<PAGE>   1



                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
                                   FORM 10-K

               [X]  ANNUAL REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934
                                Amendment No. 1
                    For the Fiscal Year Ended: JUNE 30, 1998

                                       OR

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

            For the transition period from __________ to __________.

                        Commission File Number:  0-27120

                            KENSEY NASH CORPORATION
             (Exact name of registrant as specified in its charter)

            DELAWARE                                   36-3316412
 (State or other jurisdiction              (IRS Employer Identification No.)
 of incorporation or organization)

    MARSH CREEK CORPORATE CENTER, 55 EAST UWCHLAN AVENUE, SUITE 204, EXTON,
                               PENNSYLVANIA 19341
             (Address of principal executive offices and zip code)

      Registrant's telephone number, including area code:  (610) 524-0188
        Securities registered pursuant to Section 12(b) of the Act: None
          Securities registered pursuant to Section 12(g) of the Act:
                    COMMON STOCK, PAR VALUE $.001 PER SHARE
                                (TITLE OF CLASS)

     Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days. Yes X No __

     Indicate by check mark if disclosure of delinquent filers pursuant to
Item 405 of Regulation S-K is not contained herein, and will not be contained,
to the best of registrant's knowledge, in definitive proxy or information
statements incorporated by reference in Part III of this Form 10-K or any
amendment to this Form 10-K. [ ]

     The aggregate market value of the registrant's voting stock (based upon
the per share closing price of $7.75 on September 18, 1998 and, in making such
calculation, registrant is not making a determination of the affiliate or
non-affiliate status of any holders of shares of Common Stock) was
approximately $57,809,358.

     The number of shares  outstanding of the  registrant's  Common Stock,
par value $.001, as of September 18, 1998 was 7,459,272.

                      DOCUMENTS INCORPORATED BY REFERENCE
        Portions of the following document are incorporated by reference
        into this report: Definitive Proxy Statement in connection with
                    the 1998 Annual Meeting of Stockholders

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


                                       1



<PAGE>   2

      AHP also provided the Company with operating advances which were repaid
      with the proceeds of the IPO in the year ended June 30, 1996.

      THE RESEARCH AND DEVELOPMENT AGREEMENT - The Company and its Strategic
      Alliance Partner have an agreement whereby such partner funds certain
      ongoing research and development costs incurred by the Company. The
      Company contributes one-third of such research and development costs while
      the Strategic Alliance Partner contributes the remaining two-thirds. Prior
      to the IPO, the Strategic Alliance Partner funded the Company's portion of
      such costs. Such amounts were repaid with proceeds from the IPO and the
      Company has taken no further advances from such partner.

      THE COLLAGEN SUPPLY AGREEMENT - Pursuant to an agreement with the
      Strategic Alliance Partner, the Company manufactures collagen to be used
      in the Angio-Seal. The agreement contains a minimum purchase requirement
      from the Company for five years beginning May 31, 1995.

3.    RELATED PARTY TRANSACTIONS

      The Company earned interest income of $9,322 for the fiscal year ended
      June 30, 1996 on certain notes receivable from a former officer of the
      Company which was repaid at the date of the IPO. Such amount had been
      classified as a component of stockholders' equity as it was collateralized
      primarily by common stock and common stock equivalents.

      For the fiscal year ended June 30, 1996, the Company incurred $785,524    
      (of which $496,580 was offset against proceeds of the IPO) in legal fees
      with a law firm which serves as the Company's general counsel for all
      corporate legal affairs. Certain current and former partners of such firm
      had interests in an investment partnership that owned 50,000 shares of
      the outstanding Common Stock of the Company. The shares were sold during
      the fiscal year ended June 30, 1997.

      See Note 13 for a discussion of related party transactions with certain
      former officers and transactions related to employee stock rights issued
      to current and former officers and an outside director.

4.    LEASES

      At June 30, 1998, future minimum annual rental commitments under
      non-cancelable lease obligations are as follows:

<TABLE>
<CAPTION>
                                              CAPITAL        OPERATING
                                               LEASES          LEASES
                                             ----------------------------
      <S>                                    <C>             <C>
      YEAR ENDING JUNE 30:
      1999                                   $  45,262      $  329,838
      2000                                      25,078         356,244
      2001                                      11,055         360,844
      2002                                       1,950         367,285
      2003                                                     154,953
                                             ---------      ----------
          Total minimum lease payments          83,345      $1,569,164
                                                            ==========
      Amount representing interest
      (at rates ranging from 7.25%
       to 10.25%)                              (10,722)
                                             ---------
      Present value of net minimum
       lease payments                           72,623

      Current portion                          (37,814)
                                             ---------
      Long-term portion                      $  34,809
                                             =========
</TABLE>


                                        
                                       33




<PAGE>   3
      THE CREDIT AGREEMENT - The Company had a $5 million Credit Agreement with
      its Strategic Alliance Partner. The outstanding balance of $6,517,348,
      including interest of $1,517,348, was repaid in October 1996 following
      receipt of FDA approval on September 30, 1996.

