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                                                                   EXHIBIT 10.61

                                INCENTIVE WARRANT

      THE SECURITIES EVIDENCED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED
      UNDER THE U.S. SECURITIES ACT OF 1933, AS AMENDED (THE "SECURITIES ACT"),
      OR ANY OTHER APPLICABLE SECURITIES LAWS AND HAVE BEEN ISSUED IN RELIANCE
      UPON AN EXEMPTION FROM THE REGISTRATION REQUIREMENTS OF THE SECURITIES ACT
      AND SUCH OTHER SECURITIES LAWS. NEITHER THIS SECURITY NOR ANY INTEREST OR
      PARTICIPATION HEREIN MAY BE REOFFERED, SOLD, ASSIGNED, TRANSFERRED,
      PLEDGED, ENCUMBERED, HYPOTHECATED OR OTHERWISE DISPOSED OF, EXCEPT
      PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT UNDER THE SECURITIES ACT
      OR PURSUANT TO A TRANSACTION WHICH IS EXEMPT FROM, OR NOT SUBJECT TO, SUCH
      REGISTRATION. THE HOLDER OF THIS CERTIFICATE IS THE BENEFICIARY OF CERTAIN
      OBLIGATIONS OF THE COMPANY SET FORTH IN A STOCK PURCHASE AGREEMENT, DATED
      AS OF FEBRUARY 22, 2001, BETWEEN APPLIEDTHEORY CORPORATION AND CRESCENT
      INTERNATIONAL LTD. A COPY OF THE PORTION OF THE AFORESAID AGREEMENT
      EVIDENCING SUCH OBLIGATIONS MAY BE OBTAINED FROM APPLIEDTHEORY
      CORPORATION'S EXECUTIVE OFFICES.

                                                                          [DATE]

            Warrant to Purchase up to [$3,000,000 divided by Purchase Price of
First Sale] shares of Common Stock of AppliedTheory Corporation (hereinafter,
the "Incentive Warrant").

            AppliedTheory Corporation, an entity organized and existing under
the laws of the State of Delaware (the "Company"), hereby agrees that Crescent
International Ltd. (the "Investor") or any other Warrant Holder is entitled, on
the terms and conditions set forth below, to purchase from the Company at any
time during the Exercise Period (as defined below) up to [$3,000,000 divided by
Purchase Price of First Sale] fully paid and nonassessable shares of Common
Stock, par value $0.01 per share, of the Company (the "Common Stock"), as the
same may be adjusted from time to time pursuant to Section 6 hereof, at the
Exercise Price (as defined below), as the same may be adjusted pursuant to
Section 6 hereof. The resale of the shares of Common Stock or other securities
issuable upon exercise or exchange of this Incentive Warrant is subject to the
provisions of the Registration Rights Agreement (as defined below).

            Section 1.  Definitions.

                        "Aggregate Exercise Price" shall mean, with respect to
any exercise (in whole or in part) of this Incentive Warrant, the Exercise
Price multiplied by the total number of shares of Common Stock for which this
Incentive Warrant is being exercised.

                        "Agreement" shall mean the Stock Purchase Agreement,
dated as of February 22, 2001, between the Company and the Investor.
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                        "Capital Shares" shall mean the Common Stock and any
shares of any other class of common stock whether now or hereafter authorized,
having the right to participate in the distribution of dividends (as and when
declared) or assets (upon liquidation of the Company).

                        "Exercise Date" shall mean, with respect to any exercise
(in whole or in part) of this Incentive Warrant either (i) the date this
Incentive Warrant, the Exercise Notice and the Aggregate Exercise Price are
received by the Company or (ii) the date a copy of the Exercise Notice is sent
by facsimile to the Company, provided that this Incentive Warrant, the original
Exercise Notice, and the Aggregate Exercise Price are received by the Company
within five Trading Days thereafter and provided further that if this Incentive
Warrant, the original Exercise Notice and the Aggregate Exercise Price are not
received within five Trading Days in accordance with clause (ii) above, the
Exercise Date for this clause (ii) shall be the date that the Company receives
this Incentive Warrant, the original Exercise Notice and the Aggregate Exercise
Price.

