Document:

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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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            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

                                       11<PAGE>   1
                                                                   EXHIBIT 10.62

                          REGISTRATION RIGHTS AGREEMENT

            This REGISTRATION RIGHTS AGREEMENT (this "Agreement"), dated as of
February 22, 2001, is made and entered into by and between AppliedTheory
Corporation, a Delaware corporation (the "Company"), and Crescent International
Ltd., an entity organized and existing under the laws of Bermuda (the
"Investor").

            WHEREAS, the Company and the Investor have entered into that certain
Stock Purchase Agreement, dated as of February 22, 2001 (the "Stock Purchase
Agreement"), pursuant to which the Company will issue, from time to time, to the
Investor and the Investor shall purchase up to $30,000,000 worth of shares of
common stock, par value $0.01 per share, of the Company (the "Common Stock");

            WHEREAS, pursuant to the terms of and in partial consideration for
the Investor entering into the Stock Purchase Agreement, the Company may be
required to issue to the Investor an incentive warrant exercisable from time to
time within five years following the date of issuance (the "Incentive Warrant")
for the purchase of a number of shares of Common Stock at a price to be
determined as described in such Incentive Warrant;

            WHEREAS, pursuant to the terms of and in partial consideration for
the Investor entering into the Stock Purchase Agreement, the Company may be
required to issue protective warrants to the Investor, each of which may become
exercisable from time to time as described in such warrants and in the Stock
Purchase Agreement (collectively, the "Protective Warrants" and together with
the Incentive Warrant, the "Warrants") for the purchase of a number of shares of
Common Stock at a price to be determined as described in each such Protective
Warrant;

            WHEREAS, pursuant to the terms of, and in partial consideration for,
the Investor's agreement to enter into the Stock Purchase Agreement, the Company
has agreed to provide the Investor with certain registration rights as described
herein;

            NOW, THEREFORE, in consideration of the premises, the
representations, warranties, covenants and agreements contained herein, in the
Warrants, and in the Stock Purchase Agreement, and for other good and valuable
consideration, the receipt and sufficiency of which is hereby acknowledged,
intending to be legally bound hereby, the parties hereto agree as follows
(capitalized terms used herein and not defined herein shall have the respective
meanings ascribed to them in the Stock Purchase Agreement):

                                    ARTICLE I
                               REGISTRATION RIGHTS

            Section 1.1.            REGISTRATION STATEMENTS.

                        a. Filing of Registration Statements. The Company shall
register for resale all Commitment Shares issued or issuable to the Investor
pursuant to the Stock Purchase Agreement and all Warrant Shares issued or
issuable upon full exercise of the Warrants. Subject to the
<PAGE>   2
terms and conditions of this Agreement, the Company shall effect such
registration in the manner provided below:

                                    (i) First Registration Statement. On or
                                    before the end of the 20 calendar day period
                                    immediately following the First Sale, the
                                    Company shall file with the SEC a
                                    registration statement (the "First
                                    Registration Statement") on Form S-3 if such
                                    form is then available to the Company and,
                                    if not, on such form promulgated by the SEC
                                    for which the Company qualifies, that
                                    counsel for the Company shall deem
                                    appropriate and which form shall be
                                    available for the sale of all First Sale
                                    Shares, the Incentive Warrant Shares and any
                                    Protective Warrant Shares, in accordance
                                    with the intended method of distribution of
                                    such securities. The aggregate number of
                                    shares to be registered under the First
                                    Registration Statement shall be equal to two
                                    hundred percent (200%) of the First Sale
                                    Shares plus the number of Incentive Warrant
                                    Shares;

                                    (ii) Subsequent Registration Statements.

                                         (1)  If the Company shall, pursuant to
                                              any Subsequent Sale, require the
                                              Investor to purchase shares of
                                              Common Stock not previously
                                              registered and not covered by an
                                              effective Registration Statement
                                              filed with the SEC and which is
                                              not a Failed Registration
                                              Statement (as hereinafter defined)
                                              (an "Unregistered Sale"), then on
                                              or before the end of a 10 calendar
                                              day period immediately following
                                              each Closing Date relating to each
                                              such Subsequent Sale, the Company
                                              shall file with the SEC a
                                              registration statement (each a
                                              "Subsequent Registration
                                              Statement," and together with the
                                              First Registration Statement and
                                              any other registration statement
                                              covering Registrable Securities or
                                              otherwise required to be filed by
                                              the Company with the SEC as
                                              provided in this Agreement, the
                                              "Registration Statements" or each,
                                              a "Registration Statement") on
                                              Form S-3 if such form is then
                                              available to the Company and, if
                                              not, on such form promulgated by
                                              the SEC for which the Company
                                              qualifies, that counsel for the
                                              Company shall deem appropriate and
                                              which form shall be available for
                                              the sale of the Subsequent Sale
                                              Shares purchased by the Investor
                                              and any Warrant Shares that have
                                              not been previously registered, in
                                              accordance with the intended
                                              method of distribution of such
                                              securities. The aggregate number
                                              of shares to be registered under
                                              each Subsequent Registration
                                              Statement shall be equal to two
                                              hundred percent (200%) of the
                                              number of Subsequent Sale Shares
                                              purchased by the Investor on the
                                              applicable Closing Date plus any
                                              Warrant Shares not previously
                                              registered;