      Amounts outstanding under the Company's Revolver and Patent Acquisition
      Agreement are shown in the following table.

<TABLE>
<CAPTION>
                                                JUNE 30, 
                                        ------------------------
                                          1998            1997
<S>                                     <C>             <C>
    Patent Acquisition Agreement        $  879,228      
    Revolver                             2,000,000      $500,000
                                        ----------      --------
    Total                                2,879,228       500,000
    Current portion                       (540,077)    
                                        ----------      --------
    Long-term                           $2,339,151      $500,000
                                        ==========      ========
</TABLE>

      The annual debt maturities are approximately $540,077, $536,234, $353,750,
      $400,000 and $400,000 for the years 1999 through 2003, respectively.

7.    RETIREMENT PLAN

      The Company has a 401(k) Salary Reduction Plan and Trust (the "401(k)
      Plan") in which all employees that are at least 21 years of age are
      eligible to participate. Contributions to the 401(k) Plan are made by
      employees through an employee salary reduction election. Company
      contributions are discretionary. The Company has not made any
      contributions to the 401(k) Plan to date.

8.    INCOME TAXES

      The Company accounts for income taxes under SFAS No. 109, which generally
      provides that deferred tax assets and liabilities be recognized for
      temporary differences between the financial reporting basis and the tax
      basis of the Company's assets and liabilities and expected benefits of
      utilizing net operating loss ("NOL") carryforwards. The impact on deferred
      taxes of changes in tax rates and laws, if any, applied to the years
      during which temporary differences are expected to be settled are
      reflected in the financial statements in the period of enactment.

      For 1998 the Company has not provided for current income taxes due to the
      utilization of NOLs for tax purposes  The difference between the Company's
      income tax expense (benefit) and the income tax expense (benefit) computed
      using the U.S. federal income tax rate were as follows:

<TABLE>
<CAPTION>
                                                                                     June 30,                 
                                                                   --------------------------------------------
                                                                        1998             1997           1996

<S>                                                                <C>              <C>            <C>
Net income (loss) before income taxes                               $   342,682     $  (262,476)   $ (5,915,573)
                                                                   ============================================
Tax provision at U.S. statutory rate                                $   123,121     $   (94,491)   $ (2,129,606)
State income tax provision, net of federal benefit                       17,066         (13,098)       (295,187)
Reconciliation to actual tax rate:
   Non-deductible meals and entertainment                                13,328           9,158           4,587
   Phantom stock plan                                                                                (1,295,739)
   Timing differences                                                   (80,880)          2,696        (165,950)
   Utilization of net operating loss carryforwards                      (72,635) 
   Creation of net operating loss carryforwards                                          95,735       3,881,895
                                                                   --------------------------------------------
                                                                    $               $              $
                                                                   ============================================
</TABLE>

      Significant component of the Company's deferred taxes are as follows:

<TABLE>
<CAPTION>
                                                                                 JUNE 30, 
                                                                       ---------------------------
                                                                           1998           1997
<S>                                                                    <C>             <C>
    Accrual for:                                                       
     Vacation                                                          $  102,958      $  120,403
     Bonuses                                                                               75,000
    Basis difference - patents                                            381,627         479,264  
    Basis difference - fixed assets                                       (50,520)         99,741
    Prepaid insurance                                                     (46,884)        (97,009)
    Inventory                                                             170,870         
    Other                                                                   7,491          10,000
                                                                       ----------      ----------
                                                                          565,542         687,399
    Effective tax rate                                                      40.59%          40.59%
                                                                       ----------      ----------
    Deferred tax asset                                                    229,553         279,015
    NOL carryforwards (expiring      
    between 1998 and 2012)                                              6,322,911       6,315,906  
                                                                       ----------      ----------
                                                                        6,552,464       6,594,921
                                                                       (6,552,464)     (6,594,921)
                                                                       ----------      ----------
    Less valuation allowance                                           $        0      $        0  
                                                                       ==========      ==========
</TABLE>
                                   
                                       35
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awards, consistent with the provisions of SFAS No. 123, the Company's net loss
and earnings per share would have been reduced to the proforma amounts below:

<TABLE>
<CAPTION>
                                      JUNE 30, 1998                       JUNE 30, 1997                     JUNE 30, 1996
                               ----------------------------        ---------------------------       ---------------------------
                               AS REPORTED        PRO FORMA        AS REPORTED       PRO FORMA       AS REPORTED       PRO FORMA
                               -----------        ---------        -----------       ---------       -----------       ---------
<S>                            <C>               <C>               <C>              <C>             <C>              <C>      
Net income (loss)              $342,682          ($664,398)        ($262,476)       ($818,363)      ($5,915,573)     ($5,972,087)
Income (loss) per share           $0.05             ($0.09)           ($0.04)          ($0.11)           ($1.00)          ($1.01)
</TABLE>

Subsequent to year end, the Company granted 128,500 stock options under the
Employee Plan at an option price equal to the fair market value of the
Company's stock on the date of grant (August 28, 1998) of $7.63 per share.