                        "Exercise Notice" shall mean, with respect to any
exercise (in whole or in part) of this Incentive Warrant the exercise form
attached hereto as Exhibit A, duly executed by the Warrant Holder.

                        "Exercise Period" shall mean the period beginning on the
date hereof and continuing until the expiration of the five-year period
thereafter; provided that such period shall be extended one day for each day
after the date hereof, that the Registration Statement covering (i) Commitment
Shares purchased by the Investor, (ii) the Protective Warrant Shares, if any,
related to any Sales and (iii) the Incentive Warrant Shares purchasable through
exercise of this Incentive Warrant, is not effective during the period such
Registration Statement is required to be effective pursuant to the Registration
Rights Agreement.

                        "Exercise Price" as of the date hereof shall mean [150%
of Purchase Price of First Sale] per share of Common Stock, subject to the
adjustments provided for in Section 6 of this Incentive Warrant.

                        "Per Share Warrant Value" shall mean, with respect to
any exercise (in whole or in part) of this Incentive Warrant, the difference
resulting from subtracting the Exercise Price from the Closing Price of one
share of Common Stock on the Trading Day immediately preceding the Exercise
Date.

                        "Registration Rights Agreement" shall mean the
registration rights agreement, dated February 22, 2001 between the Company and
the Investor.

                        "Warrant Holder" shall mean the Investor or any assignee
or transferee of all or any portion of this Incentive Warrant.

                        Other capitalized terms used but not defined herein
shall have their respective meanings set forth in the Agreement.

            Section 2.  Exercise; Cashless Exercise.

                        (a) Method of Exercise. This Incentive Warrant may be
exercised in whole or in part (but not as to a fractional share of Common
Stock), at any time and from time to time during the Exercise Period, by the
Warrant Holder by (i) the surrender of this Incentive Warrant, the Exercise
Notice and the Aggregate Exercise Price to the Company at the address set forth
in


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Section 11 hereof or (ii) the delivery by facsimile of an executed and completed
Exercise Notice to the Company and delivery to the Company within five Trading
Days thereafter of this Incentive Warrant, the original Exercise Notice and the
Aggregate Exercise Price.

                        (b) Payment of Aggregate Exercise Price. Subject to
paragraph (c) below, payment of the Aggregate Exercise Price shall be made by
check or bank draft payable to the order of the Company or by wire transfer to
an account designated by the Company. If the amount of the payment received by
the Company is less than the Aggregate Exercise Price, the Warrant Holder will
be notified of the deficiency and shall make payment in that amount within five
Trading Days of such notice. In the event the payment exceeds the Aggregate
Exercise Price, the Company will refund the excess to the Warrant Holder within
three Trading Days of both the receipt of such payment and the knowledge of such
excess.

                        (c) Cashless Exercise. As an alternative to payment of
the Aggregate Exercise Price in accordance with Section 2(b) above, the Warrant
Holder may elect to effect a cashless exercise by so indicating on the Exercise
Notice and including a calculation of the number of shares of Common Stock to be
issued upon such exercise in accordance with the terms hereof (a "Cashless
Exercise"). In the event of a Cashless Exercise, the Warrant Holder shall
surrender this Incentive Warrant for that number of shares of Common Stock
determined by (i) multiplying the number of Incentive Warrant Shares for which
this Incentive Warrant is being exercised by the Per Share Warrant Value and
(ii) dividing the product by the Closing Price of one share of the Common Stock
on the Trading Day immediately preceding the Exercise Date.

                        (d) Replacement Warrant. In the event that the Incentive
Warrant is not exercised in full, the number of Incentive Warrant Shares shall
be reduced by the number of such Incentive Warrant Shares for which this
Incentive Warrant is exercised, and the Company, at its expense, shall forthwith
issue and deliver to the Warrant Holder a new Incentive Warrant of like tenor in
the name of the Warrant Holder or as the Warrant Holder may request, reflecting
such adjusted number of Incentive Warrant Shares.

