APPLEWOOD ASSOCIATES L P
SC 13D/A, 2000-01-27
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                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                               S C H E D U L E 13D

                    Under the Securities Exchange Act of 1934
                              (Amendment No. 1)(1)

                       NETWORK-1 SECURITY SOLUTIONS, INC.
- --------------------------------------------------------------------------------

                                (Name of Issuer)

                          COMMON STOCK, $0.01 PAR VALUE
- --------------------------------------------------------------------------------

                         (Title of Class of Securities)

                                    64121N109
- --------------------------------------------------------------------------------
                                 (CUSIP Number)

                                    Copy to:
Wheatley Partners II, L.P.                Morrison Cohen Singer & Weinstein, LLP
80 Cuttermill Road                        750 Lexington Avenue
Great Neck, NY 11021                      New York, New York 10022
Telephone (516) 773-1024                  Telephone (212) 735-8600

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

                 (Name, Address and Telephone Number of Persons
                Authorized to Receive Notices and Communications)

                                December 22, 1999
- --------------------------------------------------------------------------------
              (Date of Event which Requires Filing this Statement)

If the filing person has previously  filed a statement on Schedule 13G to report
the  acquisition  that is the subject of this  Schedule  13D, and is filing this
schedule because of ss.ss.240.13d-1(e),  240.13d-1(f) or 240.13d-(g),  check the
following box |_|.

NOTE:  Schedules  filed in paper format shall include a signed original and five
copies of the schedule,  including all exhibits.  See  ss.ss.240.13d-7 for other
parties to whom copies are to be sent.

                        (Continued on following page(s))

- --------
     (1) The  remainder  of this cover page shall be filled out for a  reporting
person's  initial  filing on this  form with  respect  to the  subject  class of
securities,  and for any subsequent amendment containing information which would
alter disclosures provided in a prior cover page.

     The  information  required on the remainder of this cover page shall not be
deemed to be "filed"  for the purpose of Section 18 of the  Securities  Exchange
Act of 1934 ("Act") or otherwise  subject to the  liabilities of that section of
the Act but shall be subject to all other  provisions of the Act  (however,  see
the Notes).


                                   - 1 of 28-

<PAGE>



CUSIP
No.   64121N109                     13D
================================================================================
 1       Names of Reporting Persons
         I.R.S. Identification Nos. of Above Persons (Entities Only)

         Wheatley Partners II, L.P. (formerly, Applewood Associates, L.P.)
- --------------------------------------------------------------------------------
 2       Check the Appropriate Box if a Member of a Group*
                                                                         (a) |_|
                                                                         (b) |_|
- --------------------------------------------------------------------------------
 3       SEC Use Only


- --------------------------------------------------------------------------------
 4       Source of Funds*                 WC, OO

- --------------------------------------------------------------------------------
 5       Check Box if Disclosure of Legal Proceedings is Required
         Pursuant to Item 2(d) or 2(e)                                       |_|

- --------------------------------------------------------------------------------
 6       Citizenship or Place of Organization                           New York

- --------------------------------------------------------------------------------
                      7       Sole Voting Power
      Number of                    1,194,659 shares                        25.1%
       Shares         ----------------------------------------------------------
    Beneficially      8       Shared Voting Power
      Owned By                     0 shares                                   0%
        Each          ----------------------------------------------------------
      Reporting       9       Sole Dispositive Power
       Person                      1,194,659 shares                        25.1%
        With          ----------------------------------------------------------
                      10      Shared Dispositive Power
                                   0 shares                                   0%
- --------------------------------------------------------------------------------
11       Aggregate Amount Beneficially Owned By Each Reporting Person

                                1,194,659 shares
- --------------------------------------------------------------------------------
12       Check Box if the Aggregate Amount in Row (11) excludes Certain Shares*
                                                                             |_|

- --------------------------------------------------------------------------------
13       Percent of Class Represented by Amount in Row (11)
                                                                           25.1%

- --------------------------------------------------------------------------------
14       Type of Reporting Person*

                                       PN
================================================================================

                      *SEE INSTRUCTIONS BEFORE FILLING OUT!


                                   - 2 of 28-

<PAGE>


CUSIP
No.   64121N109                     13D
================================================================================
 1       Names of Reporting Persons
         I.R.S. Identification Nos. of Above Persons (Entities Only)

                             Applewood Capital Corp.
- --------------------------------------------------------------------------------
 2       Check the Appropriate Box if a Member of a Group*
                                                                         (a) |_|
                                                                         (b) |_|
- --------------------------------------------------------------------------------
 3       SEC Use Only


- --------------------------------------------------------------------------------
 4       Source of Funds*                 WC, OO

- --------------------------------------------------------------------------------
 5       Check Box if Disclosure of Legal Proceedings is Required
         Pursuant to Item 2(d) or 2(e)                                       |_|

- --------------------------------------------------------------------------------
 6       Citizenship or Place of Organization                           New York

- --------------------------------------------------------------------------------
                      7       Sole Voting Power
      Number of                    0 shares                                   0%
       Shares         ----------------------------------------------------------
    Beneficially      8       Shared Voting Power
      Owned By                     1,194,659 shares                        25.1%
        Each          ----------------------------------------------------------
      Reporting       9       Sole Dispositive Power
       Person                      0 shares                                   0%
        With          ----------------------------------------------------------
                      10      Shared Dispositive Power
                                   1,194,659 shares                        25.1%
- --------------------------------------------------------------------------------
11       Aggregate Amount Beneficially Owned By Each Reporting Person

                                1,194,659 shares
- --------------------------------------------------------------------------------
12       Check Box if the Aggregate Amount in Row (11) excludes Certain Shares*
                                                                             |_|

- --------------------------------------------------------------------------------
13       Percent of Class Represented by Amount in Row (11)
                                                                           25.1%

- --------------------------------------------------------------------------------
14       Type of Reporting Person*

                                       CO
================================================================================

                      *SEE INSTRUCTIONS BEFORE FILLING OUT!


                                   - 3 of 28-

<PAGE>



CUSIP
No.   64121N109                     13D
================================================================================
 1       Names of Reporting Persons
         I.R.S. Identification Nos. of Above Persons (Entities Only)

                                  Irwin Lieber
- --------------------------------------------------------------------------------
 2       Check the Appropriate Box if a Member of a Group*
                                                                         (a) |_|
                                                                         (b) |_|
- --------------------------------------------------------------------------------
 3       SEC Use Only


- --------------------------------------------------------------------------------
 4       Source of Funds*                 PF, OO

- --------------------------------------------------------------------------------
 5       Check Box if Disclosure of Legal Proceedings is Required
         Pursuant to Item 2(d) or 2(e)                                       |_|

- --------------------------------------------------------------------------------
 6       Citizenship or Place of Organization                      United States

- --------------------------------------------------------------------------------
                      7       Sole Voting Power
      Number of                    135,105 shares                           2.8%
       Shares         ----------------------------------------------------------
    Beneficially      8       Shared Voting Power
      Owned By                     1,194,659 shares                        25.1%
        Each          ----------------------------------------------------------
      Reporting       9       Sole Dispositive Power
       Person                      135,105 shares                           2.8%
        With          ----------------------------------------------------------
                      10      Shared Dispositive Power
                                   1,194,659 shares                        25.1%
- --------------------------------------------------------------------------------
11       Aggregate Amount Beneficially Owned By Each Reporting Person

                                1,329,764 shares
- --------------------------------------------------------------------------------
12       Check Box if the Aggregate Amount in Row (11) excludes Certain Shares*
                                                                             |_|

- --------------------------------------------------------------------------------
13       Percent of Class Represented by Amount in Row (11)
                                                                           27.3%

- --------------------------------------------------------------------------------
14       Type of Reporting Person*

                                       IN
================================================================================

                      *SEE INSTRUCTIONS BEFORE FILLING OUT!