16. EARNINGS PER SHARE

The following table shows the reconciliation between the numerators and
denominators for the basic and diluted EPS calculations, where income is the
numerator and the weighted average number of shares is the denominator. The
reconciliation is not shown for the years ended June 30, 1997 and 1996 as any
common share equivalents are antidilutive.

<TABLE>
<CAPTION>
                                                               YEAR ENDED JUNE 30, 1998
                                                   ------------------------------------------------
                                                                                          PER SHARE
                                                       INCOME               SHARES         AMOUNT
                                                   ------------------------------------------------
<S>                                                <C>                    <C>             <C> 
BASIC EPS
Income available to common shareholders            $      342,682         7,342,683       $   0.05
EFFECT OF DILUTIVE SECURITIES                                                             ========
Options                                                       -             208,913
DILUTED EPS                                        --------------         ---------
Income available to common shareholders
  including assumed conversions                    $      342,682         7,551,596       $   0.05
                                                   ==============         =========       ========
</TABLE>

17. QUARTERLY FINANCIAL DATA (UNAUDITED)

The summarized quarterly results of operations of the Company for the years
ended June 30, 1998 and June 30, 1997 are presented below:

<TABLE>
<CAPTION>
                                                          YEAR ENDED JUNE 30, 1998
                                     -------------------------------------------------------------------
                                          1ST             2ND                 3RD               4TH
                                        QUARTER         QUARTER              QUARTER          QUARTER
                                     --------------   -----------        --------------     ------------
<S>                                  <C>              <C>                <C>                <C> 
Operating revenues                   $    1,565,290   $ 2,762,081        $    3,606,955     $  3,384,406

Operating costs and expenses         $    2,365,692   $ 2,878,737        $    2,902,788     $  3,222,838

Net (loss) income                    $     (679,680)  $       492        $      809,722     $    212,148

(Loss) income per share              $        (0.09)  $        -         $         0.11     $       0.03

                                                          YEAR ENDED JUNE 30, 1997
                                     -------------------------------------------------------------------
                                          1ST             2ND                 3RD               4TH
                                        QUARTER         QUARTER              QUARTER          QUARTER
                                     --------------   -----------        --------------     ------------
Operating revenues                   $    2,328,109   $ 1,712,382        $    2,027,082     $ 1,839,422

Operating costs and expenses         $    2,114,459   $ 2,339,353        $    2,529,710     $ 2,597,457

Net income (loss)                    $      220,713   $   497,229        $     (374,444)    $  (605,974)

Income (loss) per share              $         0.03   $      0.07        $        (0.05)    $     (0.08)
</TABLE>

Quarterly and total year earnings per share are calculated independently based
on the weighted average number of shares outstanding during each period.


                                       40
<PAGE>   5
                                   SIGNATURES

         Pursuant to the requirements of Section 13 or 15(d) 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, on the 29th day of
September, 1998.

                                       KENSEY NASH CORPORATION


                                       By: /s/ JOSEPH W. KAUFMANN
                                           -----------------------
                                           Joseph W. Kaufmann
                                           Chief Executive Officer and President


         Pursuant to the requirements of the Securities Exchange Act of 1934,
this Report has been signed below by the following persons on behalf of the
Registrant and in the capacities indicated on the 29th day of September, 1998.


              SIGNATURE                              TITLES

/s/ JOSEPH W. KAUFMANN             Chief Executive Officer (Principal Executive 
------------------------------     Officer), President, Chief Financial Officer 
Joseph W. Kaufmann                 (Principal Financial and Accounting Officer),
                                   Secretary and Director

/s/ JOHN E. NASH, P.E.             Vice Chairman of the Board and Executive 
------------------------------     Vice President
John E. Nash, P.E.

/s/ KENNETH R. KENSEY, M.D.        Chairman of the Board of Directors
------------------------------
Kenneth R. Kensey, M.D.

/s/ DOUGLAS G. EVANS, P.E.         Chief Operating Officer, Assistant Secretary 
------------------------------     and Director
Douglas G. Evans, P.E.

/s/ WENDY F. DICICCO, CPA          Chief Financial Officer
------------------------------
Wendy F. DiCicco, CPA

/s/ ROBERT J. BOBB                 Director
------------------------------
Robert J. Bobb

/s/ HAROLD N. CHEFITZ              Director
------------------------------
Harold N. Chefitz

/s/ WALTER R. MAUPAY, JR.          Director
------------------------------
Walter R. Maupay, Jr.

                                        
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