            Section 3. Ten Percent Limitation. At no time may the Warrant Holder
exercise this Incentive Warrant such that the number of Incentive Warrant Shares
to be received pursuant to such exercise aggregated with all other shares of
Common Stock then owned by the Warrant Holder beneficially or deemed
beneficially owned (as such term is defined in Rule 13(d) under the Exchange
Act) by the Warrant Holder and its affiliates would result in the Warrant Holder
and its affiliates owning more than 9.9% of all of such Common Stock as would be
outstanding on such Exercise Date, as determined in accordance with Section
13(d) of the Exchange Act and the rules and regulations promulgated thereunder.

            Section 4.  Delivery of Stock Certificates.

                        (a) Subject to the terms and conditions of this
Incentive Warrant, as soon as practicable after the exercise of this Incentive
Warrant in full or in part, and in any event within five (5) Trading Days
thereafter, the Company at its expense (including, without limitation, the
payment by it of any applicable issue taxes) will cause to be issued in the name
of and delivered to the Warrant Holder, or as the Warrant Holder lawfully may
direct, a certificate or certificates for the number of validly issued, fully
paid and non-assessable Incentive Warrant Shares to


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which the Warrant Holder shall be entitled on such exercise, together with any
other stock or other securities or property (including cash, where applicable)
to which the Warrant Holder is entitled upon such exercise in accordance with
the provisions hereof; provided, however, that any such delivery to a location
outside of the United States also shall be made within five Trading Days after
the exercise of this Incentive Warrant in full or in part.

                        (b) This Incentive Warrant may not be exercised as to
fractional shares of Common Stock. In the event that the exercise of this
Incentive Warrant, in full or in part, would result in the right to acquire any
fractional share of Common Stock, then in such event such fractional share shall
be considered a whole share of Common Stock and shall be added to the number of
Incentive Warrant Shares issuable to the Investor upon exercise of this
Incentive Warrant.

            Section 5.  Representations, Warranties and Covenants of the
Company.

                        (a) The Company shall take all necessary action and
proceedings as may be required and permitted by applicable law, rule and
regulation for the legal and valid issuance of this Incentive Warrant and the
Incentive Warrant Shares to the Warrant Holder.

                        (b) At all times during the Exercise Period, the Company
shall take all steps reasonably necessary and within its control to insure that
the Common Stock remains listed or quoted on the Principal Market.

                        (c) The Incentive Warrant Shares, when issued in
accordance with the terms hereof, will be duly authorized and, when paid for or
issued in accordance with the terms hereof, shall be validly issued, fully paid
and non-assessable.

                        (d) The Company has authorized and reserved for issuance
to the Warrant Holder the requisite number of shares of Common Stock to be
issued pursuant to this Incentive Warrant. The Company at all times shall
reserve and keep available, solely for issuance and delivery as Incentive
Warrant Shares hereunder, such shares of Common Stock as from time to time shall
be issuable as Incentive Warrant Shares, and accordingly shall adjust the number
of such shares of Common Stock promptly upon the occurrence of any of the events
specified in Section 6 hereof.

            Section 6. Adjustment of the Exercise Price. The Exercise Price and,
accordingly, the number of Incentive Warrant Shares issuable upon exercise of
the Incentive Warrant, shall be subject to adjustment from time to time upon the
happening of certain events as follows:

                        (a) Reclassification, Consolidation, Merger; Mandatory
Share Exchange; Sale Transfer or Lease of Assets. If the Company, at any time
while this Incentive Warrant is unexpired and not exercised in full, (i)
reclassifies or changes its Outstanding Capital Shares (other than a change in
par value, or from par value to no par value per share, or from no par value per
share to par value or as a result of a subdivision or combination of outstanding
securities issuable upon exercise of this Incentive Warrant) or (ii)
consolidates, merges or effects a mandatory share exchange (x) with or into
another corporation (other than a merger or mandatory share exchange with
another corporation in which the Company is a continuing corporation and that
does not result in any reclassification or change, other than a change in par