                                       2
<PAGE>   3
                                         (2)  Prior to any Subsequent Sale which
                                              is not an Unregistered Sale, the
                                              Company shall file with the SEC a
                                              Subsequent Registration Statement
                                              on Form S-3 if such form is then
                                              available to the Company and, if
                                              not, on such form promulgated by
                                              the SEC for which the Company
                                              qualifies, that counsel for the
                                              Company shall deem appropriate and
                                              which form shall be available for
                                              the sale of the shares of Common
                                              Stock to be purchased by the
                                              Investor and any Warrant Shares
                                              which have not previously been
                                              registered, in accordance with the
                                              intended method of distribution of
                                              such securities. The aggregate
                                              number of shares to be registered
                                              under such Subsequent Registration
                                              Statement shall be determined by
                                              the Company.

                        b. Effectiveness of the Registration Statements. The
following conditions for effectiveness shall apply to the Registration
Statements required to be filed by the Company with the SEC pursuant to
paragraph (a) above, without limiting the Company's obligation to file such
Registration Statements. The Company shall use its best efforts: (i) to have the
First Registration Statement declared effective by the SEC in no event later
than 120 calendar days after the Closing Date relating to the First Sale, and
(ii) to have each Subsequent Registration Statement declared effective by the
SEC in no event later than 60 calendar days after the Closing Date relating to
each Unregistered Sale, and in any event prior to any further Subsequent Sales.
The Company shall ensure that all Registration Statements and any amendments
thereto remain in effect for a period ending 180 days following the later of (1)
the date of expiration of the Incentive Warrant Exercise Period (as such term is
defined in the Incentive Warrant) if the Incentive Warrant has not been
exercised in full and (2) the date all Registrable Securities issued or issuable
to the Investor pursuant to the Stock Purchase Agreement may be sold by the
Investor without registration and without any time, volume or manner limitations
pursuant to Rule 144(k) (or any similar provision then in effect) under the
Securities Act; provided that such period shall be extended one day for each day
after the applicable Effective Date that any Registration Statement covering
Registrable Securities is not effective during the period such Registration
Statement is required to be effective pursuant to this Agreement; and provided
further that the Company shall not be required to ensure that any Registration
Statement covering Registrable Securities remain in effect for such period if
the shares registered thereunder shall have become freely tradable pursuant to
Rule 144(k) of the Securities Act as such Rule may be amended from time to time,
or have otherwise been sold.

                        c. Failure to Obtain or Maintain Effectiveness of
Registration Statements.

                                    (i) In the event the Company fails for any
reason to obtain the effectiveness of any Registration Statement within the time
periods set forth in Section 1.1(b) (a "Tardy Registration Statement") or in the
event that the Company fails for any reason to maintain the effectiveness of any
Registration Statement (or the underlying prospectus) covering Registrable
Securities for the time period set forth in Section 1.1(b) (an "Ineffective
Registration Statement" together with a Tardy Registration Statement, a "Failed
Registration Statement") or upon the occurrence of any event of the kind
described in Section 2.1(g)(iv) hereof (unless the Registrable Securities
covered by such Registration Statement shall have become freely tradable
pursuant to Rule 144(k) of the Securities Act or have been otherwise sold),
then, in either event

                                       3
<PAGE>   4
an amount equal to two percent (2.0%) of the aggregate Purchase Price of all of
the Registrable Securities covered by any such Failed Registration Statement
then held by the Investor for each calendar month and for each portion of a
calendar month, pro rata, (the "Failed Registration Statement Fee") during any
period of such ineffectiveness or, in the case of the occurrence of an event of
the kind described in Section 2.1(g)(iv) hereof, until the Investor shall have
received copies of the supplemental or amended prospectus contemplated by
Section 2.1(g)(iv) hereof (an "Ineffective Period"), shall become due and
payable to Investor.

                                    (ii) If Failed Registration Statement Fees
accrue with respect to any Ineffective Registration Statement, payment of such
Failed Registration Statement Fees shall be made on the third Trading Day after
the earlier to occur of (1) the expiration of the applicable Ineffective Period
and (2) the last day of each calendar month during an Ineffective Period.

                        d. Restricted Period. While in possession of material
non-public information received from the Company, the Investor shall not dispose
of any Registrable Securities until such information is disclosed to the public
(a "Restricted Period"); provided that, if such Restricted Period exceeds 120
days, the liquidated damages described in Section 1.1(c) hereof shall be
increased to three percent (3.0%) until such restricted Period shall have
elapsed.