                                   - 4 of 28-

<PAGE>


CUSIP
No.   64121N109                     13D
================================================================================
 1       Names of Reporting Persons
         I.R.S. Identification Nos. of Above Persons (Entities Only)

                                Barry Rubenstein
- --------------------------------------------------------------------------------
 2       Check the Appropriate Box if a Member of a Group*
                                                                         (a) |_|
                                                                         (b) |_|
- --------------------------------------------------------------------------------
 3       SEC Use Only


- --------------------------------------------------------------------------------
 4       Source of Funds*                 PF, OO

- --------------------------------------------------------------------------------
 5       Check Box if Disclosure of Legal Proceedings is Required
         Pursuant to Item 2(d) or 2(e)                                       |_|

- --------------------------------------------------------------------------------
 6       Citizenship or Place of Organization                      United States

- --------------------------------------------------------------------------------
                      7       Sole Voting Power
      Number of                    110,079 shares                           2.3%
       Shares         ----------------------------------------------------------
    Beneficially      8       Shared Voting Power
      Owned By                     1,422,999 shares                        28.5%
        Each          ----------------------------------------------------------
      Reporting       9       Sole Dispositive Power
       Person                      110,079 shares                           2.3%
        With          ----------------------------------------------------------
                      10      Shared Dispositive Power
                                   1,422,999 shares                        28.5%
- --------------------------------------------------------------------------------
11       Aggregate Amount Beneficially Owned By Each Reporting Person

                                1,533,078 shares
- --------------------------------------------------------------------------------
12       Check Box if the Aggregate Amount in Row (11) excludes Certain Shares*
                                                                             |_|

- --------------------------------------------------------------------------------
13       Percent of Class Represented by Amount in Row (11)
                                                                           30.7%

- --------------------------------------------------------------------------------
14       Type of Reporting Person*

                                       IN
================================================================================

                      *SEE INSTRUCTIONS BEFORE FILLING OUT!


                                   - 5 of 28-

<PAGE>


CUSIP
No.   64121N109                     13D
================================================================================
 1       Names of Reporting Persons
         I.R.S. Identification Nos. of Above Persons (Entities Only)

                                 Barry Fingerhut
- --------------------------------------------------------------------------------
 2       Check the Appropriate Box if a Member of a Group*
                                                                         (a) |_|
                                                                         (b) |_|
- --------------------------------------------------------------------------------
 3       SEC Use Only


- --------------------------------------------------------------------------------
 4       Source of Funds*                 PF, OO

- --------------------------------------------------------------------------------
 5       Check Box if Disclosure of Legal Proceedings is Required
         Pursuant to Item 2(d) or 2(e)                                       |_|

- --------------------------------------------------------------------------------
 6       Citizenship or Place of Organization                      United States

- --------------------------------------------------------------------------------
                      7       Sole Voting Power
      Number of                    63,826 shares                            1.3%
       Shares         ----------------------------------------------------------
    Beneficially      8       Shared Voting Power
      Owned By                     1,194,659 shares                        25.1%
        Each          ----------------------------------------------------------
      Reporting       9       Sole Dispositive Power
       Person                      63,826 shares                            1.3%
        With          ----------------------------------------------------------
                      10      Shared Dispositive Power
                                   1,194,659 shares                        25.1%
- --------------------------------------------------------------------------------
11       Aggregate Amount Beneficially Owned By Each Reporting Person

                                1,258,485 shares
- --------------------------------------------------------------------------------
12       Check Box if the Aggregate Amount in Row (11) excludes Certain Shares*
                                                                             |_|

- --------------------------------------------------------------------------------
13       Percent of Class Represented by Amount in Row (11)
                                                                           26.3%

- --------------------------------------------------------------------------------
14       Type of Reporting Person*

                                       IN
================================================================================

                      *SEE INSTRUCTIONS BEFORE FILLING OUT!


                                   - 6 of 28-

<PAGE>


CUSIP
No.   64121N109                     13D
================================================================================
 1       Names of Reporting Persons
         I.R.S. Identification Nos. of Above Persons (Entities Only)

                                   Seth Lieber
- --------------------------------------------------------------------------------
 2       Check the Appropriate Box if a Member of a Group*
                                                                         (a) |_|
                                                                         (b) |_|
- --------------------------------------------------------------------------------
 3       SEC Use Only


- --------------------------------------------------------------------------------
 4       Source of Funds*                 PF, OO

- --------------------------------------------------------------------------------
 5       Check Box if Disclosure of Legal Proceedings is Required
         Pursuant to Item 2(d) or 2(e)                                       |_|

- --------------------------------------------------------------------------------
 6       Citizenship or Place of Organization                      United States

- --------------------------------------------------------------------------------
                      7       Sole Voting Power
      Number of                    4,656 shares                             0.1%
       Shares         ----------------------------------------------------------
    Beneficially      8       Shared Voting Power
      Owned By                     1,202,855 shares                        25.3%
        Each          ----------------------------------------------------------
      Reporting       9       Sole Dispositive Power
       Person                      4,656 shares                             0.1%
        With          ----------------------------------------------------------
                      10      Shared Dispositive Power
                                   1,202,855 shares                        25.3%
- --------------------------------------------------------------------------------
11       Aggregate Amount Beneficially Owned By Each Reporting Person

                                1,207,511 shares
- --------------------------------------------------------------------------------
12       Check Box if the Aggregate Amount in Row (11) excludes Certain Shares*
                                                                             |_|

- --------------------------------------------------------------------------------
13       Percent of Class Represented by Amount in Row (11)
                                                                           25.4%

- --------------------------------------------------------------------------------
14       Type of Reporting Person*

                                       IN
================================================================================

                      *SEE INSTRUCTIONS BEFORE FILLING OUT!


