAGE>   9
      the report reinforces management's original view that the claims will
      ultimately not be sustained. Accordingly, no provision has been reflected
      in the consolidated financial statements for any alleged damages. 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, in accordance with the schedule established by the judge, 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. The court has not yet ruled upon the motions.
      Management 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 in which four persons
      died. The grand jury has requested and received documents and records
      relating to a bearing manufactured by Kaydon and used in the Sikorsky
      helicopter. In addition, the Defense Logistics Agency of the Defense
      Contract Management Command and a "Mishap Board" led by Sikorsky Aircraft
      Corporation with participation from certain Federal agencies alleged that
      product quality problems or deficiencies exist with respect to the bearing
      product used in the Sikorsky helicopter described above. The Company was
      excluded from participation on this "Mishap Board", however, it
      independently evaluated the available evidence and refuted the "Mishap
      Board" findings in its report 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 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. 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 sales of
$99,548,000 in the second quarter 1998, up 17.9% from $84,454,000 in the second
quarter last year. Base business growth excluding the impact of certain
acquisitions remained strong, up 13.8%, the fifth consecutive quarter the rate
of internal growth increased. The internal business growth was broad based and
was led by the Fluid Power Products Group.

Gross profit for the quarter was consistent with the first quarter of 1998 at
40.8% compared to 42.1% in the second quarter of last year. The lower gross
margin rate reflects the growth of the Fluid Power Products Group as a percent
of the total Company's sales. In general, gross margins within the Fluid Power
Products Group have been at a lower rate.

Selling and administrative expenses were $11,424,000, up $619,000 from
$10,805,000 last year. Although the absolute dollars increased, expenses as a
percent of sales were down to 11.5% from 12.8%. This percentage decrease is
primarily attributed to slower expense growth to support the larger sales base.

Net interest income was $1,198,000, up $314,000 from $884,000 last year. This
was due to higher cash balances and slightly higher rates over second quarter
1997.

Net income for the quarter totaled $18,841,000, with return on sales at 18.9%
and earnings per share on a diluted basis at $.57. Relative to the second
quarter 1997, net income and EPS increased 18.5% and 18.8%, respectively.

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


Six Months 1998 to 1997:

Sales for the six months of 1998 were $198,657,000, an increase of 23.4% over
last year's $160,985,000. Year to date net earnings were $37,136,000, a gain of
24.7% over the 1997 earnings of $29,785,000. Earnings per share were up 24.4% on
a diluted basis at $1.12 versus $0.90 last year.

Gross margins followed the same trend year to date at 40.8% versus 41.9% last
year. This change is due to the dilutive effect of the Fluid Power Products
Group as it grew as a percent of the Company's total sales.


                                        8
<PAGE>   11
Selling and administrative expenses were $23,632,000, up $2,550,000 from
$21,082,000 in 1997. The absolute dollars are larger but in percentage terms
1998 is 11.9% of sales versus 13.1% for the six month period in 1997. This
decrease is attributed to slower expense growth to support a larger sales base.


Liquidity and Capital Resources:

Working capital was $151,534,000 at the end of the second quarter reflecting a
current ratio of 2.8 compared to $143,763,000 at year end with a current ratio
of 3.0. The increase in working capital was primarily due to increased
inventories and receivables in support of higher sales levels.

Cash and securities of $96,690,000 remained virtually flat with year end at
$96,802,000. During the quarter the Company repurchased 317,700 shares of stock
in the open market for $11,398,000, of which $3,147,000 was settled in the
quarter. There remains 2,565,385 shares of stock to be purchased of the original
6,000,000 authorized by the Board of Directors. A total of 335,109 shares were
purchased in the second quarter. In addition, net capital spending for plant and
equipment in the quarter was $5,858,000, while year to date spending was
$16,725,000. The capital expenditures support internal expansions within
existing product lines, including the purchase of a new manufacturing facility
in Mocksville, North Carolina and expansion of the Monterey, Mexico plant.

During the second quarter, additional capital expenditures were authorized
totaling approximately $2,000,000 to expand the existing manufacturing capacity
for industrial bearings in Monterey, Mexico. The additional capacity should be
operational late in the fourth quarter 1998.

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


Year 2000

The Company has a plan in place to ensure its systems are compliant with the
requirements to process transactions in the year 2000. The Company is also
working with its vendors and processing banks to ensure their systems are year
2000 compliant.

Incremental costs associated with the year 2000 modifications, if any, will be
expensed as incurred and are not expected to be material. Any year 2000
compliance costs associated with outside vendors and processors will be borne by
the parties.


                                        9
<PAGE>   12
Outlook

The backlog of unshipped orders entering the Company's seasonally lowest quarter
was essentially unchanged at $159,747,000 compared to $160,404,000 at the end of
the first quarter of 1998. The additional capacity from expansions and continued
strength in base business should provide operating flexibility and a sound basis
for long-term growth. The Company continues to be confident with operating
levels in the forthcoming quarter, and while seeing some increasing softness in
orders for the semiconductor equipment market, the Company continues to expect
growth for the remainder of the year.

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 actual results to differ
materially from those projected.


                                       10
<PAGE>   13
Part II                         OTHER INFORMATION

Item 5.     Other Information

            Effective June 24, 1998, Mr. Stephen K. Clough resigned as President
            and Chief Executive Officer of the Company. Mr. Lawrence J. Cawley
            was elected Chief Executive Officer by the Company's Board of
            Directors.


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

            On June 29, 1998, the Company filed a Form 8-K reporting the
            resignation of the Company's President and Chief Executive Officer.
            The Company's current Chairman was elected Chief Executive Officer,
            President and Chief Financial Officer by the Board of Directors at
            the Board meeting on June 24, 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


August 14, 1998            /s/ Lawrence J. Cawley
                           --------------------------------
                           Lawrence J. Cawley
                           (Chairman, CEO, President, & Chief Financial Officer)



August 14, 1998            /s/ Joseph P. Port
                           --------------------------------
                           Joseph P. Port
                           (Vice President Finance & Corporate Controller)


                                       12