                        e. Failure to Register Sufficient Number of Shares. If
the number of Protective Warrant Shares included in the First Registration
Statement or each Subsequent Registration Statement is less than the total
number of Protective Warrant Shares issuable upon exercise at the Exercise Price
(as such term is defined in each Protective Warrant) (such deficit in the number
of shares is referred to herein as the "Deficit Shares"), then (i) the Company
shall immediately amend such Registration Statement (or file a new Registration
Statement) to cover the Deficit Shares (such amended or new Registration
Statement is referred to herein as a "Deficit Shares Registration Statement")
and (ii) the Company shall pay to the Investor in immediately available funds
into an account designated by the Investor an amount equal to 2.0% of the
product of (x) the number of Deficit Shares multiplied by (y) the Closing Price
of the Common Stock on the applicable Effective Date, for each calendar month
and for each portion of a calendar month, pro rata, during the period from the
Effective Date of the applicable Registration Statement to the Effective Date of
the applicable Deficit Shares Registration Statement.

                        f. Liquidated Damages. The Company and the Investor
hereby acknowledge and agree that the sums payable under subsections 1.1(c),
1.1(d) and 1.1(e) hereof shall constitute liquidated damages and not penalties.
The parties further acknowledge that (i) the amount of loss or damages likely to
be incurred is incapable or is difficult to estimate precisely, (ii) the amounts
specified in such subsections bear a reasonable proportion and are not plainly
or grossly disproportionate to the probable loss likely to be incurred in
connection with any failure by the Company to obtain or maintain the
effectiveness of a Registration Statement, (iii) one of the reasons for the
Company and the Investor reaching an agreement as to such amounts was the
uncertainty and cost of litigation regarding the question of actual damages, and
(iv) the Company and the Investor are sophisticated business parties and have
been represented by sophisticated and able legal and financial counsel and
negotiated this Agreement at arm's length.

                                       4
<PAGE>   5
                                   ARTICLE II
                             REGISTRATION PROCEDURES

            Section 2.1. FILINGS; INFORMATION. The Company will effect the
registration of the Registrable Securities in accordance with the intended
methods of disposition thereof as furnished to the Company by any proposed
seller of such Registrable Securities prior to the filing of a Registration
Statement therefor. Without limiting the foregoing, the Company in each such
case will do the following as expeditiously as possible, but in no event later
than the deadline, if any, prescribed therefor in this Agreement:

                        a. The Company shall (i) prepare and file with the SEC
the Registration Statement(s) covering the shares as described in subsection
1.1(a) above; (ii) use its best efforts to cause such filed Registration
Statement(s) to become and remain effective (pursuant to Rule 415 under the
Securities Act or otherwise) for the period prescribed by Section 1.1(b); (iii)
prepare and file with the SEC such amendments and supplements to each
Registration Statement and the prospectus used in connection therewith as may be
necessary to keep each Registration Statement effective for the time period
prescribed by Section 1.1(b); and (iv) comply with the provisions of the
Securities Act with respect to the disposition of all securities covered by each
Registration Statement during such period in accordance with the intended
methods of disposition by the Investor set forth in each Registration Statement.

                        b. The Company shall file all necessary amendments to
each Registration Statement in order to effectuate the purpose of this
Agreement, the Stock Purchase Agreement, and the Warrants.

                        c. Five Trading Days prior to filing each Registration
Statement or prospectus, or any amendment or supplement thereto (excluding
amendments deemed to result from the filing of documents incorporated by
reference therein), the Company shall deliver to the Investor and one firm of
counsel representing the Investor, in accordance with the notice provisions of
Section 4.8, copies of such Registration Statement as proposed to be filed,
together with exhibits thereto, which documents will be subject to review and
comment by the Investor and such counsel, and thereafter deliver to the Investor
and such counsel, in accordance with the notice provisions of Section 4.8, such
number of copies of such Registration Statement, each amendment and supplement
thereto (in each case including all exhibits thereto), the prospectus included
in such Registration Statement (including each preliminary prospectus) and such
other documents or information as the Investor or counsel may reasonably request
in order to facilitate the disposition of the Registrable Securities.

                        d. The Company shall deliver, in accordance with the
notice provisions of Section 4.8, to each broker as directed by the Investor
such number of conformed copies of such Registration Statement and of each
amendment and supplement thereto (in each case including all exhibits and
documents incorporated by reference), such number of copies of the prospectus
contained in such Registration Statement (including each preliminary prospectus
and any summary prospectus) and any other prospectus filed under Rule 424
promulgated under the Securities Act relating to the Registrable Securities, and
such other documents, as may be reasonably requested to facilitate the
disposition of the Registrable Securities.

                        e. After the filing of each Registration Statement, the
Company shall promptly notify the Investor of any stop order issued or
threatened by the SEC in connection therewith and

                                       5
<PAGE>   6
take all commercially reasonable actions required to prevent the entry of such
stop order or to remove it if entered.