                                   - 7 of 28-

<PAGE>


CUSIP
No.   64121N109                     13D
================================================================================
 1       Names of Reporting Persons
         I.R.S. Identification Nos. of Above Persons (Entities Only)

                                 Jonathan Lieber
- --------------------------------------------------------------------------------
 2       Check the Appropriate Box if a Member of a Group*
                                                                         (a) |_|
                                                                         (b) |_|
- --------------------------------------------------------------------------------
 3       SEC Use Only


- --------------------------------------------------------------------------------
 4       Source of Funds*                 PF, OO

- --------------------------------------------------------------------------------
 5       Check Box if Disclosure of Legal Proceedings is Required
         Pursuant to Item 2(d) or 2(e)                                       |_|

- --------------------------------------------------------------------------------
 6       Citizenship or Place of Organization                      United States

- --------------------------------------------------------------------------------
                      7       Sole Voting Power
      Number of                    3,104 shares                             0.1%
       Shares         ----------------------------------------------------------
    Beneficially      8       Shared Voting Power
      Owned By                     1,202,855 shares                        25.3%
        Each          ----------------------------------------------------------
      Reporting       9       Sole Dispositive Power
       Person                      3,104 shares                             0.1%
        With          ----------------------------------------------------------
                      10      Shared Dispositive Power
                                   1,202,855 shares                        25.3%
- --------------------------------------------------------------------------------
11       Aggregate Amount Beneficially Owned By Each Reporting Person

                                1,205,959 shares
- --------------------------------------------------------------------------------
12       Check Box if the Aggregate Amount in Row (11) excludes Certain Shares*
                                                                             |_|

- --------------------------------------------------------------------------------
13       Percent of Class Represented by Amount in Row (11)
                                                                           25.3%

- --------------------------------------------------------------------------------
14       Type of Reporting Person*

                                       IN
================================================================================

                      *SEE INSTRUCTIONS BEFORE FILLING OUT!


                                   - 8 of 28-

<PAGE>


CUSIP
No.   64121N109                     13D
================================================================================
 1       Names of Reporting Persons
         I.R.S. Identification Nos. of Above Persons (Entities Only)

                              Woodland Venture Fund
- --------------------------------------------------------------------------------
 2       Check the Appropriate Box if a Member of a Group*
                                                                         (a) |_|
                                                                         (b) |_|
- --------------------------------------------------------------------------------
 3       SEC Use Only


- --------------------------------------------------------------------------------
 4       Source of Funds*               WC, OO

- --------------------------------------------------------------------------------
 5       Check Box if Disclosure of Legal Proceedings is Required
         Pursuant to Item 2(d) or 2(e)                                       |_|

- --------------------------------------------------------------------------------
 6       Citizenship or Place of Organization                           New York

- --------------------------------------------------------------------------------
                      7       Sole Voting Power
      Number of                    106,702 shares                           2.2%
       Shares         ----------------------------------------------------------
    Beneficially      8       Shared Voting Power
      Owned By                     121,638 shares                           2.5%
        Each          ----------------------------------------------------------
      Reporting       9       Sole Dispositive Power
       Person                      106,702 shares                           2.2%
        With          ----------------------------------------------------------
                      10      Shared Dispositive Power
                                   121,638 shares                           2.5%
- --------------------------------------------------------------------------------
11       Aggregate Amount Beneficially Owned By Each Reporting Person

                                 228,340 shares
- --------------------------------------------------------------------------------
12       Check Box if the Aggregate Amount in Row (11) excludes Certain Shares*
                                                                             |_|

- --------------------------------------------------------------------------------
13       Percent of Class Represented by Amount in Row (11)
                                                                            4.6%

- --------------------------------------------------------------------------------
14       Type of Reporting Person*

                                       PN
================================================================================

                      *SEE INSTRUCTIONS BEFORE FILLING OUT!


                                   - 9 of 28-

<PAGE>



CUSIP
No.   64121N109                     13D
================================================================================
 1       Names of Reporting Persons
         I.R.S. Identification Nos. of Above Persons (Entities Only)

                                 Seneca Ventures
- --------------------------------------------------------------------------------
 2       Check the Appropriate Box if a Member of a Group*
                                                                         (a) |_|
                                                                         (b) |_|
- --------------------------------------------------------------------------------
 3       SEC Use Only


- --------------------------------------------------------------------------------
 4       Source of Funds*               WC, OO

- --------------------------------------------------------------------------------
 5       Check Box if Disclosure of Legal Proceedings is Required
         Pursuant to Item 2(d) or 2(e)                                       |_|

- --------------------------------------------------------------------------------
 6       Citizenship or Place of Organization                           New York

- --------------------------------------------------------------------------------
                      7       Sole Voting Power
      Number of                    56,066 shares                            1.2%
       Shares         ----------------------------------------------------------
    Beneficially      8       Shared Voting Power
      Owned By                     172,274 shares                           3.5%
        Each          ----------------------------------------------------------
      Reporting       9       Sole Dispositive Power
       Person                      56,066 shares                            1.2%
        With          ----------------------------------------------------------
                      10      Shared Dispositive Power
                                   172,274 shares                           3.5%
- --------------------------------------------------------------------------------
11       Aggregate Amount Beneficially Owned By Each Reporting Person

                                 228,340 shares
- --------------------------------------------------------------------------------
12       Check Box if the Aggregate Amount in Row (11) excludes Certain Shares*
                                                                             |_|

- --------------------------------------------------------------------------------
13       Percent of Class Represented by Amount in Row (11)
                                                                            4.6%

- --------------------------------------------------------------------------------
14       Type of Reporting Person*

                                       PN
================================================================================

                      *SEE INSTRUCTIONS BEFORE FILLING OUT!


                                   - 10 of 28-

<PAGE>


CUSIP
No.   64121N109                     13D
================================================================================
 1       Names of Reporting Persons
         I.R.S. Identification Nos. of Above Persons (Entities Only)

                               Marilyn Rubenstein
- --------------------------------------------------------------------------------
 2       Check the Appropriate Box if a Member of a Group*
                                                                         (a) |_|
                                                                         (b) |_|
- --------------------------------------------------------------------------------
 3       SEC Use Only


- --------------------------------------------------------------------------------
 4       Source of Funds*                 OO

- --------------------------------------------------------------------------------
 5       Check Box if Disclosure of Legal Proceedings is Required
         Pursuant to Item 2(d) or 2(e)                                       |_|

- --------------------------------------------------------------------------------
 6       Citizenship or Place of Organization                      United States

- --------------------------------------------------------------------------------
                      7       Sole Voting Power
      Number of                    0 shares                                   0%
       Shares         ----------------------------------------------------------
    Beneficially      8       Shared Voting Power
      Owned By                     228,340 shares                           4.6%
        Each          ----------------------------------------------------------
      Reporting       9       Sole Dispositive Power
       Person                      0 shares                                   0%
        With          ----------------------------------------------------------
                      10      Shared Dispositive Power
                                   228,340 shares                           4.6%
- --------------------------------------------------------------------------------
11       Aggregate Amount Beneficially Owned By Each Reporting Person

                                 228,340 shares
- --------------------------------------------------------------------------------
12       Check Box if the Aggregate Amount in Row (11) excludes Certain Shares*
                                                                             |_|

- --------------------------------------------------------------------------------
13       Percent of Class Represented by Amount in Row (11)
                                                                            4.6%

- --------------------------------------------------------------------------------
14       Type of Reporting Person*

                                       IN
================================================================================

                      *SEE INSTRUCTIONS BEFORE FILLING OUT!


