Exhibit 1.2



          WARRANT AGREEMENT dated as of _________, 1998 between Network-1
Security Solutions, Inc., a Delaware corporation (the "Company"), and Whale
Securities Co., L.P. (hereinafter referred to as the "Underwriter").

                                 W I T N E S S E T H:

          WHEREAS, the Company proposes to issue to the Underwriter warrants
(the "Warrants") to purchase up to 187,500 (as such number may be adjusted from
time to time pursuant to Article 8 of this Agreement) shares (the "Shares") of
common stock, par value $.01 per share (the "Common Stock"), of the Company; and

          WHEREAS, the Underwriter has agreed, pursuant to the underwriting
agreement (the "Underwriting Agreement") dated _________, 1998 between the
Underwriter and the Company, to act as the underwriter in connection with the
Company's proposed public offering (the "Public Offering") of 1,875,000 shares
of Common Stock (the "Public Shares") at an initial public offering price of
$8.00 per Public Share; and

          WHEREAS, the Warrants issued pursuant to this Agreement are being
issued by the Company to the Underwriter or to its designees who are officers
and partners of the Underwriter or to members of the selling group participating
in the distribution of the Public Shares to the public in the Public Offering
and/or their respective directors, officers or partners (collectively, the
"Designees"), in consideration for, and as part of the Underwriter's
compensation in connection with, the Underwriter acting as the Underwriter
pursuant to the Underwriting Agreement;





          NOW, THEREFORE, in consideration of the premises, the payment by the
Underwriter to the Company of ONE HUNDRED EIGHTY SEVEN DOLLARS AND FIFTY CENTS
($187.50), the agreements herein set forth and other good and valuable
consideration, the receipt and sufficiency of which are hereby acknowledged, 
the parties hereto agree as follows:

               1.   Grant.  

               The Underwriter, and/or the Designees are hereby granted the 
right to purchase, at any time from __________, 1999 until 5:00 P.M., New 
York time, on _______, 2003 (the "Warrant Exercise Term"), up to 187,500 
fully-paid and non-assessable Shares at an initial exercise price (subject to 
adjustment as provided in Article 8 hereof) of $13.20 per Share.

          2.   Warrant Certificates.  

          The warrant certificates delivered and to be delivered pursuant to
this Agreement (the "Warrant Certificates") shall be in the form set forth in
Exhibit A attached hereto and made a part hereof, with such appropriate
insertions, omissions, substitutions and other variations as required or
permitted by this Agreement.

          3.   Exercise of Warrant.  

               3.1. Cash Exercise.  The Warrants initially are exercisable at a
price of $13.20 per Share, payable in cash or by check to the order of the
Company, or any combination thereof, subject to adjustment as provided in
Article 8 hereof.  Upon surrender of the Warrant Certificate with the annexed
Form of 

                                       -2-





Election to Purchase duly executed, together with payment of the Exercise Price
(as hereinafter defined) for the Shares purchased, at the Company's principal
offices (currently located at 909 Third Avenue, 9th Floor, New York, New York
10022) the registered holder of a Warrant Certificate ("Holder" or "Holders")
shall be entitled to receive a certificate or certificates for the Shares so
purchased.  The purchase rights represented by each Warrant Certificate are
exercisable at the option of the Holder thereof, in whole or in part (but not as
to fractional Shares).  In the case of the purchase of less than all the Shares
purchasable under any Warrant Certificate, the Company shall cancel said Warrant
Certificate upon the surrender thereof and shall execute and deliver a new
Warrant Certificate of like tenor for the balance of the Shares purchasable
thereunder.

               3.2. Cashless Exercise.  At any time during the Warrant Exercise
Term, the Holder may, at the Holder's option, exchange, in whole or in part, the
Warrants represented by such Holder's Warrant Certificate (a "Warrant
Exchange"), into the number of Shares determined in accordance with this Section
3.2, by surrendering such Warrant Certificate at the principal office of the
Company or at the office of its transfer agent, accompanied by a notice stating
such Holder's intent to effect such exchange, the number of Warrants to be so
exchanged and the date on which the Holder requests that such Warrant Exchange
occur (the "Notice of Exchange").  The Warrant Exchange shall take place on the
date specified in the Notice of Exchange or, if later, the date the Notice of
Exchange is received by the Company 