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value, or from par value to no par value per share, or from no par value per
share to par value, or (y) as a result of a subdivision or combination of
Outstanding Capital Shares issuable upon exercise of the Incentive Warrant) or
(iii) sells, transfers or leases all or substantially all of its assets, then in
any such event the Company, or such successor or purchasing corporation, as the
case may be, shall, without payment by the Warrant Holder of any additional
consideration therefor, amend this Incentive Warrant or issue a new warrant
providing that the Warrant Holder shall have rights not less favorable to the
Warrant Holder than those then applicable to this Incentive Warrant and to
receive upon exercise under such amendment of this Incentive Warrant or new
warrant, in lieu of each share of Common Stock theretofore issuable upon
exercise of this Incentive Warrant hereunder, the kind and amount of shares of
stock, other securities, money or property receivable upon such
reclassification, change, consolidation, merger, mandatory share exchange,
lease, sale or transfer by the holder of one share of Common Stock issuable upon
exercise of this Incentive Warrant had this Incentive Warrant been exercised
immediately prior to such reclassification, change, consolidation, merger,
mandatory share exchange or sale or transfer (without giving effect to the
limitation on ownership set forth in Section 3 hereof), and an appropriate
provision for the foregoing shall be made by the Company as part of any such
event. Such amended Incentive Warrant or new warrant shall provide for
adjustments that shall be as nearly equivalent as may be practicable to the
adjustments provided for in this Section 6. The provisions of this Section 6(a)
shall similarly apply to successive reclassifications, changes, consolidations,
mergers, mandatory share exchanges, sales, transfers and leases.

                        (b) Subdivision or Combination of Shares; Stock
Dividends. If the Company, at any time while this Incentive Warrant is unexpired
and not exercised in full, shall subdivide its Common Stock, combine its Common
Stock, pay a dividend in its Capital Shares, or make any other distribution of
its Capital Shares, then the Exercise Price shall be adjusted, as of the date
the Company shall take a record of the holders of its Capital Shares for the
purpose of effecting such subdivision, combination or dividend or other
distribution (or if no such record is taken, as of the effective date of such
subdivision, combination, dividend or other distribution), to that price
determined by multiplying the Exercise Price in effect immediately prior to such
subdivision, combination, dividend or other distribution by a fraction:

                                    (i) the numerator of which shall be the
total number of Outstanding Capital Shares immediately prior to such
subdivision, combination, dividend or other distribution, and

                                    (ii) the denominator of which shall be the
total number of Outstanding Capital Shares immediately after such subdivision,
combination, dividend or other distribution. The provisions of this Section 6(b)
shall not apply under any of the circumstances for which an adjustment is made
pursuant to Section 6(a).

                        (c) Liquidating Dividends, Etc. If the Company, at any
time while this Incentive Warrant is unexpired and not exercised in full, makes
a distribution of its assets or evidences of indebtedness to the holders of its
Capital Shares as a dividend in liquidation or by way of return of capital or
other than as a dividend payable out of earnings or surplus legally available
for dividends under applicable law or any distribution to such holders made in
respect of the sale of all or substantially all of the Company's assets, or any
spin-off of any of the Company's lines of business, divisions or subsidiaries
(other than under the circumstances


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provided for in the foregoing subsections (a) and (b)), then the Warrant Holder
shall be entitled to receive upon such exercise of the Incentive Warrant in
addition to the Incentive Warrant Shares receivable in connection therewith, and
without payment of any consideration other than the Exercise Price, an amount in
cash equal to the value of such distribution per Capital Share multiplied by the
number of Incentive Warrant Shares that, on the record date for such
distribution, are issuable upon such exercise of the Incentive Warrant (without
giving effect to the limitation on ownership set forth in Section 3 hereof), and
an appropriate provision therefor shall be made by the Company as part of any
such distribution. No further adjustment shall be made following any event that
causes a subsequent adjustment in the number of Incentive Warrant Shares
issuable. The value of a distribution that is paid in other than cash shall be
determined in good faith by the Board of Directors of the Company.