                                   - 11 of 28-

<PAGE>


CUSIP
No.   64121N109                     13D
================================================================================
 1       Names of Reporting Persons
         I.R.S. Identification Nos. of Above Persons (Entities Only)

                             Woodland Services Corp.
- --------------------------------------------------------------------------------
 2       Check the Appropriate Box if a Member of a Group*
                                                                         (a) |_|
                                                                         (b) |_|
- --------------------------------------------------------------------------------
 3       SEC Use Only


- --------------------------------------------------------------------------------
 4       Source of Funds*                 OO

- --------------------------------------------------------------------------------
 5       Check Box if Disclosure of Legal Proceedings is Required
         Pursuant to Item 2(d) or 2(e)                                       |_|

- --------------------------------------------------------------------------------
 6       Citizenship or Place of Organization                           New York

- --------------------------------------------------------------------------------
                      7       Sole Voting Power
      Number of                    0 shares                                   0%
       Shares         ----------------------------------------------------------
    Beneficially      8       Shared Voting Power
      Owned By                     228,340 shares                           4.6%
        Each          ----------------------------------------------------------
      Reporting       9       Sole Dispositive Power
       Person                      0 shares                                   0%
        With          ----------------------------------------------------------
                      10      Shared Dispositive Power
                                   228,340 shares                           4.6%
- --------------------------------------------------------------------------------
11       Aggregate Amount Beneficially Owned By Each Reporting Person

                                 228,340 shares
- --------------------------------------------------------------------------------
12       Check Box if the Aggregate Amount in Row (11) excludes Certain Shares*
                                                                             |_|

- --------------------------------------------------------------------------------
13       Percent of Class Represented by Amount in Row (11)
                                                                            4.6%

- --------------------------------------------------------------------------------
14       Type of Reporting Person*

                                       CO
================================================================================

                      *SEE INSTRUCTIONS BEFORE FILLING OUT!


                                   - 12 of 28-

<PAGE>


CUSIP
No.   64121N109                     13D
================================================================================
 1       Names of Reporting Persons
         I.R.S. Identification Nos. of Above Persons (Entities Only)

                               Woodland Partners
- --------------------------------------------------------------------------------
 2       Check the Appropriate Box if a Member of a Group*
                                                                         (a) |_|
                                                                         (b) |_|
- --------------------------------------------------------------------------------
 3       SEC Use Only


- --------------------------------------------------------------------------------
 4       Source of Funds*               WC, OO

- --------------------------------------------------------------------------------
 5       Check Box if Disclosure of Legal Proceedings is Required
         Pursuant to Item 2(d) or 2(e)                                       |_|

- --------------------------------------------------------------------------------
 6       Citizenship or Place of Organization                           New York

- --------------------------------------------------------------------------------
                      7       Sole Voting Power
      Number of                    32,786 shares                            0.7%
       Shares         ----------------------------------------------------------
    Beneficially      8       Shared Voting Power
      Owned By                     195,554 shares                           4.0%
        Each          ----------------------------------------------------------
      Reporting       9       Sole Dispositive Power
       Person                      32,786 shares                            0.7%
        With          ----------------------------------------------------------
                      10      Shared Dispositive Power
                                   195,554 shares                           4.0%
- --------------------------------------------------------------------------------
11       Aggregate Amount Beneficially Owned By Each Reporting Person

                                 228,340 shares
- --------------------------------------------------------------------------------
12       Check Box if the Aggregate Amount in Row (11) excludes Certain Shares*
                                                                             |_|

- --------------------------------------------------------------------------------
13       Percent of Class Represented by Amount in Row (11)
                                                                            4.6%

- --------------------------------------------------------------------------------
14       Type of Reporting Person*

                                       PN
================================================================================

                      *SEE INSTRUCTIONS BEFORE FILLING OUT!


                                   - 13 of 28-

<PAGE>


CUSIP
No.   64121N109                     13D
================================================================================
 1       Names of Reporting Persons
         I.R.S. Identification Nos. of Above Persons (Entities Only)

                            Brookwood Partners, L.P.
- --------------------------------------------------------------------------------
 2       Check the Appropriate Box if a Member of a Group*
                                                                         (a) |_|
                                                                         (b) |_|
- --------------------------------------------------------------------------------
 3       SEC Use Only


- --------------------------------------------------------------------------------
 4       Source of Funds*               WC, OO

- --------------------------------------------------------------------------------
 5       Check Box if Disclosure of Legal Proceedings is Required
         Pursuant to Item 2(d) or 2(e)                                       |_|

- --------------------------------------------------------------------------------
 6       Citizenship or Place of Organization                           New York

- --------------------------------------------------------------------------------
                      7       Sole Voting Power
      Number of                    32,786 shares                            0.7%
       Shares         ----------------------------------------------------------
    Beneficially      8       Shared Voting Power
      Owned By                     195,554 shares                           4.0%
        Each          ----------------------------------------------------------
      Reporting       9       Sole Dispositive Power
       Person                      32,786 shares                            0.7%
        With          ----------------------------------------------------------
                      10      Shared Dispositive Power
                                   195,554 shares                           4.0%
- --------------------------------------------------------------------------------
11       Aggregate Amount Beneficially Owned By Each Reporting Person

                                 228,340 shares
- --------------------------------------------------------------------------------
12       Check Box if the Aggregate Amount in Row (11) excludes Certain Shares*
                                                                             |_|

- --------------------------------------------------------------------------------
13       Percent of Class Represented by Amount in Row (11)
                                                                            4.6%

- --------------------------------------------------------------------------------
14       Type of Reporting Person*

                                       PN
================================================================================

                      *SEE INSTRUCTIONS BEFORE FILLING OUT!


                                   - 14 of 28-

<PAGE>


CUSIP
No.   64121N109                     13D
================================================================================
 1       Names of Reporting Persons
         I.R.S. Identification Nos. of Above Persons (Entities Only)

                               Applegreen Partners
- --------------------------------------------------------------------------------
 2       Check the Appropriate Box if a Member of a Group*
                                                                         (a) |_|
                                                                         (b) |_|
- --------------------------------------------------------------------------------
 3       SEC Use Only


- --------------------------------------------------------------------------------
 4       Source of Funds*               WC, OO

- --------------------------------------------------------------------------------
 5       Check Box if Disclosure of Legal Proceedings is Required
         Pursuant to Item 2(d) or 2(e)                                       |_|

- --------------------------------------------------------------------------------
 6       Citizenship or Place of Organization                           New York

- --------------------------------------------------------------------------------
                      7       Sole Voting Power
      Number of                    8,196 shares                             0.2%
       Shares         ----------------------------------------------------------
    Beneficially      8       Shared Voting Power
      Owned By                     0 shares                                   0%
        Each          ----------------------------------------------------------
      Reporting       9       Sole Dispositive Power
       Person                      8,196 shares                             0.2%
        With          ----------------------------------------------------------
                      10      Shared Dispositive Power
                                   0 shares                                   0%
- --------------------------------------------------------------------------------
11       Aggregate Amount Beneficially Owned By Each Reporting Person

                                  8,196 shares
- --------------------------------------------------------------------------------
12       Check Box if the Aggregate Amount in Row (11) excludes Certain Shares*
                                                                             |_|

- --------------------------------------------------------------------------------
13       Percent of Class Represented by Amount in Row (11)
                                                                            0.2%

- --------------------------------------------------------------------------------
14       Type of Reporting Person*

                                       PN
================================================================================

                      *SEE INSTRUCTIONS BEFORE FILLING OUT!