                                       -3-





(the "Exchange Date").  Certificates for the Shares issuable upon such Warrant
Exchange and, if applicable, a new Warrant Certificate of like tenor
representing the Warrants which were subject to the surrendered Warrant
Certificate and not included in the Warrant Exchange, shall be issued as of the
Exchange Date and delivered to the Holder within three (3) days following the
Exchange Date.  In connection with any Warrant Exchange, the Holder shall be
entitled to subscribe for and acquire (i) the number of Shares (rounded to the
next highest integer) which would, but for the Warrant Exchange, then be
issuable pursuant to the provision of Section 3.1 above upon the exercise of the
Warrants specified by the Holder in its Notice of Exchange (the "Total Number")
less (ii) the number of Shares equal to the quotient obtained by dividing (a)
the product of the Total Number and the existing Exercise Price (as hereinafter
defined) by (b) the Market Price (as hereinafter defined) of a Public Share on
the day preceding the Warrant Exchange.  "Market Price" at any date shall be
deemed to be the last reported sale price, or, in case no such reported sales
takes place on such day, the average of the last reported sale prices for the
last three (3) trading days, in either case as officially reported by the
principal securities exchange on which the Common Stock is listed or admitted to
trading or as reported in the NASDAQ National market System, or, if the Common
Stock is not listed or admitted to trading on any national securities exchange
or quoted on the NASDAQ National Market System, the closing bid price as
furnished by (i) the National Association of Securities Dealers, Inc. 

                                       -4-





through NASDAQ or (ii) a similar organization if NASDAQ is no longer reporting
such information.

          4.   Issuance of Certificates.  

          Upon the exercise of the Warrants, the issuance of certificates for
the Shares purchased shall be made forthwith (and in any event within three (3)
business days thereafter) without charge to the Holder thereof including,
without limitation, any tax which may be payable in respect of the issuance
thereof, and such certificates shall (subject to the provisions of Article 5
hereof) be issued in the name of, or in such names as may be directed by, the
Holder thereof; provided, however, that the Company shall not be required to pay
any tax which may be payable in respect of any transfer involved in the issuance
and delivery of any such certificates in a name other than that of the Holder
and the Company shall not be required to issue or deliver such certificates
unless or until the person or persons requesting the issuance thereof shall have
paid to the Company the amount of such tax or shall have established to the
satisfaction of the Company that such tax has been paid.

          The Warrant Certificates and the certificates representing the Shares
shall be executed on behalf of the Company by the manual or facsimile signature
of the present or any future Chairman or Vice Chairman of the Board of
Directors, Chief Executive Officer or President or Vice President of the Company
under its corporate seal reproduced thereon, attested to by the manual or
facsimile signature of the present or any future Secretary or Assistant
Secretary of the Company.  Warrant 

                                       -5-





Certificates shall be dated the date of execution by the Company upon initial
issuance, division, exchange, substitution or transfer.

          Upon exercise, in part or in whole, of the Warrants,  certificates
representing the Shares shall bear a legend substantially similar to the
following:

     "The securities represented by this certificate have not been
     registered for purposes of public distribution under the Securities
     Act of 1933, as amended (the "Act"), and may not be offered or sold
     except (i) pursuant to an effective registration statement under the
     Act, (ii) to the extent applicable, pursuant to Rule 144 under the Act
     (or any similar rule under such Act relating to the disposition of
     securities), or (iii) upon the delivery by the holder to the Company
     of an opinion of counsel, reasonably satisfactory to counsel to the
     Company, stating that an exemption from registration under such Act is
     available."

          5.   Restriction on Transfer of Warrants.  

          The Holder of a Warrant Certificate, by the Holder's acceptance
thereof, covenants and agrees that the Warrants are being acquired as an
investment and not with a view to the distribution thereof, and that the
Warrants may not be sold, transferred, assigned, hypothecated or otherwise
disposed of, in whole or in part, for a period of one (1) year from the date
hereof, except to the Designees.

          6.   Price.

               6.1. Initial and Adjusted Exercise Price.  The initial exercise
price of each Warrant shall be $13.20 per Share.  The adjusted exercise price
per Share shall be the price which shall result from time to time from any and
all adjustments of 

                                       -6-





the initial exercise price per Share in accordance with the provisions of
Article 8 hereof.

               6.2. Exercise Price.  The term "Exercise Price" herein shall mean
the initial exercise price or the adjusted exercise price, depending upon the
context.

          7.   Registration Rights.

               7.1. Registration Under the Securities Act of 1933.  None of the
Warrants or Shares have been registered for purposes of public distribution
under the Securities Act of 1933, as amended (the "Act"). 