                        (d) Adjustment of Number of Shares. Upon each adjustment
of the Exercise Price pursuant to any provisions of this Section 6, the number
of Incentive Warrant Shares issuable hereunder at the option of the Warrant
Holder shall be calculated, to the nearest one hundredth of a whole share,
multiplying the number of Incentive Warrant Shares issuable prior to an
adjustment by a fraction:

                                    (i) the numerator of which shall be the
Exercise Price before any adjustment pursuant to this Section 6; and

                                    (ii) the denominator of which shall be the
Exercise Price after such adjustment.

                        (e) Other Action Affecting Capital Shares. In the event
after the date hereof the Company shall take any action affecting the number of
Outstanding Capital Shares, other than an action specifically described in any
of the foregoing subsections (a) through (c) hereof, inclusive (including,
without limitation, a subdivision or combination of Common Stock, or the payment
of a dividend in its Capital Shares or any other distribution), that in the
reasonable opinion of the Warrant Holder would have a materially adverse effect
upon the rights of the Warrant Holder at the time of exercise of the Incentive
Warrant, the Exercise Price shall be adjusted in such manner and at such time as
the Board of Directors on the advice of the Company's independent public
accountants shall in good faith determine to be equitable in the circumstances.

                        (f) Notice of Certain Actions. In the event the Company
shall, at a time while the Incentive Warrant is unexpired and outstanding, take
any action pursuant to subsections (a) through (e) of this Section 6 that may
result in an adjustment of the Exercise Price, the Company shall notify the
Warrant Holder of such action 10 days in advance of its effective date in order
to afford to the Warrant Holder an opportunity to exercise the Incentive Warrant
prior to such action becoming effective.

                        (g) Notice of Adjustments. Whenever the Exercise Price
or number of Incentive Warrant Shares shall be adjusted pursuant to Section 6
hereof, the Company shall promptly deliver by facsimile, with the original
delivered by express courier service in accordance with Section 11 hereof, a
certificate, which shall be signed by the Company's President or a Vice
President and by its Treasurer or Assistant Treasurer or its Secretary or


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Assistant Secretary, setting forth in reasonable detail the event requiring the
adjustment, the amount of the adjustment, the method by which such adjustment
was calculated (including a description of the basis on which the Company's
Board of Directors made any determination hereunder), and the Exercise Price and
number of Incentive Warrant Shares purchasable at that Exercise Price after
giving effect to such adjustment.

            Section 7. No Impairment. The Company will not, by amendment of its
Certificate or By-Laws or through any reorganization, transfer of assets,
consolidation, merger, dissolution, issue or sale of securities or any other
voluntary action, avoid or seek to avoid the observance or performance of any of
the terms of this Incentive Warrant, but will at all times in good faith assist
in the carrying out of all such terms and in the taking of all such action as
may be necessary or appropriate in order to protect the rights of the Warrant
Holder against impairment. Without limiting the generality of the foregoing, the
Company (a) will not increase the par value of any Incentive Warrant Shares
above the amount payable therefor on such exercise, and (b) will take all such
action as may be reasonably necessary or appropriate in order that the Company
may validly and legally issue fully paid and nonassessable Incentive Warrant
Shares on the exercise of this Incentive Warrant.

            Section 8. Rights As Stockholder. Prior to exercise of this
Incentive Warrant and except as provided in Section 6 hereof, the Warrant Holder
shall not be entitled to any rights as a stockholder of the Company with respect
to the Incentive Warrant Shares, including (without limitation) the right to
vote such shares, receive dividends or other distributions thereon or be
notified of stockholder meetings. However, in the event of any taking by the
Company of a record of the holders of any class of securities for the purpose of
determining the holders thereof who are entitled to receive any dividend (other
than a cash dividend) or other distribution, any right to subscribe for,
purchase or otherwise acquire any shares of stock of any class or any other
securities or property, or to receive any other right, the Company shall mail to
each Warrant Holder, at least ten days prior to the date specified therein, a
notice specifying the date on which any such record is to be taken for the
purpose of such dividend, distribution or right, and the amount and character of
such dividend, distribution or right.