                                   - 15 of 28-

<PAGE>



     This statement, dated December 22, 1999, constitutes Amendment No. 1 to the
Schedule 13D, dated November 12, 1998, regarding the reporting persons'
ownership of certain securities of Network-1 Security Solutions, Inc. (the
"Issuer").

     This Schedule 13D is hereinafter referred to as the "Schedule." All
capitalized terms used herein and otherwise undefined shall have the meanings
ascribed in the Schedule.

     This Amendment No. 1 to the Schedule is filed in accordance with Rule 13d-2
of the Securities Exchange Act of 1934, as amended, by the reporting persons. It
shall refer only to information which has materially changed since the filing of
the Schedule.

ITEM 1. Security and Issuer.

          (g)  Option, to purchase 10,000 shares of Common Stock, expiring June
               22, 2009, entitling the holder thereof to purchase Common Stock
               at $3.75 per share, with options to purchase 2,500 shares
               exercisable commencing on June 22, 1999. Options to purchase
               one-third of the balance of the shares vests quarterly commencing
               90 days from the date of grant (the "June 22, 1999 Directors
               Option").

          (h)  Option, to purchase 7,500 shares of Common Stock, expiring
               October 25, 2009, entitling the holder thereof to purchase Common
               Stock at $1.50 per share. Options to purchase one-quarter of the
               total number of shares vests quarterly, commencing 90 days from
               the date of grant (the "October 1999 Directors Option").

          (i)  Series D Convertible Preferred Stock, (the "Series D Preferred
               Stock"), may be converted at any time into an equal number of
               shares of Common Stock, at the option of the holder, subject to
               anti-dilution and other adjustments. The Series D Preferred Stock
               vote separately as a class on all matters which impact the
               rights, value or ranking of the Series D Preferred Stock;
               otherwise, they vote together with the holders of the Common
               Stock on an as-converted basis. The holders of the Series D
               Preferred Stock are entitled to a liquidation preference equal to
               (i) the aggregate purchase price of the Series D Preferred Stock,
               and (ii) any declared but unpaid dividends. The Issuer may not
               issue any shares of capital stock or preferred stock that is
               senior to, or equal to the Series D Preferred Stock, without the
               approval of at least a majority in interest of the Series D
               Preferred Stock.

          (j)  Warrants, five year warrants, exercisable immediately, entitling
               the holder thereof to purchase one share of Common Stock at an
               exercise price of $3.00 per share, subject to adjustment based on
               the product revenue achieved by the Issuer (the "Series D
               Warrants").

          (k)  Notes, two year notes, at an interest rate of 8% per annum (the
               "Series D Notes"). The Series D Notes are convertible into Series
               D Preferred Stock


                                   - 16 of 28-

<PAGE>


               and Series D Warrants, subject to stockholders' approval at the
               request of a majority of the Series D noteholders. The number of
               shares of Series D Preferred Stock and Series D Warrants to be
               received upon the conversion is determined by dividing the
               principal amount being converted plus accrued and unpaid
               interest, by $3.05, subject to adjustment.

ITEM 2. Identity And Background.

         1.    (a)  Wheatley Partners II, L.P. (formerly Applewood Associates,
                    L.P.), a limited partnership organized under the laws of the
                    State of New York ("Wheatley II").
               (b)  Address:         c/o Applewood Capital Corp.
                                     68 Wheatley Road
                                     Brookville, New York 11545
               (c)  Principal Business:       Investments.
               (d)  No.
               (e)  No.

         3.    (a)  Barry Rubenstein, a general partner of Wheatley II, an
                    officer and director of Applewood Capital and a general
                    partner of Woodland Venture Fund, Seneca Ventures, Woodland
                    Partners and Brookwood Partners, L.P. Mr. Rubenstein
                    resigned as a director of the Issuer on December 16, 1999.

               (b)  Address:         68 Wheatley Road
                                     Brookville, New York 11545
               (c)  Principal Business:       Investments.
               (d)  No.
               (e)  No.
               (f)  Citizenship:     United States

               Barry Rubenstein is the husband of Marilyn Rubenstein.

         4.    (a)  Irwin Lieber, a general partner of Wheatley II, and an
                    officer and director of Applewood Capital. Mr. Lieber
                    resigned as a director of the Issuer on December 16, 1999.

               (b)  Address:         767 Fifth Avenue
                                     New York, New York 10153
               (c)  Principal Business: Investments.
               (d)  No.
               (e)  No.
               (f)  Citizenship:     United States



                                   - 17 of 28-

<PAGE>



         7.    (a)  Jonathan Lieber, a general partner of Wheatley II, an
                    officer of Applewood Capital, and general partner of
                    Applegreen Partners, a New York partnership.

               (b)  Address:         767 Fifth Avenue
                                     New York, New York 10153
               (c)  Principal Occupation: Investments.
               (d)  No.
               (e)  No.
               (f)  Citizenship:     United States.

         8.    (a)  Seth Lieber, a general partner of Wheatley II, an officer of
                    Applewood Capital, and general partner of Applegreen
                    Partners, a New York partnership.

               (b)  Address:         767 Fifth Avenue
                                     New York, New York 10153
               (c)  Principal Occupation: Investments.
               (d)  No.
               (e)  No.
               (f)  Citizenship:     United States.

         10.   (a)  Marilyn Rubenstein, an officer of Services and a general
                    partner of Woodland Partners and Brookwood Partners, L.P.
               (b)  Address:         68 Wheatley Road
                                     Brookville, New York 11545
               (c)  Principal Occupation:  Investments.
               (d)  No.
               (e)  No.
               (f)  Citizenship:     United States.

         12.   (a)  Woodland Partners, a partnership organized under the laws of
                    the State of New York.
               (b)  Address:         68 Wheatley Road
                                     Brookville, New York 11545
               (c)  Principal Occupation:  Investments.
               (d)  No.
               (e)  No.

         13.   (a)  Brookwood Partners, L.P., a limited partnership organized
                    under the laws of the State of New York ("Brookwood").
               (b)  Address:         68 Wheatley Road
                                     Brookville, New York 11545
               (c)  Principal Occupation: Investments.
               (d)  No.
               (e)  No.