               7.2. Registrable Securities.  As used herein the term
"Registrable Security" means each of the Warrants, the Shares and any shares of
Common Stock issued upon any stock split or stock dividend in respect of such
Shares; provided, however, that with respect to any particular Registrable
Security, such security shall cease to be a Registrable Security when, as of the
date of determination, (i) it has been effectively registered under the Act and
disposed of pursuant thereto, (ii) registration under the Act is no longer
required for the subsequent public distribution of such security or (iii) it has
ceased to be outstanding.  The term "Registrable Securities" means any and/or
all of the securities falling within the foregoing definition of a "Registrable
Security."  In the event of any merger, reorganization, consolidation,
recapitalization or other change in corporate structure affecting the Common
Stock, such adjustment shall be made in the definition of "Registrable 

                                       -7-





Security" as is appropriate in order to prevent any dilution or enlargement of
the rights granted pursuant to this Article 7.

               7.3. Piggyback Registration.  If, at any time during the seven
years following the effective date of the Public Offering, the Company proposes
to prepare and file one or more post-effective amendments to the registration
statement filed in connection with the Public Offering or any new registration
statement or post-effective amendments thereto covering equity or debt
securities of the Company, or any such securities of the Company held by its
shareholders (in any such case, other than in connection with a merger,
acquisition or pursuant to Form S-8 or successor form), (for purposes of this
Article 7, collectively, the "Registration Statement"), it will give written
notice of its intention to do so by registered mail ("Notice"), at least thirty
(30) business days prior to the filing of each such Registration Statement, to
all holders of the Registrable Securities.  Upon the written request of such a
holder (a "Requesting Holder"), made within twenty (20) business days after
receipt of the Notice, that the Company include any of the Requesting Holder's
Registrable Securities in the proposed Registration Statement, the Company
shall, as to each such Requesting Holder, use its best efforts to effect the
registration under the Act of the Registrable Securities which it has been so
requested to register ("Piggyback Registration"), at the Company's sole cost and
expense and at no cost or expense to the Requesting Holders.  Notwithstanding
the provisions of this Section 7.3, the Company shall have the right at any time
after it shall have given 

                                       -8-





written notice pursuant to this Section 7.3 (irrespective of whether any written
request for inclusion of Registrable Securities shall have already been made) to
elect not to file any such proposed Registration Statement, or to withdraw the
same after the filing but prior to the effective date thereof.

               7.4. Demand Registration.

                    (a)  At any time during the Warrant Exercise Term, any
"Majority Holder" (as such term is defined in Section 7.4(c) below) of the
Registrable Securities shall have the right (which right is in addition to the
piggyback registration rights provided for under Section 7.3 hereof),
exercisable by written notice to the Company (the "Demand Registration
Request"), to have the Company prepare and file with the Securities and Exchange
Commission (the "Commission"), on one occasion, at the sole expense of the
Company (except as provided in Section 7.5(b) hereof), a Registration Statement
and such other documents, including a prospectus, as may be necessary (in the
opinion of both counsel for the Company and counsel for such Majority Holder),
in order to comply with the provisions of the Act, so as to permit a public
offering and sale of the Registrable Securities by the holders thereof.  The
Company shall use its best efforts to cause the Registration Statement to become
effective under the Act, so as to permit a public offering and sale of the
Registrable Securities by the holders thereof.  Once effective, the Company will
use its best efforts to maintain the effectiveness of the Registration Statement
until the earlier of (i) the date that all of the Registrable Securities have
been 

                                      -9-





sold or (ii) the date that the holders of the Registrable Securities receive an
opinion of counsel to the Company that all of the Registrable Securities may be
freely traded (without limitation or restriction as to quantity or timing and
without registration under the Act) under Rule 144(k) promulgated under the Act
or otherwise.  

                    (b)  The Company covenants and agrees to give written notice
of any Demand Registration Request to all holders of the Registrable Securities
within ten (10) business days from the date of the Company's receipt of any such
Demand Registration Request.  After receiving notice from the Company as
provided in this Section 7.4(b), holders of Registrable Securities may request
the Company to include their Registrable Securities in the Registration
Statement to be filed pursuant to Section 7.4(a) hereof by notifying the Company
of their decision to have such securities included within ten (10) days of their
receipt of the Company's notice.

                    (c)  The term "Majority Holder" as used in Section 7.4
hereof shall mean any holder or any combination of holders of Registrable
Securities, if included in such holders' Registrable Securities are that
aggregate number of shares of Common Stock (including Shares already issued and
Shares issuable pursuant to the exercise of outstanding Warrants) as would
constitute a majority of the aggregate number of Shares (including Shares
already issued and Shares issuable pursuant to the exercise of outstanding
Warrants) included in all the Registrable Securities.

                                      -10-







               7.5. Covenants of the Company With Respect to Registration.  The
Company covenants and agrees as follows:

                    (a)  In connection with any registration under Section 7.4
hereof, the Company shall file the Registration Statement as expeditiously as
possible, but in any event no later than twenty (20) days following receipt of
any demand therefor, shall use its best efforts to have any such Registration
Statement declared effective at the earliest possible time, and shall furnish
each holder of Registrable Securities such number of prospectuses as shall
reasonably be requested.

