<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 April 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: 813/531-1101
---------------------------------------------     ------------------------------



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 May 14, 1998 - 33,023,163 shares, $0.10 par value.


<PAGE>   2



                          KAYDON CORPORATION FORM 10-Q

                       FOR THE QUARTER ENDED APRIL 4, 1998

<TABLE>
<CAPTION>
                                      INDEX
-------------------------------------------------------------------------------------------------

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

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

         Consolidated Condensed Statements of Income -
         Three Months Ended April 4, 1998 and March 29, 1997                                   2

         Consolidated Condensed Statements of Cash Flows -
         Three Months Ended April 4, 1998 and March 29, 1997                                   3

         Notes to Consolidated Condensed Financial Statements                              4 - 7

         Management's Discussion and Analysis of
         Financial Condition and Results of Operations                                     8 - 9


Part II - Other Information:

         Item 4. - Submission of Matters to a Vote of Security Holders                        10

         Item 5. - Other Information                                                          10

         Item 6. - Exhibits and Reports on Form 8-K                                           10


         Signatures                                                                           11
</TABLE>


<PAGE>   3



                               KAYDON CORPORATION

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

<TABLE>
<CAPTION>


                                             April 4, 1998     December 31, 1997  
                                             -------------     ----------------- 
                                             (Unaudited)                
                                                                        
<S>                                         <C>                <C>                
Assets:                                                                 
------                                                                   
Cash and cash equivalents                   $ 59,225,000          $ 74,735,000       
Marketable securities                         41,987,000            22,067,000       
Accounts receivable, net                      51,798,000            42,690,000       
Inventories, net                              64,951,000            60,548,000       
Other current assets                          15,412,000            14,738,000       
                                            ------------          ------------       
                                                                                     
Total current assets                         233,373,000           214,778,000       
                                                                                     
                                                                                     
Plant and equipment, net                      93,147,000            85,510,000       
Cost in excess of net tangible                                                       
  assets of purchased businesses, net         66,409,000            66,687,000       
Other assets                                  19,111,000            17,010,000       
                                            ------------          ------------       
                                                                                     
Total assets                                $412,040,000          $383,985,000       
                                            ============          ============       
                                                                                     
Liabilities and Stockholders' Investment:                                            
----------------------------------------       
Accounts payable                            $ 15,854,000          $ 11,574,000       
Accrued expenses                              53,019,000            52,782,000       
Federal income tax payable                    14,995,000             6,659,000       
                                            ------------          ------------       
                                                                                     
Total current liabilities                     83,868,000            71,015,000       
                                                                                     
Other long-term liabilities                   29,777,000            29,374,000       
Stockholders' investment                     298,395,000           283,596,000       
                                            ------------          ------------       
Total liabilities and                                                                
    stockholders' investment                $412,040,000          $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

                                            April 4, 1998       March 29, 1997
                                            -------------       --------------
<S>                                         <C>                 <C>         
   Net Sales                                $ 99,109,000        $ 76,531,000


   Gross Profit                               40,468,000          31,823,000


   Operating Income                           28,260,000          21,546,000

   Interest Income, net                        1,249,000             879,000
                                            ------------        ------------

   Income before Income Taxes                 29,509,000          22,425,000

   Provision for Income Taxes                 11,214,000           8,544,000
                                            ------------        ------------


   Net Income                               $ 18,295,000        $ 13,881,000
                                            ============        ============


   Earnings Per Share:
     Basic                                  $       0.55        $       0.42
     Diluted                                $       0.55        $       0.42

   Average Common Shares Outstanding:
     Basic                                    33,006,000          32,951,000
     Diluted                                  33,265,000          33,086,000
</TABLE>


See accompanying notes to consolidated condensed financial statements.