                                   - 18 of 28-

<PAGE>



         14.   (a)  Applegreen Partners, a partnership organized under the laws
                    of the State of New York ("Applegreen").

               (b)  Address:         8 Applegreen Drive
                                     Old Westbury, New York 11568
               (c)  Principal Occupation:  Investments.
               (d)  No.
               (e)  No.

ITEM 3. Source and Amount of Funds or Other Consideration.

     On December 22, 1999, the reporting persons purchased in a private
placement an aggregate of $362,500 Series D Notes, 118,850 shares of Series D
Preferred Stock, and Series D Warrants to purchase 118,850 shares of Common
Stock from the Issuer (the "1999 Financing"). The Series D Preferred Stock, the
Series D Warrants and the Series D Notes were offered together. The reporting
persons paid $3.05 for each share of Series D Preferred Stock with a Series D
Warrant.

     Each of Irwin Lieber and Barry Fingerhut obtained funds for the purchase of
the securities from personal funds and other funds.

     Each of Woodland Venture Fund, Seneca Ventures, Woodland Partners,
Brookwood Partners, L.P., and Applegreen Partners obtained funds for the
purchase of the securities from working capital and other funds.

     The amount of funds used in acquiring the securities are set forth below:


                                                            Total
                                                        Consideration
                                                     -------------------
Irwin Lieber                                                    $100,000
Barry Fingerhut                                                 $100,000
Woodland Venture Fund                                           $200,000
Seneca Ventures                                                 $100,000
Woodland Partners                                               $100,000
Brookwood Partners, L.P.                                        $100,000
Applegreen Partners                                             $ 25,000



                                   - 19 of 28-

<PAGE>



ITEM 4. Purpose of Transaction.

     No reporting person has any present plan or proposal which would relate to
or result in any of the matters set forth in subparagraphs (a) - (j) of Item 4
of Schedule 13D except as set forth herein.

ITEM 5. Interests in Securities of the Issuer.

     (a) The following list sets forth the aggregate number and percentage
(based on 4,372,375 shares of Common Stock outstanding as reported in the
Issuer's Form 10-Q for the quarter ended September 30, 1999, plus 382,696 shares
issued upon the reporting persons' conversion of the Series C Convertible
Preferred Stock) of outstanding shares of Common Stock owned beneficially by
each reporting person named in Item 2, as of December 22, 1999:


                               Shares of Common            Percentage of Shares
                              Stock Beneficially              of Common Stock
               Name                 Owned(2)               Beneficially Owned(2)
               ----                 --------               ---------------------
Wheatley Partners II, L.P.        1,194,659                        25.1%
Applewood Capital Corp.           1,194,659(3)                     25.1%
Barry Rubenstein                  1,533,078(3,4,5,6,7,8)           30.7%

- --------
     (2)  Includes shares of Common Stock issuable upon the exercise of the
          Advisory Option, the 1996 Advisory Option, the 1998 Directors Option,
          the June 1999 Directors Option and the October 1999 Directors Option.

     (3)  The reporting person disclaims beneficial ownership of these
          securities, except to the extent of his/her/its equity interest
          therein.

     (4)  Includes 31,040 shares of Common Stock owned individually by Barry
          Rubenstein, 31,040 shares of Common Stock issuable upon the exercise
          of the Advisory Option, 18,624 shares of Common Stock issuable upon
          the exercise of the 1996 Advisory Option, 20,000 shares of Common
          Stock issuable upon the exercise of the 1998 Directors Option, 7,500
          shares of Common Stock issuable upon the exercise of the June 1999
          Directors Option and 1,875 shares of Common Stock issuable upon the
          exercise of the October 1999 Directors Option.

     (5)  Includes 41,128 shares of Common Stock owned by the Fund, 32,787
          shares of Common Stock issuable upon the conversion of the Series D
          Preferred Stock and 32,787 shares of Common Stock issuable upon the
          exercise of the Series D Warrants.

     (6)  Includes 23,280 shares of Common Stock owned by Seneca, 16,393, shares
          of Common Stock issuable upon the conversion of the Series D Preferred
          Stock and 16,393 shares of Common Stock issuable upon the exercise of
          the Series D Warrants.

     (7)  Includes 16,393 shares of Common Stock issuable upon the conversion of
          the Series D Preferred Stock and 16,393 shares of Common Stock
          issuable upon the exercise of the Series D Warrants owned by Woodland
          Partners.

     (8)  Includes 16,393 shares of Common Stock issuable upon the conversion of
          the Series D Preferred Stock and 16,393 shares of Common Stock
          issuable upon the exercise of the Series D Warrants owned by Brookwood
          Partners, L.P.


                                   - 20 of 28-

<PAGE>



Irwin Lieber                         1,329,764(3,9)                   27.3%
Barry Fingerhut                      1,258,485(3,10)                  26.3%
Seth Lieber                          1,207,511(3,11,13)               25.4%
Jonathan Lieber                      1,205,959(3,12,13)               25.3%
Woodland Venture Fund                  228,340(3,5,6,7,8)              4.6%
Seneca Ventures                        228,340(3,5,6,7,8)              4.6%
Marilyn Rubenstein                     228,340(3,5,6,7,8)              4.6%
Woodland Services Corp.                228,340(3,5,6,7,8)              4.6%
Woodland Partners                      228,340(3,5,6,7,8)              4.6%
Brookwood Partners, L.P.               228,340(3,5,6,7,8)              4.6%
Applegreen Partners                      8,096(13)                     0.2%

     (b) Wheatley Partners II, L.P. has sole power to vote and to dispose of
1,194,659 shares of Common Stock, representing approximately 25.1% of the
outstanding Common Stock.

     Applewood Capital, by virtue of being a general partner of Wheatley
Partners II, L.P., may be deemed to have shared power to vote and to dispose of
1,194,659 shares of Common Stock, representing approximately 25.1% of the
outstanding Common Stock.

     Barry Rubenstein, by virtue of being a general partner of Wheatley Partners
II, L.P., the Fund and Seneca, Woodland Partners and Brookwood Partners, L.P.,
may be deemed to

- --------
     (9)  Includes 23,280 shares of Common Stock owned individually by Irwin
          Lieber, 31,040 shares of Common Stock issuable upon the exercise of
          the Advisory Option, 18,624 shares of Common Stock issuable upon the
          exercise of the 1996 Advisory Option, 20,000 shares of Common Stock
          issuable upon the exercise of the 1998 Directors Option, 7,500 shares
          of Common Stock issuable upon the exercise of the June 1999 Directors
          Option, 1,875 shares of Common Stock issuable upon the exercise of the
          October 1999 Directors Option, 16,393 shares of Common Stock issuable
          upon the conversion of the Series D Preferred Stock and 16,393 shares
          of Common Stock issuable upon the exercise of the Series D Warrants.

     (10) Includes 31,040 shares of Common Stock owned individually by Barry
          Fingerhut, 16,393 shares of Common Stock issuable upon the conversion
          of the Series D Preferred Stock and 16,393 shares of Common Stock
          issuable upon the exercise of the Series D Warrants.