                    (b)  The Company shall pay all costs, fees and expenses
(other than underwriting fees, discounts and nonaccountable expense allowance
applicable to the Registrable Securities and the fees and expenses of counsel
retained by the holders of Registrable Securities) in connection with all
Registration Statements filed pursuant to Sections 7.3 and 7.4(a) hereof
including, without limitation, the Company's legal and accounting fees, printing
expenses, and blue sky fees and expenses.  

                    (c)  The Company will take all necessary action which may be
required in qualifying or registering the Registrable Securities included in the
Registration Statement for offering and sale under the securities or blue sky
laws of such states as are reasonably requested by the holders of such
securities.

                    (d)  The Company shall indemnify any holder of the
Registrable Securities to be sold pursuant to any Regis-

                                      -11-





tration Statement and any underwriter or person deemed to be an underwriter
under the Act and each person, if any, who controls such holder or underwriter
or person deemed to be an underwriter within the meaning of Section 15 of the
Act or Section 20(a) of the Securities Exchange Act of 1934, as amended
("Exchange Act"), against all loss, claim, damage, expense or liability
(including all expenses reasonably incurred in investigating, preparing or
defending against any claim whatsoever) to which any of them may become subject
under the Act, the Exchange Act or otherwise, arising from such registration
statement to the same extent and with the same effect as the provisions pursuant
to which the Company has agreed to indemnify the Underwriter as set forth in
Section 7 of the Underwriting Agreement and to provide for just and equitable
contribution as set forth in Section 8 of the Underwriting Agreement.

                    (e)  Any holder of Registrable Securities to be sold
pursuant to a registration statement, and such Holder's successors and assigns,
shall severally, and not jointly, indemnify, the Company, its officers and
directors and each person, if any, who controls the Company within the meaning
of Section 15 of the Act or Section 20(a) of the Exchange Act, against all loss,
claim, damage or expense or liability (including all expenses reasonably
incurred in investigating, preparing or defending against any claim whatsoever)
to which they may become subject under the Act, the Exchange Act or otherwise,
arising from information furnished by or on behalf of such holder, or such
Holder's successors or assigns, for specific inclusion in such 

                                      -12-






Registration Statement to the same extent and with the same effect as the
provisions pursuant to which the Underwriter has agreed to indemnify the Company
as set forth in Section 7 of the Underwriting Agreement and to provide for just
and equitable contribution as set forth in Section 8 of the Underwriting
Agreement.

                    (f)  Nothing contained in this Agreement shall be construed
as requiring any Holder to exercise the Warrants held by such Holder prior to
the initial filing of any registration statement or the effectiveness thereof.

                    (g)  If the Company shall fail to comply with the provisions
of this Article 7, the Company shall, in addition to any other equitable or
other relief available to the holders of Registrable Securities, be liable for
any or all incidental, special and consequential damages sustained by the
holders of Registrable Securities, requesting registration of their Registrable
Securities.

                    (h)  The Company shall promptly deliver copies of all
correspondence between the Commission and the Company, its counsel or auditors
and all memoranda relating to discussions with the Commission or its staff with
respect to the Registration Statement to each holder of Registrable Securities
included for such registration in such Registration Statement pursuant to
Section 7.3 hereof or Section 7.4 hereof requesting such correspondence and
memoranda and to the managing underwriter, if any, of the offering in connection
with which such Holder's Registrable Securities are being registered and 

                                      -13-





shall permit each holder of Registrable Securities and such underwriter to do
such reasonable investigation, upon reasonable advance notice, with respect to
information contained in or omitted from the Registration Statement as it deems
reasonably necessary to comply with applicable securities laws or rules of the
National Association of Securities Dealers, Inc.  Such investigation shall
include access to books, records and properties and opportunities to discuss the
business of the Company with its officers and independent auditors, all to such
reasonable extent and at such reasonable times and as often as any such holder
of Registrable Securities or underwriter shall reasonably request.

          8.   Adjustments of Exercise Price and Number of Shares.

               8.1.  Computation of Adjusted Price.  In case the Company shall
at any time after the date hereof pay a dividend in shares of Common Stock or
make a distribution in shares of Common Stock, then upon such dividend or
distribution the Exercise Price in effect immediately prior to such dividend or
distribution shall forthwith be reduced to a price determined by dividing:

                         (a) an amount equal to the total number of shares of
Common Stock outstanding immediately prior to such dividend or distribution
multiplied by the Exercise Price in effect immediately prior to such dividend or
distribution, by

                         (b) the total number of shares of Common Stock
outstanding immediately after such issuance or sale.

