<PAGE>   1
                                                                   EXHIBIT 10.72

         THIS SECURITY HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933,
AS AMENDED (THE "ACT"), OR ANY STATE SECURITIES LAWS. IT MAY NOT BE TRANSFERRED,
ASSIGNED, SOLD OR OFFERED FOR SALE EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION
STATEMENT UNDER SAID ACT AND ANY APPLICABLE STATE SECURITIES LAW OR AN OPINION
OF COUNSEL, IN FORM AND SUBSTANCE REASONABLY ACCEPTABLE TO THE COMPANY, THAT
REGISTRATION IS NOT REQUIRED BECAUSE OF AN APPLICABLE EXEMPTION FROM SUCH
REGISTRATION REQUIREMENTS.

         THIS DEBENTURE DOES NOT REQUIRE PHYSICAL SURRENDER OF THE DEBENTURE IN
THE EVENT OF A REDEMPTION OR CONVERSION. AS A RESULT, FOLLOWING ANY REDEMPTION
OR CONVERSION OF ANY PORTION OF THIS DEBENTURE, THE OUTSTANDING PRINCIPAL AMOUNT
REPRESENTED BY THIS DEBENTURE MAY BE LESS THAN THE PRINCIPAL AMOUNT AND THE
ACCRUED INTEREST SET FORTH BELOW. ACCORDINGLY, ANY POTENTIAL ASSIGNEE MAY WISH
TO, BUT IS NOT OBLIGATED TO, CONFIRM THE OUTSTANDING PRINCIPAL AMOUNT
REPRESENTED HEREBY WITH THE COMPANY, IN ADDITION TO THE ASSIGNOR.

NO. ____                                                              $_________

DATED:  AS OF JUNE 5, 2000
LAST AMENDED:  JULY 10, 2001

                            APPLIEDTHEORY CORPORATION

                    5% CONVERTIBLE DEBENTURE DUE JUNE 5, 2003

         THIS DEBENTURE ("DEBENTURE") is one of a duly authorized issue of
debentures of APPLIEDTHEORY CORPORATION (the "COMPANY"), a corporation duly
organized and existing under the laws of the State of Delaware, designated as
the Company's 5% Convertible Debentures Due June 5, 2003, in an aggregate
principal amount of Thirty Million U.S. Dollars (U.S. $30,000,000) (the
"DEBENTURES").

         FOR VALUE RECEIVED, the Company promises to pay to ______________, the
initial holder hereof, or its order (including successors-in-interest, the
"HOLDER"), the principal sum of ____________ U.S. Dollars [TO BE INSERTED] (U.S.
$_______) on June 5, 2003 (the "MATURITY DATE") and to pay interest on the
principal sum outstanding under this Debenture ("OUTSTANDING PRINCIPAL AMOUNT"),
at the rate of 5% per annum, compounded semi-annually, payable in arrears on the
first day of December and June of each year and on the Maturity Date (each an
"INTEREST PAYMENT DATE"), with the first such payment due on December 5, 2000.
Interest shall accrue daily commencing on the date hereof and shall continue
until payment in full of all amounts due under this Debenture. The interest so
payable will be paid to the person in whose name this Debenture is registered on
the records of the Company regarding registration and
<PAGE>   2
transfers of the Debenture (the "DEBENTURE REGISTER"). Capitalized terms used
herein and not otherwise defined shall have the meanings set forth in the
Amendment Agreement dated July 10, 2001 among the Company, the Holder, et. al.
(the "AMENDMENT AGREEMENT"), the Amended and Restated Purchase Agreement dated
as of June 5, 2000 between the Company, the Holder, et. al. (the "PURCHASE
AGREEMENT") or the Amended and Restated Registration Rights Agreement dated as
of June 5, 2000 between the Company, the Holder, et. al. (the "REGISTRATION
RIGHTS AGREEMENT").

         The interest on this Debenture is payable, at the Company's option:

            (a) in such coin or currency of the United States as of the time of
payment is legal tender for payment of public and private debts, at the address
last appearing on the Debenture Register of the Company as designated in writing
by the Holder hereof from time to time;

            (b) by adding the amount thereof to the Outstanding Principal Amount
due under this Debenture ("PIK INTEREST"); or

            (c) provided that there is Effective Registration (as defined in the
Purchase Agreement) at such time, in Common Stock (as defined below) ("STOCK
INTEREST"). For purposes of calculating the number of shares of Common Stock to
be delivered by the Company to the Holder on the applicable Interest Payment
Date pursuant hereto, the dollar amount then payable will be divided by the
average of the Market Price for Shares of Common Stock (as defined below and as
adjusted appropriately for stock splits, reverse stock splits,
recapitalizations, stock dividends and the like) for the five (5) consecutive
Trading Days immediately preceding and excluding such Interest Payment Date.