     (11) Includes 4,656 shares of Common Stock owned individually by Seth
          Lieber.

     (12) Includes 3,104 shares of Common Stock owned individually by Jonathan
          Lieber.

     (13) Includes 4,098 shares of Common Stock issuable upon the conversion of
          the Series D Preferred Stock and 4,098 shares of Common Stock issuable
          upon the exercise of the Series D Warrants owned by Applegreen
          Partners.


                                   - 21 of 28-

<PAGE>



have shared power to vote and to dispose of 1,422,999 shares of Common Stock
(including 81,966 shares issuable upon the conversion of the Series D Preferred
Stock and 81,966 shares issuable upon the exercise of the Series D Warrants),
representing approximately 28.5% of the outstanding Common Stock. Barry
Rubenstein has sole power to vote and to dispose of 110,079 shares of Common
Stock (which includes shares issuable upon the exercise of the Advisory Option,
the 1996 Advisory Option, the 1998 Directors Option, the June 1999 Directors
Option, and the October 1999 Directors Option), representing approximately 2.3%
of the outstanding Common Stock.

     Irwin Lieber, by virtue of being a general partner of Wheatley Partners II,
L.P., may be deemed to have shared power to vote and to dispose of 1,194,659
shares of Common Stock, representing approximately 25.1% of the outstanding
Common Stock. Irwin Lieber has sole power to vote and to dispose of 135,105
shares of Common Stock (which includes shares issuable upon the exercise of the
Advisory Option, the 1996 Advisory Option, the 1998 Directors Option, the June
1999 Directors Option, the October 1999 Directors Option, 16,393 shares issuable
upon the conversion of the Series D Preferred Stock and 16,393 shares issuable
upon the exercise of the Series D Warrants), representing approximately 2.8% of
the outstanding Common Stock.

     Barry Fingerhut, by virtue of being a general partner of Wheatley Partners
II, L.P., may be deemed to have shared power to vote and to dispose of 1,194,659
shares of Common Stock, representing approximately 25.1% of the outstanding
Common Stock. Barry Fingerhut has sole power to vote and to dispose of 63,826
shares of Common Stock (including 16,393 shares issuable upon the conversion of
the Series D Preferred Stock and 16,393 shares issuable upon the exercise of the
Series D Warrants), representing approximately 1.3% of the outstanding Common
Stock.

     Seth Lieber, by virtue of being a general partner of Wheatley Partners II,
L.P., and a general partner of Applegreen, may be deemed to have shared power to
vote and to dispose of 1,202,855 shares of Common Stock (including 4,098 shares
issuable upon the conversion of the Series D Preferred Stock and 4,098 shares
issuable upon the exercise of the Series D Warrants), representing approximately
25.4% of the outstanding Common Stock. Seth Lieber has sole power to vote and to
dispose of 4,656 shares of Common Stock, representing approximately 0.1% of the
outstanding Common Stock.

     Jonathan Lieber, by virtue of being a general partner of Wheatley Partners
II, L.P., and managing general partner of Applegreen, may be deemed to have
shared power to vote and to dispose of 1,202,855 shares of Common Stock
(including 4,098 shares issuable upon the conversion of the Series D Preferred
Stock and 4,098 shares issuable upon the exercise of the Series D Warrants),
representing approximately 25.3% of the outstanding Common Stock. Jonathan
Lieber has sole power to vote and to dispose of 3,104 shares of Common Stock,
representing approximately 0.1% of the outstanding Common Stock.

     The Fund has sole power to vote and to dispose of 106,702 shares of Common
Stock (including 32,787 shares issuable upon the conversion of the Series D
Preferred Stock and 32,787 shares issuable upon the exercise of the Series D
Warrants), representing approximately


                                   - 22 of 28-

<PAGE>



2.2% of the outstanding Common Stock, and may be deemed to have shared power to
vote and to dispose of 121,638 shares of Common Stock (including 49,179 shares
issuable upon the conversion of the Series D Preferred Stock and 49,179 shares
issuable upon the exercise of the Series D Warrants), representing approximately
2.5% of the outstanding Common Stock.

     Seneca has sole power to vote and to dispose of 56,066 shares of Common
Stock, representing approximately 1.2% of the outstanding Common Stock
(including 16,393 shares issuable upon the conversion of the Series D Preferred
Stock and 16,393 shares issuable upon the exercise of the Series D Warrants),
and may be deemed to have shared power to vote and to dispose of 172,274 shares
of Common Stock (including 65,573 shares issuable upon the conversion of the
Series D Preferred Stock and 65,573 shares issuable upon the exercise of the
Series D Warrants), representing approximately 3.5% of the outstanding Common
Stock.

     Marilyn Rubenstein, by virtue of being an officer of Services and a general
partner of Woodland Partners and Brookwood Partners, L.P., may be deemed to have
shared power to vote and to dispose of 228,340 shares of Common Stock (including
81,966 shares issuable upon the conversion of the Series D Preferred Stock and
81,966 shares issuable upon the exercise of the Series D Warrants), representing
approximately 4.6% of the outstanding Common Stock.

     Services by virtue of being a general partner of the Fund and Seneca, may
be deemed to have shared power to vote and to dispose of 228,340 shares of
Common Stock (including 81,966 shares issuable upon the conversion of the Series
D Preferred Stock and 81,966 shares issuable upon the exercise of the Series D
Warrants), representing approximately 4.6% of the outstanding Common Stock.

     Woodland Partners has sole power to vote and to dispose of 32,786 shares of
Common Stock, representing approximately 0.7% of the outstanding Common Stock
and may be deemed to have shared power to vote and to dispose of 195,554 shares
of Common Stock (including 81,966 shares issuable upon the conversion of the
Series D Preferred Stock and 81,966 shares issuable upon the exercise of the
Series D Warrants), representing approximately 4.0% of the outstanding Common
Stock.

     Brookwood Partners, L.P. has sole power to vote and to dispose of 32,786
shares of Common Stock, representing approximately 0.7% of the outstanding
Common Stock, and may be deemed to have shared power to vote and to dispose of
195,554 shares of Common Stock, (including 81,966 shares issuable upon the
conversion of the Series D Preferred Stock and 81,966 shares issuable upon the
exercise of the Series D Warrants), representing approximately 4.0% of the
outstanding Common Stock.

     Applegreen Partners has sole power to vote and to dispose of 8,196 shares
of Common Stock, representing approximately 0.2% of the outstanding Common
Stock.