                        f. The Company shall use its best efforts to (i)
register or qualify the Registrable Securities under such other securities or
blue sky laws of such jurisdictions in the United States as the Investor may
reasonably (in light of its intended plan of distribution) request, and (ii)
cause the Registrable Securities to be registered with or approved by such other
governmental agencies or authorities in the United States as may be necessary by
virtue of the business and operations of the Company and do any and all other
acts and things that may be reasonably necessary or advisable to enable the
Investor to consummate the disposition of the Registrable Securities; provided,
however, that the Company will not be required to qualify generally to do
business in any jurisdiction where it would not otherwise be required to qualify
but for this paragraph (f), subject itself to taxation in any such jurisdiction,
or consent or subject itself to general service of process in any such
jurisdiction.

                        g. The Company shall immediately notify the Investor,
but in no event later than two (2) business days by facsimile and by overnight
courier, upon the occurrence of any of the following events in respect of a
Registration Statement or related prospectus in respect of an offering of
Registrable Securities: (i) receipt of any request for additional information by
the SEC or any other federal or state governmental authority during the period
of effectiveness of the Registration Statement for amendments or supplements to
the Registration Statement or related prospectus; (ii) the issuance by the SEC
or any other federal or state governmental authority of any stop order
suspending the effectiveness of a Registration Statement or the initiation of
any proceedings for that purpose; (iii) receipt of any notification with respect
to the suspension of the qualification or exemption from qualification of any of
the Registrable Securities for sale in any jurisdiction or the initiation or
threatening of any proceeding for such purpose; (iv) the happening of any event
that makes any statement made in such Registration Statement or related
prospectus or any document incorporated or deemed to be incorporated therein by
reference untrue in any material respect or that requires the making of any
changes in the Registration Statement, related prospectus or documents so that,
in the case of a Registration Statement, it will not contain any untrue
statement of a material fact or omit to state any material fact required to be
stated therein or necessary to make the statements therein not misleading, and
that in the case of the related prospectus, it will not contain any untrue
statement of a material fact or omit to state any material fact required to be
stated therein or necessary to make the statements therein, in the light of the
circumstances under which they were made, not misleading; (v) the declaration by
the SEC of the effectiveness of a Registration Statement; and (vi) the Company's
reasonable determination that a post-effective amendment to the Registration
Statement would be appropriate, and the Company promptly shall make available to
the Investor any such supplement or amendment to the related prospectus.

                        h. The Company shall enter into customary agreements and
take such other actions as are reasonably required in order to expedite or
facilitate the disposition of such Registrable Securities (whereupon the
Investor, at its option, may require that any or all of the representations,
warranties and covenants of the Company also be made to and for the benefit of
the Investor).

                        i. The Company shall make available to the Investor (and
will deliver to Investor's counsel), subject to restrictions imposed by the
United States government or any

                                       6
<PAGE>   7
agency or instrumentality thereof, copies of all correspondence between the SEC
and the Company, concerning any Registration Statement, and also will make
available for inspection by the Investor and any attorney, accountant or other
professional retained by the Investor (collectively, the "Inspectors"), all
financial and other records, pertinent corporate documents and properties of the
Company (collectively, the "Records") as shall be reasonably necessary to enable
them to exercise their due diligence responsibility, and cause the Company's
officers and employees to supply all information reasonably requested by any
Inspectors in connection with any Registration Statement. Records that the
Company determines, in good faith, to be confidential and that it notifies the
Inspectors are confidential shall not be disclosed by the Inspectors unless (i)
the disclosure of such Records is necessary to avoid or correct a misstatement
or omission in any Registration Statement or (ii) the disclosure or release of
such Records is requested or required pursuant to oral questions,
interrogatories, requests for information or documents or a subpoena or other
order from a court of competent jurisdiction or other process; provided,
however, that prior to any disclosure or release pursuant to clause (ii), the
Inspectors shall provide the Company with prompt notice of any such request or
requirement so that the Company may seek an appropriate protective order or
waive such Inspectors' obligation not to disclose such Records; and, provided,
further, that if failing the entry of a protective order or the waiver by the
Company permitting the disclosure or release of such Records, the Inspectors,
upon advice of counsel, are compelled to disclose such Records, the Inspectors
may disclose that portion of the Records that counsel has advised the Inspectors
that the Inspectors are compelled to disclose. The Investor agrees that
information obtained by it solely as a result of such inspections (not including
any information obtained from a third party who, insofar as is known to the
Investor after reasonable inquiry, is not prohibited from providing such
information by a contractual, legal or fiduciary obligation to the Company)
shall be deemed confidential and, if material non-public information, the
Investor shall not while in possession of such information engage in market
transactions in the securities of the Company or its Affiliates unless and until
such information is made generally available to the public. The Investor further
agrees that, upon learning that disclosure of such Records is sought in a court
of competent jurisdiction, it will give notice to the Company and allow the
Company, at its expense, to undertake appropriate action to prevent disclosure
of the Records deemed confidential.