         Except as herein provided for interest, all amounts payable under this
Debenture shall be paid as provided in clause (a) above.

         The Company shall exercise its option hereunder by delivering an
irrevocable statement in the form of Exhibit 1 hereto ("PAYMENT STATEMENT")
delivered at least ten (10) Trading Days prior to the applicable Interest
Payment Date and applicable for such Interest Payment Date only. If the Payment
Statement is not timely delivered to the Holder as provided herein, the payment
with respect to such Interest Payment Date shall be in PIK Interest. If the
Company selects either cash interest or Stock Interest in the Payment Statement
and fails to deliver such cash or Common Stock on or before the Interest Payment
Date, the Holder shall have the right to require the Company to pay PIK Interest
in lieu thereof. Any PIK Interest when so added to the Outstanding Principal
Amount due under this Debenture shall, for all purposes of this Debenture, be
deemed to be part of the principal indebtedness evidenced by this Debenture
including, without limitation, for purposes of determining interest payable
hereunder after the applicable Interest Payment Date for which such PIK Interest
is paid and amounts convertible into Common Shares hereunder after the
applicable Interest Payment Date for which such PIK Interest is paid.
<PAGE>   3

         The Company will pay any principal due and all accrued and unpaid
interest due upon this Debenture to the person that is the Holder of this
Debenture on the records of the Company as of the applicable Interest Payment
Date and addressed to such Holder at the last address appearing on the Debenture
Register.

         The Outstanding Principal Amount and interest due hereunder shall bear
interest, from and after the day following the occurrence and during the
continuance of an Event of Default hereunder, at the per annum rate equal to the
lower of the Citibank Prime Rate per annum plus six (6%) percent or the highest
rate permitted by law. The Holder shall have the option to receive such interest
as cash interest, PIK Interest or Stock Interest and shall exercise its option
by delivering to the Company a statement in a form substantially similar to the
Payment Statement which shall be effective until the earlier of (a) the date
upon which the applicable default is cured or (b) Holder delivers an additional
statement to the contrary. If the Holder elects to receive the interest in cash,
it shall be payable on demand.

         Additional cash payments (referred to as "DEFAULT PAYMENTS") may be
required pursuant to the Registration Rights Agreement if there occurs an
"INTERFERING EVENT" (as defined therein), or pursuant to the Purchase Agreement
under the terms set forth in Section 3.14 therein. Such default payments, if not
paid in cash when due, may be treated by the Holder in its sole discretion as
being added to the Outstanding Principal Amount due under this Debenture.

         Subject to applicable law, any interest otherwise payable that is not
paid for any applicable period because it would exceed the highest rate
permitted by law shall become payable whenever the payment thereof, together
with other interest due for any such subsequent period, would not exceed such
highest legal rate.

         The Holder of this Debenture is entitled to certain rights and remedies
pursuant to the Purchase Agreement, Registration Rights Agreement, the Amendment
Agreement and the Security Agreement including without limitation provisions
requiring mandatory redemption of the Debenture. This Debenture does not provide
voting rights to the Holder.

         This Debenture is subject to the following additional provisions:

         1. EXCHANGE. This Debenture is exchangeable for an equal aggregate
principal amount of Debentures of different denominations, as requested by the
Holder surrendering the same. No service charge will be made for such
registration or transfer or exchange.
<PAGE>   4

         2. TRANSFERS. This Debenture may be transferred or exchanged in the
United States only in compliance with the Act and applicable state securities
laws, or applicable exemptions therefrom. Prior to due presentment for transfer
of this Debenture, the Company may treat the person in whose name this Debenture
is duly registered on the Company's Debenture Register as the owner hereof for
the purpose of receiving payment as herein provided, whether or not this
Debenture is overdue.

         3. DEFINITIONS. For purposes hereof the following definitions shall
apply:

                  "ACCEPTABLE DELIVERY DATE" shall mean within three (3) Trading
Days of the delivery to the Company of the Conversion Notice provided, that, if
book entry transfer under Section 5(f) below is not being used for a particular
conversion, the Acceptable Delivery Date with respect to such conversion shall
be no later than the later of the date set forth above or one (1) Trading Day
following the delivery to the Company of the Debenture submitted for conversion.

                  "ACT" shall have the meaning set forth in the legend set forth
on the face of this Debenture.