     (c) The following is a description of all transactions in shares of Common
Stock of the Issuer by the reporting persons identified in Item 2 of this
Schedule 13D effected from October 13, 1999 through December 22, 1999,
inclusive:



                                   - 23 of 28-

<PAGE>


<TABLE>
<CAPTION>
                                               Number of
                                               Shares of
                                               Series D             Number of         Purchase Price Per share
                                               Preferred            Series D           of Series D Preferred
                                Purchase       Stock                Warrants          Stock with one Series D        Series D Notes
Name of Shareholder             Date           Purchased            Purchased                 Warrant                  Purchased
- -------------------             ----           ---------            ---------                 -------                  ---------
<S>                           <C>              <C>                   <C>                       <C>                      <C>
Irwin Lieber                  12/22/99         16,393                16,393                    $3.05                    $ 50,000
Barry Fingerhut               12/22/99         16,393                16,393                    $3.05                    $ 50,000
Woodland Venture Fund         12/22/99         32,787                32,787                    $3.05                    $100,000
Seneca Ventures               12/22/99         16,393                16,393                    $3.05                    $ 50,000
Woodland Partners             12/22/99         16,393                16,393                    $3.05                    $ 50,000
Brookwood Partners, L.P.      12/22/99         16,393                16,393                    $3.05                    $ 50,000
Applegreen Partners           12/22/99          4,098                 4,098                    $3.05                    $ 12,500
</TABLE>

     On December 14, 1999, Wheatley II converted 382,696 shares of Series C
Preferred Stock into 382,696 shares of Common Stock of the Issuer.

     On October 25, 1999, the Issuer granted the October 1999 Directors Option
to each of Barry Rubenstein and Irwin Lieber.

     (d) No other person has the right to receive or the power to direct the
receipt of dividends from, or the proceeds from the sale of such securities.

     (e) Not applicable.

ITEM 6. Contracts Arrangements Understanding or Relationships with Respect to
        Securities of the Issuer.

     The Issuer agreed to file a Form S-3 Registration Statement to register the
Common Stock underlying the Series D Preferred Stock, the Series D Warrants and
the Series D Notes, within 45 days of the closing of the purchase of the above
mentioned securities.

ITEM 7. Materials to be Filed as Exhibits

     Exhibit A. Agreement among the reporting persons by which they have agreed
to file this Schedule 13D and all necessary amendments, as required by Rule 13d-
1(f).



                                   - 24 of 28-

<PAGE>

                                    SIGNATURE

     After reasonable inquiry and to the best of his/her/its knowledge and
belief, each of the undersigned hereby certifies that the information set forth
in this Schedule is true, complete and correct.

Dated: January 26, 2000
                                           WHEATLEY PARTNERS II, L.P.

                                           By:      /s/Irwin Lieber
                                               ---------------------------------
                                           Irwin Lieber, General Partner


                                           APPLEWOOD CAPITAL CORP.

                                           By:      /s/Barry Rubenstein
                                               ---------------------------------
                                           Barry Rubenstein, President


                                           SENECA VENTURES

                                           By:      /s/Barry Rubenstein
                                               ---------------------------------
                                           Barry Rubenstein, General Partner


                                           WOODLAND VENTURE FUND

                                           By:      /s/Barry Rubenstein
                                               ---------------------------------
                                           Barry Rubenstein, General Partner


                                           WOODLAND SERVICES CORP.

                                           By:      /s/Barry Rubenstein
                                               ---------------------------------
                                           Barry Rubenstein, President







                                                          - 25 of 28-

<PAGE>




                                                    /s/Barry Rubenstein
                                               ---------------------------------
                                                    Barry Rubenstein

                                                    /s/Irwin Liber
                                               ---------------------------------
                                                    Irwin Lieber

                                                    /s/Barry Fingerhut
                                               ---------------------------------
                                                    Barry Fingerhut

                                                    /s/Marilyn Rubenstein
                                               ---------------------------------
                                                    Marilyn Rubenstein

                                                    /s/Seth Lieber
                                               ---------------------------------
                                                    Seth Lieber

                                                    /s/Jonathan Lieber
                                               ---------------------------------
                                                    Jonathan Lieber


                                           WOODLAND PARTNERS

                                           By:      /s/Barry Rubenstein
                                               ---------------------------------
                                           Barry Rubenstein, General Partner


                                           BROOKWOOD PARTNERS, L.P.

                                           By:      /s/Barry Rubenstein
                                               ---------------------------------
                                           Barry Rubenstein, General Partner


                                           APPLEGREEN PARTNERS

                                           By: /s/Jonathan Lieber
                                               ---------------------------------
                                                Jonathan Lieber, General Partner


ATTENTION: INTENTIONAL MISSTATEMENTS OR OMISSIONS OF FACT CONSTITUTE FEDERAL
CRIMINAL VIOLATIONS (SEE 18 U.S.C. 1001).





                                   - 26 of 28-

<PAGE>



                                                                       Exhibit A

                             JOINT FILING AGREEMENT

     In accordance with Rule 13d-1(f) under the Securities Exchange Act of 1934,
as amended, the undersigned hereby agree to the joint filing on behalf of each
of them of a statement on Schedule 13D (including amendments thereto) with
respect to the Common Stock, par value $.01 per share, of NETWORK - 1 SECURITY
SOLUTIONS, INC. and that this Agreement be filed as an Exhibit to such statement
on Schedule 13D.

     IN WITNESS WHEREOF, the undersigned hereby execute this Agreement effective
as of the 22nd day of December, 1999.

                                        WHEATLEY PARTNERS II, L.P.

                                        By:  /s/Irwin Lieber
                                            ------------------------------------
                                             Irwin Lieber, A General Partner


                                        APPLEWOOD CAPITAL CORP.

                                        By:  /s/Barry Rubenstein
                                            ------------------------------------
                                             Barry Rubenstein, President


                                        SENECA VENTURES

                                        By:  /s/Barry Rubenstein
                                            ------------------------------------
                                             Barry Rubenstein, A General Partner


                                        WOODLAND VENTURE FUND

                                        By:  /s/Barry Rubenstein
                                            ------------------------------------
                                             Barry Rubenstein, A General Partner


                                   - 27 of 28-

<PAGE>





                                        WOODLAND SERVICES CORP.


                                        By:  /s/Barry Rubenstein
                                            ------------------------------------
                                             Barry Rubenstein, President

                                             /s/Barry Rubenstein
                                            ------------------------------------
                                             Barry Rubenstein

                                             /s/Irwin Liber
                                            ------------------------------------
                                             Irwin Lieber

                                             /s/Barry Fingerhut
                                            ------------------------------------
                                             Barry Fingerhut

                                             /s/Marilyn Rubenstein
                                            ------------------------------------
                                             Marilyn Rubenstein

                                             /s/Seth Lieber
                                            ------------------------------------
                                             Seth Lieber

                                             /s/Jonathan Lieber
                                            ------------------------------------
                                             Jonathan Lieber

                                        WOODLAND PARTNERS


                                        By:  /s/Barry Rubenstein
                                            ------------------------------------
                                             Barry Rubenstein, A General Partner


                                        BROOKWOOD PARTNERS, L.P.

                                        By:  /s/Barry Rubenstein
                                            ------------------------------------
                                             Barry Rubenstein, A General Partner


                                        APPLEGREEN PARTNERS

                                        By   /s/Jonathan Lieber
                                            ------------------------------------
                                             Jonathan Lieber, A General Partner



                                   - 28 of 28-


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