                        j. To the extent required by law or reasonably necessary
to effect a sale of Registrable Securities in accordance with prevailing
business practices at the time of any sale of Registrable Securities pursuant to
a Registration Statement, the Company shall deliver to the Investor a signed
counterpart, addressed to the Investor, of (1) an opinion or opinions of counsel
to the Company and (2) a comfort letter or comfort letters from the Company's
independent public accountants, each in customary form and covering such matters
of the type customarily covered by opinions of comfort letters, as the case may
be, as the Investor therefor reasonably requests.

                        k. The Company otherwise shall comply with all
applicable rules and regulations of the SEC, including, without limitation,
compliance with applicable reporting requirements under the Exchange Act.

                        l. The Company may require the Investor to furnish
promptly in writing to the Company such information as may be legally required
in connection with any registration including, without limitation, all such
information as may be requested by the SEC or the

                                       7
<PAGE>   8
National Association of Securities Dealers, Inc. (the "NASD"). The Investor
agrees to provide such information requested in connection with any registration
within ten Trading Days after receiving such written request and the Company
shall not be responsible for any delays in obtaining or maintaining the
effectiveness of a Registration Statement caused by the Investor's failure to
timely provide such information. Each seller of Registrable Securities shall
notify the Company as promptly as practicable of any inaccuracy or change in
information previously furnished by such seller to the Company or of the
occurrence of any event, in either case as a result of which any prospectus
relating to the Registrable Securities contains or would contain an untrue
statement of a material fact regarding such seller or its intended method of
disposition of such Registrable Securities or omits to state any material fact
regarding such seller or such seller's intended method of disposition of such
Registrable Securities required to be stated therein or necessary to make the
statements therein, in the light of the circumstances under which they were
made, not misleading, and promptly furnish to the Company any additional
information required to correct and update any previously furnished information
or required so that such prospectus shall not contain, with respect to such
seller or the disposition of such Registrable Securities, an untrue statement of
a material fact or omit to state a material fact required to be stated therein
or necessary to make the statements therein, in the light of the circumstances
under which they were made, not misleading.

            Section 2.2.            REGISTRATION EXPENSES.

                        a. In connection with each Registration Statement, the
Company shall pay all registration expenses incurred in connection with the
registration thereunder (the "Registration Expenses"), including, without
limitation: (i) all registration, filing, securities exchange listing and fees
required by NASD, (ii) all registration, filing, qualification and other fees
and expenses of compliance with securities or blue sky laws (including
reasonable fees and disbursements of counsel in connection with blue sky
qualifications of the Registrable Securities required hereby), (iii) all of the
Company's word processing, duplicating, printing, messenger and delivery
expenses, (iv) the Company's internal expenses (including, without limitation,
all salaries and expenses of its officers and employees performing legal or
accounting duties), (v) the fees and expenses incurred by the Company in
connection with the listing of the Registrable Securities, (vi) reasonable fees
and disbursements of counsel for the Company and, subject to paragraph (b)
below, the Investor, and customary fees and expenses for independent certified
public accountants retained by the Company (including the expenses of any
special audits or comfort letters or costs associated with the delivery by
independent certified public accountants of such special audit(s) or comfort
letter(s) requested pursuant to Section 2.1(j) hereof), (vii) the fees and
expenses of any special experts retained by the Company in connection with such
registration, (viii) premiums and other costs of policies of insurance purchased
at the discretion of the Company against liabilities arising out of any public
offering of the Registrable Securities being registered, and (ix) any fees and
disbursements of underwriters customarily paid by issuers or sellers of
securities, but excluding underwriting fees, discounts, transfer taxes or
commissions, if any, attributable to the sale of Registrable Securities, which
shall be payable by each holder of Registrable Securities pro rata on the basis
of the number of Registrable Securities of each such holder that are included in
a registration under this Agreement.

                        b. In addition, the Company shall pay all reasonable
fees and expenses of counsel for the Investor incurred in connection with the
review, and assistance in preparation, of each Registration Statement up to
$5,000 per Registration Statement, unless a greater amount is

                                       8
<PAGE>   9
required due to the nature of the review performed by Investor's counsel or the
extent of assistance provided by Investor's counsel (an estimate of such greater
fees and expenses of such firm of counsel to the Investor shall be provided to
the Company prior to the undertaking of such counsel's additional review or
assistance).