            Section 9. Replacement of Incentive Warrant. Upon receipt of
evidence reasonably satisfactory to the Company of the loss, theft, destruction
or mutilation of the Incentive Warrant and, in the case of any such loss, theft
or destruction of the Incentive Warrant, upon delivery of an indemnity agreement
or security reasonably satisfactory in form and amount to the Company or, in the
case of any such mutilation, on surrender and cancellation of such Incentive
Warrant, the Company at its expense will execute and deliver, in lieu thereof, a
new Incentive Warrant of like tenor.

            Section 10. Restricted Securities.

                        (a) Registration or Exemption Required. This Incentive
Warrant has been issued in a transaction exempt from the registration
requirements of the Securities Act in reliance upon Section 4(2) of the
Securities Act. This Incentive Warrant and the Incentive Warrant Shares issuable
upon exercise of this Incentive Warrant may not be resold except pursuant to an
effective registration statement or an exemption to the registration
requirements of the Securities Act and applicable state laws.


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                        (b) Legend. Any replacement Incentive Warrants issued
pursuant to Section 2 hereof and any Incentive Warrant Shares issued upon
exercise hereof, shall bear the following legend:

                        "THE SECURITIES EVIDENCED BY THIS CERTIFICATE HAVE NOT
                        BEEN REGISTERED UNDER THE U.S. SECURITIES ACT OF 1933,
                        AS AMENDED (THE "SECURITIES ACT"), OR ANY OTHER
                        APPLICABLE SECURITIES LAWS AND HAVE BEEN ISSUED IN
                        RELIANCE UPON AN EXEMPTION FROM THE REGISTRATION
                        REQUIREMENTS OF THE SECURITIES ACT AND SUCH OTHER
                        SECURITIES LAWS. NEITHER THIS SECURITY NOR ANY INTEREST
                        OR PARTICIPATION HEREIN MAY BE REOFFERED, SOLD,
                        ASSIGNED, TRANSFERRED, PLEDGED, ENCUMBERED, HYPOTHECATED
                        OR OTHERWISE DISPOSED OF, EXCEPT PURSUANT TO AN
                        EFFECTIVE REGISTRATION STATEMENT UNDER THE SECURITIES
                        ACT OR PURSUANT TO A TRANSACTION WHICH IS EXEMPT FROM,
                        OR NOT SUBJECT TO, SUCH REGISTRATION. THE HOLDER OF THIS
                        CERTIFICATE IS THE BENEFICIARY OF CERTAIN OBLIGATIONS OF
                        THE COMPANY SET FORTH IN A STOCK PURCHASE AGREEMENT,
                        DATED AS OF FEBRUARY 22, 2001, BETWEEN APPLIEDTHEORY
                        CORPORATION AND CRESCENT INTERNATIONAL LTD. A COPY OF
                        THE PORTION OF THE AFORESAID AGREEMENT EVIDENCING SUCH
                        OBLIGATIONS MAY BE OBTAINED FROM APPLIEDTHEORY
                        CORPORATION'S EXECUTIVE OFFICES."

      Removal of such legend shall be in accordance with the legend removal
provisions in the Agreement.

                        (c) No Other Legend or Stock Transfer Restrictions. No
legend other than the one specified in paragraph (b) of this Section 10 has been
or shall be placed on the share certificates representing the Incentive Warrant
Shares and no instructions or "stop transfer orders," so called, "stock transfer
restrictions" or other restrictions have been or shall be given to the Company's
transfer agent with respect thereto other than as expressly set forth in this
Section 10.