                                      -14-







                    For the purposes of any computation to be made in accordance
with the provisions of this Section 8.1, the Common Stock issuable by way of
dividend or other distribution on any stock of the Company shall be deemed to
have been issued immediately after the opening of business on the date following
the date fixed for the determination of stockholders entitled to receive such
dividend or other distribution.

               8.2. Subdivision and Combination.  In case the Company shall at
any time subdivide or combine the outstanding shares of Common Stock, the
Exercise Price shall forthwith be proportionately decreased in the case of
subdivision or increased in the case of combination.

               8.3. Adjustment in Number of Shares.  Upon each adjustment of the
Exercise Price pursuant to the provisions of this Article 8, the number of
Shares issuable upon the exercise of each Warrant shall be adjusted to the
nearest full number by multiplying a number equal to the Exercise Price in
effect immediately prior to such adjustment by the number of Shares issuable
upon exercise of the Warrants immediately prior to such adjustment and dividing
the product so obtained by the adjusted Exercise Price.

               8.4. Reclassification, Consolidation, Merger, etc.  In case of
any reclassification or change of the outstanding shares of Common Stock (other
than a change in par value to no par value, or from no par value to par value,
or as a result of a subdivision or combination), or in the case of any
consolidation of the Company with, or merger of the Company into, another 


                                      -15-





corporation (other than a consolidation or merger in which the Company is the
surviving corporation and which does not result in any reclassification or
change of the outstanding shares of Common Stock, except a change as a result of
a subdivision or combination of such shares or a change in par value, as
aforesaid), or in the case of a sale or conveyance to another corporation of the
property of the Company as an entirety, the Holders shall thereafter have the
right to purchase the kind and number of shares of stock and other securities
and property receivable upon such reclassification, change, consolidation,
merger, sale or conveyance as if the Holders were the owners of the shares of
Common Stock underlying the Warrants immediately prior to any such events at a
price equal to the product of (x) the number of shares of Common Stock issuable
upon exercise of the Holder's Warrants and (y) the Exercise Price in effect
immediately prior to the record date for such reclassification, change,
consolidation, merger, sale or conveyance as if such Holders had exercised the
Warrants.

               8.5.  Determination of Outstanding Shares of Common Stock.  The
number of shares of Common Stock at any one time outstanding shall include the
aggregate number of shares of Common Stock issued and the aggregate number of
shares of Common Stock issuable upon the exercise of options, rights, warrants
and upon the conversion or exchange of convertible or exchangeable securities.

               8.6. Dividends and Other Distributions with Respect to
Outstanding Securities.  In the event that the Company 

                                      -16-





shall at any time prior to the exercise of all Warrants make any distribution of
its assets to holders of its Common Stock as a liquidating or a partial
liquidating dividend, then the holder of Warrants who exercises its Warrants
after the record date for the determination of those holders of Common Stock
entitled to such distribution of assets as a liquidating or partial liquidating
dividend shall be entitled to receive for the Warrant Price per Warrant, in
addition to each share of Common Stock, the amount of such distribution (or, at
the option of the Company, a sum equal to the value of any such assets at the
time of such distribution as determined by the Board of Directors of the Company
in good faith) which would have been payable to such holder had he been the
holder of record of the Common Stock receivable upon exercise of his Warrant on
the record date for the determination of those entitled to such distribution. 
At the time of any such dividend or distribution, the Company shall make
appropriate reserves to ensure the timely performance of the provisions of this
Subsection 8.6.

               8.7. Subscription Rights for Shares of Common Stock or Other
Securities.  In the case that the Company or an affiliate of the Company shall
at any time after the date hereof and prior to the exercise of all the Warrants
issue any rights, warrants or options to subscribe for shares of Common Stock or
any other securities of the Company or of such affiliate to all the shareholders
of the Company, the Holders of unexercised Warrants on the record date set by
the Company or such affiliate in connection with such issuance of rights,
warrants or options 

                                      -17-





shall be entitled, in addition to the shares of Common Stock or other securities
receivable upon the exercise of the Warrants, to receive such rights, warrants
or options shall be entitled, in addition to the shares of Common Stock or other
securities receivable upon the exercise of the Warrants, to receive such rights
at the time such rights, warrants or options that such Holders would have been
entitled to receive had they been, on such record date, the holders of record of
the number of whole shares of Common Stock then issuable upon exercise of their
outstanding Warrants (assuming for purposes of this Section 8.7), that the
exercise of the Warrants is permissible immediately upon issuance).