                                   ARTICLE III
                        INDEMNIFICATION AND CONTRIBUTION

                        Section 3.1. INDEMNIFICATION BY THE COMPANY. The Company
agrees to indemnify and hold harmless the Investor, its partners, Affiliates,
officers, directors, employees and duly authorized agents, and each Person or
entity, if any, who controls the Investor within the meaning of Section 15 of
the Securities Act or Section 20 of the Exchange Act, together with its
controlling persons from and against any and all losses, claims, damages,
liabilities, costs and expenses (including, without limitation, any and all
reasonable attorneys' fees and disbursements and costs and expenses of
investigating and defending any such claim and any and all amounts paid in
settlement of, any action, suit or proceeding between any of the indemnified
parties and any indemnifying parties or between any indemnified party and any
third party, or otherwise, or any claim asserted) (collectively, "Damages"),
joint or several, and any action in respect thereof to which the Investor, its
partners, Affiliates, officers, directors, employees and duly authorized agents,
and any such controlling person, becomes subject to under the Securities Act,
the Exchange Act or other federal or state statutory law or regulation, at
common law or otherwise, as and when incurred, insofar as such Damages (or
actions or proceedings in respect thereof) (i) arise out of, or are based upon,
any untrue statement or alleged untrue statement of a material fact contained in
any Registration Statement, or in any preliminary prospectus, final prospectus,
summary prospectus, documents filed under the Exchange Act and deemed to be
incorporated by reference into any Registration Statement, application or other
document executed by or on behalf of the Company or based on written information
furnished by or on behalf of the Company filed in any jurisdiction in order to
qualify the Registrable Securities under the securities or blue sky laws thereof
or filed with the SEC, amendment or supplement relating to the Registrable
Securities or (ii) arise out of, or are based upon, any omission or alleged
omission to state therein a material fact required to be stated therein or
necessary to make the statements therein not misleading, and shall reimburse the
Investor, its partners, Affiliates, officers, directors, employees and duly
authorized agents, and each such controlling person, for any legal and other
expenses reasonably incurred by the Investor, its partners, Affiliates,
officers, directors, employees and duly authorized agents, or any such
controlling person, as incurred, in investigating or defending or preparing to
defend against any such Damages or actions or proceedings; provided, however,
that the Company shall not be liable to the extent that any such Damages arise
out of the Investor's failure to send or give a copy of the final prospectus or
supplement at or prior to the written confirmation of the sale of Registrable
Securities to the persons asserting an untrue statement or alleged untrue
statement or omission or alleged omission at or prior to the written
confirmation of the sale of Registrable Securities to such person if such
statement or omission was corrected in such final prospectus or supplement, and
provided that the Investor had been obligated under applicable law to deliver
such final prospectus or supplement to such person; provided, further, that the
Company shall not be liable to the extent that any such Damages arise out of or
are based upon an untrue statement or alleged untrue statement or omission or
alleged omission made in such Registration Statement, or any

                                       9
<PAGE>   10
such preliminary prospectus, final prospectus, summary prospectus, amendment or
supplement in reliance upon and in conformity with written information furnished
to the Company by the Investor or any other person who participates as a seller
or as an underwriter in the offering or sale of such securities, in either case,
in any questionnaire or other request by the Company, or otherwise specifically
stating that it is for use in the preparation thereof and provided that such
written information furnished to the Company by the Investor, or any other
person who participates as a seller or as an underwriter in the offering or sale
of such securities, is not materially altered by the Company. All claims for
indemnification shall be asserted and resolved as set forth in Section 9.2 of
the Stock Purchase Agreement.

            Section 3.2. ARBITRATION. Any controversy, claim or dispute arising
out of or in connection with this Agreement, including any question regarding
its existence, validity, interpretation, breach, or termination, shall be
referred to and finally resolved in accordance with Section 9.3 of the Stock
Purchase Agreement.

            Section 3.3. OTHER INDEMNIFICATION. Indemnification similar to that
specified in the preceding paragraphs of this Article III (with appropriate
modifications) shall be given by the Company with respect to any required
registration or other qualification of securities under any federal or state law
or regulation of any governmental authority other than the Securities Act. The
provisions of this Article III shall be in addition to any other rights to
indemnification, contribution or other remedies which an Indemnified Party may
have pursuant to law, equity, contract or otherwise.

            Section 3.4. CONTRIBUTION. If the indemnification and reimbursement
obligations provided for in any section of this Article III is unavailable or
insufficient to hold harmless the Indemnified Parties in respect of any Damages
referred to herein, then the Indemnifying Party, in lieu of indemnifying such
Indemnified Party, shall contribute to the amount paid or payable by such
Indemnified Party as a result of such Damages as between the Company on the one
hand and the Investor or seller on the other, in such proportion as is
appropriate to reflect the relative fault of the Company and of the Investor or
seller in connection with such statements or omissions, as well as other
equitable considerations. The relative fault of the Company on the one hand and
of the Investor or seller on the other shall be determined by reference to,
among other things, whether the untrue or alleged untrue statement of a material
fact or the omission or alleged omission to state a material fact relates to
information supplied by such party, and the parties' relative intent, knowledge,
access to information and opportunity to correct or prevent such statement or
omission.