                                        2


<PAGE>   5




                               KAYDON CORPORATION

                 CONSOLIDATED CONDENSED STATEMENTS OF CASH FLOWS
                                   (UNAUDITED)

<TABLE>
<CAPTION>
----------------------------------------------------------------------------------------

                                                              THREE MONTHS ENDED

                                                        Apr 4, 1998         Mar 29, 1997
                                                       ------------        -------------
<S>                                                    <C>                 <C>
Cash flows from operating activities                   $ 18,944,000        $ 11,261,000
                                                       ------------        ------------

Cash flows from investing activities:
 Purchases of marketable securities                     (19,920,000)        (59,733,000)
 Maturities of marketable securities                              0          29,000,000
 Capital expenditures, net                              (10,867,000)         (2,396,000)
 Acquisition of businesses, net of cash acquired             11,000          (4,412,000)
                                                       ------------        ------------

 Cash used in investing activities                      (30,776,000)        (37,541,000)
                                                       ------------        ------------

Cash flows from financing activities:
 Proceeds from issuance of common stock                   1,238,000             732,000
 Dividends paid                                          (2,969,000)         (2,305,000)
 Purchase of treasury stock                              (2,739,000)           (629,000)
 Payment of short term debt                                       0             (31,000)
                                                       ------------        ------------

 Cash used in financing activities                       (4,470,000)         (2,233,000)
                                                       ------------        ------------

Effect of exchange rate changes on cash
 and cash equivalents                                       792,000            (320,000)
                                                       ------------        ------------

Net decrease in cash and cash equivalents               (15,510,000)        (28,833,000)

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

Cash and cash equivalents - End of period              $ 59,225,000        $ 25,610,000
                                                       ============        ============

Cash expended for income taxes                         $  2,700,000        $  4,679,000
                                                       ============        ============

Cash expended for interest                             $     10,000        $    109,000
                                                       ============        ============
</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 April 4, 1998 and the results of its operations and
         its cash flows for the three 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>
                                      Apr 4, 1998        Dec 31, 1997
                                     ------------        ------------
         <S>                         <C>                 <C>        
         Raw Material                $22,183,000         $20,282,000
         Work in Process              22,966,000          19,424,000
         Finished Goods               19,802,000          20,842,000
                                     -----------         -----------
                                     $64,951,000         $60,548,000
                                     ===========         ===========
</TABLE>


(4)      On March 5, 1998, the Company purchased a manufacturing facility and
         adjacent property in Mocksville, North Carolina for $4,630,500. This
         facility will produce custom bearings for various commercial
         applications and represents additional capacity for the continuing
         growth of its Bearings Division. The Company anticipates limited
         production to commence in the third quarter, and upon reaching full
         production levels, to eventually employ approximately 125 people.

                                        4


<PAGE>   7



(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 $974,000 and ($1,472,000), resulting in comprehensive
         income of $19,269,000 and $12,409,000 for the quarters ended April 4,
         1998 and March 29, 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.

         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
                                                       April 4, 1998       March 29, 1997
                                                      --------------       --------------
         <S>                                          <C>                  <C>         
         Numerators:
           Numerators for both basic
           and diluted earnings per share,
           net income                                  $ 18,295,000        $ 13,881,000
                                                       ============        ============

         Denominators:
           Denominators for basic earnings
           per share, weighted average
           common shares outstanding                     33,006,000          32,951,000

         Potential dilutive shares resulting
         from stock option plans                            259,000             135,000
                                                       ------------        ------------

         Denominator for dilutive
         earnings per share                              33,265,000          33,086,000
                                                       ============        ============

         Earnings Per Share:
         Basic                                         $        .55        $        .42
         Diluted                                       $        .55        $        .42
                                                       ============        ============
</TABLE>


                                        5


<PAGE>   8




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

         Options to purchase 416,400 shares of common stock at $21.75 per share
         were outstanding during the first quarter of 1997, but were not
         included in the computation of diluted EPS because the options' price
         was greater than the average market price of the 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, 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.