          9.   Exchange and Replacement of Warrant Certificates.

          Each Warrant Certificate is exchangeable without expense, upon the
surrender thereof by the registered Holder at the principal executive office of
the Company, for a new Warrant Certificate of like tenor and date representing
in the aggregate the right to purchase the same number of securities in such
denominations as shall be designated by the Holder thereof at the time of such
surrender.

          Upon receipt by the Company of evidence reasonably satisfactory to it
of the loss, theft, destruction or mutilation of any Warrant Certificate, and,
in case of loss, theft or destruction, of indemnity or security reasonably
satisfactory to it, and reimbursement to the Company of all reasonable expenses
incidental thereto, and upon surrender and cancellation of the 

                                     -18-





Warrant Certificate, if mutilated, the Company will make and deliver a new
Warrant Certificate of like tenor, in lieu thereof.

          10.  Elimination of Fractional Interests.

          The Company shall not be required to issue certificates representing
fractions of Shares, nor shall it be required to issue scrip or pay cash in lieu
of fractional interests, it being the intent of the parties that all fractional
interests shall be eliminated by rounding any fraction up to the nearest whole
number of Shares.

          11.  Reservation and Listing of Securities.

          The Company shall at all times reserve and keep available out of its
authorized shares of Common Stock, solely for the purpose of issuance upon the
exercise of the Warrants, such number of shares of Common Stock as shall be
issuable upon the exercise thereof.  The Company covenants and agrees that, upon
exercise of the Warrants and payment of the Exercise Price therefor, all Shares
issuable upon such exercise shall be duly and validly issued, fully paid,
non-assessable and not subject to the preemptive rights of any shareholder.  As
long as the Warrants shall be outstanding, the Company shall use its best
efforts to cause all shares of Common Stock issuable upon the exercise of the
Warrants to be listed on or quoted by NASDAQ or listed on such national
securities exchange, in the event the Common Stock is listed on a national
securities exchange.


          12.  Notices to Warrant Holders.


                                      -19-






          Nothing contained in this Agreement shall be construed as conferring
upon the Holder or Holders the right to vote or to consent or to receive notice
as a shareholder in respect of any meetings of shareholders for the election of
directors or any other matter, or as having any rights whatsoever as a
shareholder of the Company.  If, however, at any time prior to the expiration of
the Warrants and their exercise, any of the following events shall occur:

                    (a)  the Company shall take a record of the holders of its
          shares of Common Stock for the purpose of entitling them to receive a
          dividend or distribution payable otherwise than in cash, or a cash
          dividend or distribution payable otherwise than out of current or
          retained earnings, as indicated by the accounting treatment of such
          dividend or distribution on the books of the Company; or

                    (b)  the Company shall offer to all the holders of its
          Common Stock any additional shares of capital stock of the Company or
          securities convertible into or exchangeable for shares of capital
          stock of the Company, or any option, right or warrant to subscribe
          therefor; or

                    (c)  a dissolution, liquidation or winding up of the Company
          (other than in connection with a consolidation or merger) or a sale of
          all or substantially all of its property, assets and business as an
          entirety shall be proposed; or


                                      -20-






                    (d)  reclassification or change of the outstanding shares of
          Common Stock (other than a change in par value to no par value, or
          from no par value to par value, or as a result of a subdivision or
          combination), consolidation of the Company with, or merger of the
          Company into, another corporation (other than a consolidation or
          merger in which the Company is the surviving corporation and which
          does not result in any reclassification or change of the outstanding
          shares of Common Stock, except a change as a result of a subdivision
          or combination of such shares or a change in par value, as aforesaid),
          or a sale or conveyance to another corporation of the property of the
          Company as an entirety is proposed; or

                    (e)  The Company or an affiliate of the Company shall
          propose to issue any rights to subscribe for shares of Common Stock or
          any other securities of the Company or of such affiliate to all the
          shareholders of the Company;

then, in any one or more of said events, the Company shall give written notice
to the Holder or Holders of such event at least fifteen (15) days prior to the
date fixed as a record date or the date of closing the transfer books for the
determination of the shareholders entitled to such dividend, distribution,
convertible or exchangeable securities or subscription rights, options or
warrants, or entitled to vote on such proposed dissolution, liquidation, winding
up or sale.  Such notice shall specify such 

                                      -21-





record date or the date of closing the transfer books, as the case may be. 
Failure to give such notice or any defect therein shall not affect the validity
of any action taken in connection with the declaration or payment of any such
dividend or distribution, or the issuance of any convertible or exchangeable
securities or subscription rights, options or warrants, or any proposed
dissolution, liquidation, winding up or sale.