            The Company and the Investor agree that it would not be just and
equitable if contribution pursuant to this Section 3.4 were determined by pro
rata allocation or by any other method of allocation that does not take account
of the equitable considerations referred to in the immediately preceding
paragraph. The amount paid or payable by an Indemnified Party as a result of the
Damages referred to in the immediately preceding paragraph shall be deemed to
include, subject to the limitations set forth above, any legal or other expenses
reasonably incurred by such Indemnified Party in connection with investigating
or defending any such action or claim. Notwithstanding the provisions of this
Section 3.4, the Investor or seller shall in no event be required to contribute
any amount in excess of the amount by which the total price at which the
Registrable Securities of the Investor or seller were sold to the public (less
underwriting discounts and commissions) exceeds the amount of any damages which
the

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<PAGE>   11
Investor or seller has otherwise been required to pay by reason of such untrue
or alleged untrue statement or omission or alleged omission. No Person guilty of
fraudulent misrepresentation (within the meaning of Section 11(f) of the
Securities Act) shall be entitled to contribution from any Person who was not
guilty of such fraudulent misrepresentation.

                                   ARTICLE IV
                                  MISCELLANEOUS

            Section 4.1. OUTSTANDING REGISTRATION RIGHTS. Except as set forth on
Schedule 4.1 hereto, the Company represents and warrants to the Investor that
there is not in effect on the date hereof any agreement by the Company pursuant
to which any holders of securities of the Company have a right to cause the
Company to register or qualify such securities under the Securities Act or any
securities or blue sky laws of any jurisdiction. The Company hereby covenants
and agrees that until 60 calendar days after the Registration Statement has been
declared effective by the SEC it will not, without the prior written consent of
the Investor, enter into or amend any agreement by the Company pursuant to which
any holders of securities of the Company have a right to cause the Company to
register or qualify securities under the Securities Act or any securities or
blue sky laws of any jurisdiction; provided, however, that the foregoing shall
not apply (i) to a Third Party Sale (as such term is defined in the Stock
Purchase Agreement) for which the Investor has elected not to exercise its right
of first refusal pursuant to Section 6.12 of the Stock Purchase Agreement, (ii)
to a Third Party who is a Strategic Investor or (iii) in connection with an
acquisition of another entity or assets related to the Company's current or
future business

            Section 4.2. TERM. The registration rights provided to the holders
of Registrable Securities hereunder shall terminate at such time as all
Registrable Securities have been issued and have ceased to be Registrable
Securities. Notwithstanding the foregoing, paragraphs (c) and (d) of Section
1.1, Article III, Section 4.8, and Section 4.9 shall survive the termination of
this Agreement.

            Section 4.3. RULE 144. If the Company is required to file reports
under the Exchange Act, the Company will file in a timely manner, information,
documents and reports in compliance with the Securities Act and the Exchange Act
and, at its expense, promptly will take such further action as holders of
Registrable Securities reasonably may request to enable such holders of
Registrable Securities to sell Registrable Securities without registration under
the Securities Act within the limitation of the exemptions provided by (a) Rule
144 under the Securities Act ("Rule 144"), as such Rule may be amended from time
to time, or (b) any similar rule or regulation hereafter adopted by the SEC. If
at any time the Company is not required to file such reports, it will, at its
expense, forthwith upon the written request of any holder of Registrable
Securities who intends to make a sale under Rule 144, make available adequate
current public information with respect to the Company within the meaning of
paragraph (c)(2) of Rule 144 or such other information as necessary to permit
sales pursuant to Rule 144. Upon the request of the Investor, the Company will
deliver to the Investor a written statement, signed by the Company's principal
financial officer, as to whether it has complied with such requirements. This
Section 4.3 shall terminate at the same time as the registration rights as
provided in Section 4.2.

                                       11
<PAGE>   12
            Section 4.4. CERTIFICATE. The Company will, at its expense,
forthwith upon the request of any holder of Registrable Securities, deliver to
such holder a certificate, signed by the Company's principal financial officer,
stating (a) the Company's name, address and telephone number (including area
code), (b) the Company's Internal Revenue Service identification number, (c) the
Company's SEC file number, (d) the number of shares of each class of stock
outstanding as shown by the most recent report or statement published by the
Company, and (e) whether the Company has filed the reports required to be filed
under the Exchange Act for a period of at least ninety (90) days prior to the
date of such certificate and in addition has filed the most recent annual report
required to be filed thereunder.

            Section 4.5. AMENDMENT AND MODIFICATION. Any provision of this
Agreement may be waived, provided that such waiver is set forth in a writing
executed by both parties to this Agreement. The provisions of this Agreement,
including the provisions of this sentence, may not be amended, modified or
supplemented, and waivers or consents to departures from the provisions hereof
may not be given, unless the Company has obtained the written consent of the
holders of a majority of the then outstanding Registrable Securities.
Notwithstanding the foregoing, the waiver of any provision hereof with respect
to a matter that relates exclusively to the rights of holders of Registrable
Securities whose securities are being sold pursuant to a Registration Statement
and does not directly or indirectly affect the rights of other holders of
Registrable Securities may be given by holders of at least a majority of the
Registrable Securities being sold by such holders; provided that the provisions
of this sentence may not be amended, modified or supplemented except in
accordance with the provisions of the immediately preceding sentence. No course
of dealing between or among any Person having any interest in this Agreement
will be deemed effective to modify, amend or discharge any part of this
Agreement or any rights or obligations of any person under or by reason of this
Agreement.