                                        6


<PAGE>   9



         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. For
         one of the incidents subsequent to May 9, 1996, which occurred October
         19, 1996, the NADEP Cherry Point Marine Facility distributed a report
         dated August 21, 1997 analyzing potential causes for that incident. The
         Company is currently in the process of reviewing this report.
         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
$99,109,000 in the first quarter 1998, up 29.5% from $76,531,000 in the first
quarter last year. Approximately 67% of the increase was contributed by the
Company's base businesses while the remainder was attributed to the 1997
acquisitions in the Fluid Power Products Group. Growth in base businesses was
broad based and was led by increases in the existing Fluid Power operations, in
addition to across-the-board increases in the Bearings operations. The Ring and
Seal Division was essentially flat from 1997 due to lower sales in industrial
seals. The quarter's growth benefited from four additional shipping days in 1998
versus 1997. Without the impact of the longer schedule, base businesses growth
approximated 12.5% over the first quarter last year.

Gross profit as a percent of sales decreased slightly to 40.8% from 41.6% in the
first quarter of last year. The decrease resulted from the dilutive impact of
the 1997 acquisitions. Without the acquisition impact, the gross profit rate
would have increased slightly reflecting continued favorable operating
conditions.

Selling and administrative expenses were $12,208,000, up $1,931,000 from
$10,277,000 last year. Although the absolute dollars increased, expenses as a
percent of sales were down to 12.3% from 13.4% in the first quarter last year.
This percentage decrease is primarily attributable to slower expense growth to
support the larger sales base.

Net interest income was $1,249,000, up $370,000 from $879,000 last year. This
was due to higher cash balances, favorable interest rates and the repayment of
all outstanding debt in April 1997.

The effective tax rate of 38.0% was flat with the 38.1% rate in first quarter
1997.

Liquidity and Capital Resources

Working capital was $149,505,000 at the end of the first 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 reflects the higher sales in the first
quarter 1998 over the fourth quarter 1997, yet the increase was modest relative
to the higher volume. Cash flow from operating activities was $18,944,000
compared to $11,261,000 in the first quarter 1997, reflecting the increase in
earnings and improved working capital. Depreciation and amortization totaled
$3,698,000 compared to $3,231,000 in the first quarter 1997.

                                        8


<PAGE>   11



Cash and securities of $101,212,000 were up $4,410,000 over the balance at year
end of $96,802,000. This increase reflects strong operating cash flow offset by
$10,867,000 paid for capital expenditures.

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 agreement that
could be utilized to meet its 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 venders and processing banks to ensure their systems are year
2000 compliant.

Incremental costs associated with 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
those parties.

Outlook

The Company's backlog of unfilled orders increased once again to $160,404
compared to $155,548,000 at year end and $123,911,000 this time last year. The 
Company is pleased to see the continuing increased activity in the business and 
anticipates a good second quarter and full year 1998.


                                       9


<PAGE>   12


Part II                            OTHER INFORMATION

Item 4.  Submission of Matters to a Vote of Security Holders

         The fourteenth Annual Stockholders' Meeting of Kaydon Corporation was
         held at the Tampa Airport Marriott on April 30, 1998. Represented at
         this meeting in person or by proxy were 28,907,720 shares of Kaydon
         common stock, representing 87.5% of the total outstanding as of the
         February 27, 1998 record date.

         The stockholders elected Gerald J. Breen, Brian P. Campbell, Lawrence
         J. Cawley, and Stephen K. Clough to serve as Directors until the 1999
         Annual Meeting. The results of the votes are as follows:

<TABLE>
<CAPTION>
              Election of Directors                      For                       Withhold
              ---------------------                --------------                  --------
              <S>                                  <C>                             <C>   
              G. Breen                                 28,817,147                    90,573
              B. Campbell                              28,826,011                    81,709
              L. Cawley                                28,823,615                    84,105
              S. Clough                                28,824,553                    83,167
</TABLE>

         There was no other official business to come before the meeting.

Item 5.  Other Information

         Effective April, 1998, Mr. John H.F. Haskell, Jr. retired from 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

                           No reports on Form 8-K were filed during the
                           quarter ended April 4, 1998.



                                       10



<PAGE>   13



                                   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

May 18, 1998

                                      /s/ Stephen K. Clough
                                      ------------------------------------------
                                      (President, CEO & Chief Financial Officer)

May 18, 1998

                                      /s/ Joseph P. Port
                                      ------------------------------------------
                                      (Vice President Finance & Corporate 
                                      Controller)


                                       11