                        (d) Assignment. Assuming the conditions of Section 10(a)
above regarding registration or exemption have been satisfied, the Warrant
Holder may, upon the prior written consent of the Company, which consent shall
not be unreasonably withheld, sell, transfer, assign, pledge or otherwise
dispose of this Incentive Warrant, in whole or in part. The Warrant Holder shall
deliver a written notice to the Company substantially in the form of the
assignment form attached hereto as Exhibit B (the "Assignment Notice")
indicating the person or persons to whom this Incentive Warrant shall be
assigned and the respective number of warrants to be assigned to each assignee.
The Company shall effect the assignment within ten days of receipt of such
Assignment Notice, and shall deliver to the assignee(s) designated by the
Warrant Holder a Incentive Warrant or Incentive Warrants of like tenor and terms
for the specified number of shares.


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                        (e) Investor's Compliance. Nothing in this Section 10
shall affect in any way the Investor's obligations under any agreement to comply
with all applicable securities laws upon resale of the Common Stock.

            Section 11. Notices. All notices, demands, requests, consents,
approvals, and other communications required or permitted hereunder shall be in
writing and shall be deemed duly given (i) upon delivery if hand delivered at
the address designated below (if delivered on a business day during normal
business hours where such notice is to be received), or the first business day
following such delivery (if delivered other than on a business day during normal
business hours where such notice is to be received), (ii) on the fifth business
day after deposit into the mail, if deposited in the mail, registered or
certified, return receipt requested, postage prepaid, addressed to the address
designated below, (iii) upon delivery if delivered by reputable express courier
service to the address designated below, or (iv) upon confirmation of
transmission if transmitted by facsimile to the facsimile number designated
below (if delivered on a business day during normal business hours where such
notice is to be received), or the first business day following such delivery (if
delivered other than on a business day during normal business hours where such
notice is to be received). The addresses and facsimile numbers for such
communications shall be:

            if to the Company:

                        AppliedTheory Corporation
                        1500 Broadway
                        New York, NY 10036
                        Attention:     Robert F. Mechur, Esq., General Counsel
                        Telephone:     (315) 453-2912, ext. 5229
                        Facsimile:     (315) 479-0824

            with a copy (which shall not constitute notice) to:

                        Dewey Ballantine LLP
                        1301 Avenue of the Americas
                        Attention:      Frank E. Morgan II, Esq.
                        Telephone:      (212) 259-8320
                        Facsimile:      (212) 259-6333


            if to the Investor:

                         Crescent International Ltd.
                         c/o GreenLight (Switzerland) SA
                         84, av Louis-Casai
                         P.O. Box 42
                         1216 Geneva, Cointrin
                         Switzerland
                         Attention:     Mel Craw/Maxi Brezzi
                         Telephone:     +41 22 791 71 69
                         Facsimile:     +41 22 929 53 94


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<PAGE>   10
            with a copy (which shall not constitute notice) to:

                    Clifford Chance Rogers & Wells LLP
                    200 Park Avenue
                    New York, NY  10166
                    Attention:     Sara P. Hanks, Esq./Earl S. Zimmerman, Esq.
                    Telephone:     (212) 878-8000
                    Facsimile:     (212) 878-8375

      Either party hereto may from time to time change its address or facsimile
      number for notices under this Section 11 by giving at least ten (10) days'
      prior written notice of such changed address or facsimile number to the
      other party hereto.

            Section 12. Miscellaneous. This Incentive Warrant and any term
hereof may be changed, waived, discharged or terminated only by an instrument in
writing signed by the party against which enforcement of such change, waiver,
discharge or termination is sought. The headings in this Incentive Warrant are
for purposes of reference only, and shall not limit or otherwise affect any of
the terms hereof. The invalidity or unenforceability of any provision hereof
shall in no way affect the validity or enforceability of any other provision.


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                        IN WITNESS WHEREOF, this Incentive Warrant was duly
executed by the undersigned, thereunto duly authorized, as of the date first
set forth above.

APPLIEDTHEORY CORPORATION


By:
        Name:
        Title:



Attested:


By:
        Name:
        Title:          Secretary


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