            Section 4.6. SUCCESSORS AND ASSIGNS; ENTIRE AGREEMENT. This
Agreement and all of the provisions hereof shall be binding upon and inure to
the benefit of the parties hereto and their respective successors and assigns;
provided, that the Investor may assign its rights under this Agreement to any
Affiliate of the Investor only; and provided further, that the Company shall
have the right to require such Affiliate to execute a counterpart of this
Agreement and agree to be bound by the provisions of this Agreement as a
condition to such Affiliate's claim to any rights hereunder. This Agreement,
together with the Stock Purchase Agreement, the Warrants and the exhibits and
schedules to such agreements together set forth the entire agreement and
understanding between the parties as to the subject matter hereof and merges and
supersedes all prior discussions, agreements and understandings of any and every
nature among them.

            Section 4.7. SEVERABILITY. In the event that any provision of this
Agreement or the application of any provision hereof is declared to be illegal,
invalid or otherwise unenforceable by a court of competent jurisdiction, the
remainder of this Agreement shall not be affected except to the extent necessary
to delete such illegal, invalid or unenforceable provision unless that provision
held invalid shall substantially impair the benefits of the remaining portions
of this Agreement.

            Section 4.8. NOTICES. All notices, demands, requests, consents,
approvals, and other communications required or permitted hereunder shall be in
writing and shall be (i) deposited in the mail, registered or certified, return
receipt requested, postage prepaid, (ii) delivered by

                                       12
<PAGE>   13
reputable air courier service with charges prepaid, or (iii) transmitted by hand
delivery, telegram or facsimile, addressed as set forth below or to such other
address as such party shall have specified most recently by written notice. Any
notice or other communication required or permitted to be given hereunder shall
be deemed effective (a) upon hand delivery or delivery by facsimile, with
accurate confirmation generated by the transmitting facsimile machine, at the
address or 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) or (b) on the third business
day following the date of mailing by express courier service, fully prepaid,
addressed to such address, or upon actual receipt of such mailing, whichever
shall first occur. 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
                        New York, NY 10019
                        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
                        1216 Geneva, Cointrin
                        Switzerland
                        Attention: Mel Craw/Maxi Brezzi
                        Telephone: +41 22 791 71 69
                        Facsimile: +41 22 929 53 94

                                       13
<PAGE>   14
            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 4.8 by giving at least 10 days'
      prior written notice of such changed address or facsimile number to the
      other party hereto.

            Section 4.9. GOVERNING LAW. This Agreement shall be construed under
the laws of the State of New York.

            Section 4.10. HEADINGS. The headings in this Agreement are for
convenience of reference only and shall not constitute a part of this Agreement,
nor shall they affect their meaning, construction or effect.

            Section 4.11. COUNTERPARTS. This Agreement may be executed in
multiple counterparts, each of which shall be deemed to be an original
instrument and all of which together shall constitute one and the same
instrument.

            Section 4.12. FURTHER ASSURANCES. Each party shall cooperate and
take such action as may be reasonably requested by another party in order to
carry out the provisions and purposes of this Agreement and the transactions
contemplated hereby.

            Section 4.13. ABSENCE OF PRESUMPTION. This Agreement shall be
construed without regard to any presumption or rule requiring construction or
interpretation against the party drafting or causing any instrument to be
drafted.

            Section 4.14. REMEDIES. In the event of a breach or a threatened
breach by any party to this Agreement of its obligations under this Agreement,
any party injured or to be injured by such breach will be entitled to specific
performance of its rights under this Agreement or to injunctive relief, in
addition to being entitled to exercise all rights provided in this Agreement and
granted by law. The parties agree that the provisions of this Agreement shall be
specifically enforceable, it being agreed by the parties that the remedy at law,
including monetary damages, for breach of any such provision may be inadequate
compensation for any loss.

                                       14
<PAGE>   15
            IN WITNESS WHEREOF, the parties hereto have caused this Registration
Rights Agreement to be executed by the undersigned, thereunto duly authorized,
as of the date first set forth above.

                                   CRESCENT INTERNATIONAL LTD.

                                   By:    /s/ Mel Craw          /s/ Michel Peche
                                          GreenLight (Switzerland) S.A. as
                                            Investor's manager
                                          Name:  Mel Craw / Michel Peche
                                          Title:

                                   APPLIEDTHEORY CORPORATION

                                   By:    /s/ David A. Buckel
                                   Name:  David A. Buckel
                                   Title: Sr. VP / CFO

                                       15

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