          13.  Notices.

          All notices, requests, consents and other communications hereunder
shall be in writing and shall be deemed to have been duly made when delivered,
or mailed by registered or certified mail, return receipt requested:

                    (a)  If to a registered Holder of the Warrants, to the
          address of such Holder as shown on the books of the Company; or

                    (b)  If to the Company, to the address set forth in Section
          3 of this Agreement or to such other address as the Company may
          designate by notice to the Holders.

          14.  Supplements and Amendments.

          The Company and the Underwriter may from time to time supplement or
amend this Agreement without the approval of any Holders of Warrant Certificates
in order to cure any ambiguity, to correct or supplement any provision contained
herein which may be defective or inconsistent with any provisions herein, or to
make any other provisions in regard to matters or questions arising hereunder
which the Company and the Underwriter may deem 

                                      -22-





necessary or desirable and which the Company and the Underwriter deem not to
adversely affect the interests of the Holders of Warrant Certificates.

          15.  Successors.

          All the covenants and provisions of this Agreement by or for the
benefit of the Company and the Holders inure to the benefit of their respective
successors and assigns hereunder.

          16.  Termination.

          This Agreement shall terminate at the close of business on __________,
2006.  Notwithstanding the foregoing, this Agreement will terminate on any
earlier date when all Warrants have been exercised and all the Shares issuable
upon exercise of the Warrants have been resold to the public; provided, however,
that the provisions of Section 7 shall survive any termination pursuant to this
Section 16 until the close of business on _________, 2009.

          17.  Governing Law.

          This Agreement and each Warrant Certificate issued hereunder shall be
deemed to be a contract made under the laws of the State of New York and for all
purposes shall be construed in accordance with the laws of said State.

          18.  Benefits of This Agreement.

          Nothing in this Agreement shall be construed to give to any person or
corporation other than the Company and the Underwriter and any other registered
holder or holders of the Warrant Certificates, Warrants or the Shares any legal
or equitable right, remedy or claim under this Agreement; and this Agreement 

                                      -23-





shall be for the sole and exclusive benefit of the Company and the Underwriter
and any other holder or holders of the Warrant Certificates, Warrants or the
Shares.

          19.  Counterparts.

          This Agreement may be executed in any number of counterparts and each
of such counterparts shall for all purposes be deemed to be an original, and
such counterparts shall together constitute but one and the same instrument.


          IN WITNESS WHEREOF, the parties hereto have caused this Agreement to
be duly executed, as of the day and year first above written.



[SEAL]                   NETWORK-1 SECURITY SOLUTIONS, INC.



                         By:__________________________________
                            Name:
                            Title:

Attest:


_______________________




                         WHALE SECURITIES CO., L.P.

                         By:  Whale Securities Corp.,
                              General Partner



                         By:__________________________________
                            Name:
                            Title:      

                                      -24-






                                                       EXHIBIT A

THE WARRANTS REPRESENTED BY THIS CERTIFICATE AND THE OTHER SECURITIES ISSUABLE
UPON EXERCISE THEREOF HAVE NOT BEEN REGISTERED FOR PURPOSES OF PUBLIC
DISTRIBUTION UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE "ACT"), AND MAY
NOT BE OFFERED OR SOLD EXCEPT (i) PURSUANT TO AN EFFECTIVE REGISTRATION
STATEMENT UNDER THE ACT, (ii) TO THE EXTENT APPLICABLE, PURSUANT TO RULE 144
UNDER SUCH ACT (OR ANY SIMILAR RULE UNDER SUCH ACT RELATING TO THE DISPOSITION
OF SECURITIES), OR (iii) UPON THE DELIVERY BY THE HOLDER TO THE COMPANY OF AN
OPINION OF COUNSEL, REASONABLY SATISFACTORY TO COUNSEL FOR THE COMPANY, STATING
THAT AN EXEMPTION FROM REGISTRATION UNDER SUCH ACT IS AVAILABLE.

THE TRANSFER OR EXCHANGE OF THE WARRANTS REPRESENTED BY THIS CERTIFICATE IS
RESTRICTED IN ACCORDANCE WITH THE WARRANT AGREEMENT REFERRED TO HEREIN.

                               EXERCISABLE ON OR BEFORE
                      5:00 P.M., NEW YORK TIME, _________, 2003

No. W-1                                                       187,500 Warrants

                                 WARRANT CERTIFICATE

          This Warrant Certificate certifies that Whale Securities Co., L.P. or
registered assigns, is the registered holder of 187,500 Warrants to purchase, at
any time from _______, 1999 until 5:00 P.M. New York City time on ________, 2003
("Expiration Date"), up to 187,500 fully-paid and non-assessable shares
("Shares") of common stock, par value $.01 per share (the "Common Stock"), of
Network-1 Security Solutions, Inc., a Delaware corporation (the "Company"), at
the initial exercise price, subject to adjustment in certain events (the
"Exercise Price"), of $13.20 per Share upon surrender of this Warrant
Certificate and payment of the Exercise Price at an office or agency of the
Company, but subject to the conditions set forth herein and in the warrant
agreement dated as of ____________, 1998 between the Company and Whale
Securities Co., L.P. (the "Warrant Agreement").  Payment of the Exercise Price
may be made in cash, or by certified or official bank check in New York Clearing
House funds payable to the order of the Company, or any combination thereof.

          No Warrant may be exercised after 5:00 P.M., New York City time, on
the Expiration Date, at which time all Warrants evidenced hereby, unless
exercised prior thereto, shall thereafter be void.

          The Warrants evidenced by this Warrant Certificate are part of a duly
authorized issue of Warrants issued pursuant to the Warrant Agreement, which
Warrant Agreement is hereby incorporated by reference in and made a part of this
instrument and is 







hereby referred to in a description of the rights, limitation of rights,
obligations, duties and immunities thereunder of the Company and the holders
(the words "holders" or "holder" meaning the registered holders or registered
holder) of the Warrants.

          The Warrant Agreement provides that upon the occurrence of certain
events, the Exercise Price and the type and/or number of the Company's
securities issuable thereupon may, subject to certain conditions, be adjusted. 
In such event, the Company will, at the request of the holder, issue a new
Warrant Certificate evidencing the adjustment in the Exercise Price and the
number and/or type of securities issuable upon the exercise of the Warrants;
provided, however, that the failure of the Company to issue such new Warrant
Certificates shall not in any way change, alter, or otherwise impair, the rights
of the holder as set forth in the Warrant Agreement.

          Upon due presentment for registration of transfer of this Warrant
Certificate at an office or agency of the Company, a new Warrant Certificate or
Warrant Certificates of like tenor and evidencing in the aggregate a like number
of Warrants shall be issued to the transferee(s) in exchange for this Warrant
Certificate, subject to the limitations provided herein and in the Warrant
Agreement, without any charge except for any tax, or other governmental charge
imposed in connection therewith.

          Upon the exercise of less than all of the Warrants evidenced by this
Certificate, the Company shall forthwith issue to the holder hereof a new
Warrant Certificate representing such number of unexercised Warrants.

          The Company may deem and treat the registered holder(s) hereof as the
absolute owner(s) of this Warrant Certificate (notwithstanding any notation of
ownership or other writing hereon made by anyone), for the purpose of any
exercise hereof, and of any distribution to the holder(s) hereof, and for all
other purposes, and the Company shall not be affected by any notice to the
contrary.

          All terms used in this Warrant Certificate which are defined in the
Warrant Agreement shall have the meanings assigned to them in the Warrant
Agreement.

          IN WITNESS WHEREOF, the Company has caused this Warrant Certificate to
be duly executed under its corporate seal.

Dated:  ___________, 1998     NETWORK-1 SECURITY SOLUTIONS, INC.

[SEAL]                            By:__________________________
                                     Name:
                                     Title:
Attest:
______________________ 







                            [FORM OF ELECTION TO PURCHASE]

          The undersigned hereby irrevocably elects to exercise the right,
represented by this Warrant Certificate, to purchase _________ shares of Common
Stock and herewith tenders in payment for such securities cash or a certified or
official bank check payable in New York Clearing House Funds to the order of
Network-1 Security Solutions, Inc. in the amount of $           , all in
accordance with the terms hereof.  The undersigned requests that a certificate
for such securities be registered in the name of                      , whose
address is __________________, and that such Certificate be delivered to
__________________, whose address is _____________.


Dated:                        Signature: ______________________________________

                              (Signature must conform in all respects to name of
                              holder as specified on the face of the Warrant
                              Certificate.)

                           ________________________________

                           ________________________________
                           (Insert Social Security or Other
                            Identifying Number of Holder) 









                                 [FORM OF ASSIGNMENT]

               (To be executed by the registered holder if such holder
                    desires to transfer the Warrant Certificate.)


          FOR VALUE RECEIVED _________________________________________

hereby sells, assigns and transfers unto __________________________________

___________________________________________________________________________
(Please print name and address of transferee)

this Warrant Certificate, together with all right, title and interest therein,
and does hereby irrevocably constitute and appoint _______________, Attorney, to
transfer the within Warrant Certificate on the books of the within-named
Company, with full power of substitution.



Dated:                        Signature: ________________________________

                              (Signature must conform in all respects to name of
                              holder as specified on the face of the Warrant
                              Certificate)


_______________________________

_______________________________
(Insert Social Security or Other
Identifying Number of Assignee)