                  "AFFECTED CONVERSION PRICE" shall have the meaning set forth
in Section 8(a).

                  "AMENDMENT AGREEMENT" shall have the meaning set forth in the
preamble.

                  "CHANGE IN CONTROL CONSIDERATION" shall have the meaning set
forth in Section 4 hereof.

                  "CHANGE IN CONTROL TRANSACTION" shall mean the occurrence of
(x) any consolidation or merger of the Company with or into any other
corporation or other entity or person (whether or not the Company is the
surviving corporation), or any other corporate reorganization or transaction or
series of related transactions in which in excess of 50% of the Company's voting
power is transferred through a merger, consolidation, tender offer or similar
transaction, or (y) any person (as defined in Section 13(d) of the Securities
Exchange Act of 1934, as amended (the "EXCHANGE ACT")), together with its
affiliates and associates (as such terms are defined in Rule 405 under the Act),
beneficially owning or being deemed to beneficially own (as described in Rule
13d-3 under the Exchange Act with beneficial ownership including the right to
acquire beneficial ownership even if such right is not exercisable within 60
days) in excess of 50% of the Company's voting power.

                  "CLOSING DATE" shall mean the date of the original issuance of
this Debenture.

                  "COMMON STOCK" shall mean the common stock, par value $0.01,
of the Company.

                  "COMPANY" shall have the meaning set forth in the Preamble.
<PAGE>   5

                  "CONVERSION NOTICE" shall have the meaning set forth in
Section 5(a)(iii).

                  "CONVERTIBLE SECURITIES" shall have the meaning set forth in
Section 8(b)(ii).

                  "CONVERSION PRICE" shall be _______ [TO BE INSERTED] as may be
adjusted in accordance herewith.

                  "CONVERSION RATE" shall have the meaning set forth in Section
5(a)(ii).

                  "DEBENTURE" shall have the meaning set forth in the Preamble.

                  "DEBENTURES" shall have the meaning set forth in the Preamble.

                  "DEBENTURE REGISTER" shall have the meaning set forth in the
Preamble.

                  "DEFAULT PAYMENTS" shall have the meaning set forth in the
Preamble.

                  "DISTRIBUTED PROPERTY" shall have the meaning set forth in
Section 8(c).


                  "DTC" shall have the meaning set forth in Section 5(e).

                  "DWAC" shall have the meaning set forth in Section 5(e).

                  "EVENTS OF DEFAULT" shall have the meaning set forth in
Section 18 hereof.

                  "FAST" shall have the meaning set forth in Section 5(e).

                  "HOLDER CONVERSION DATE" shall mean the date on which the
person or persons entitled to receive shares of Common Stock issuable upon a
given conversion shall be treated for all purposes as the record holder or
holders of such shares of Common Stock.

                  "INTEREST PAYMENT DATE" shall have the meaning set forth in
the Preamble.

                  "MATURITY DATE" shall have the meaning set forth in the
Preamble.

                  "MARKET PRICE FOR SHARES OF COMMON STOCK" shall mean the price
of one share of Common Stock determined as follows:

                      (i) If the Common Stock is approved for trading on the
NASDAQ National Market System or the Nasdaq Small-Cap Market, the closing price
thereon on the date of valuation;

                      (ii) If (i) does not apply and the Common Stock is listed
on NYSE or the American Stock Exchange, the closing price on such exchange on
the date of valuation;
<PAGE>   6

                      (iii) If neither (i) nor (ii) apply but the Common Stock
is quoted in the over-the-counter market, another recognized exchange, on the
pink sheets or bulletin board, (A) the last sales price on the date of valuation
or, if there is no such sales price, (B) the mean between the last reported
"bid" and "asked" prices thereof on the date of valuation; and

                      (iv) If neither clause (i), (ii) or (iii) above applies,
the market value as determined by a nationally recognized investment banking
firm or other nationally recognized financial advisor retained by the Company
and approved by the Holder for such purpose, taking into consideration, among
other factors, the earnings history, book value and prospects for the Company,
and the prices at which shares of Common Stock recently have been traded. Such
determination shall be conclusive and binding on all persons.

                  "NYSE" shall mean the New York Stock Exchange.

                  "OUTSTANDING PRINCIPAL AMOUNT" shall have the meaning set
forth in the Preamble.

                  "PAYMENT STATEMENT" shall have the meaning set forth in the
Preamble.

                  "PIK INTEREST" shall have the meaning set forth in the
Preamble.

                  "PUBLIC ANNOUNCEMENT" shall mean any public filing with the
Securities and Exchange Commission, any press release by either the Company or a
third party or any other public statement, that announces a proposed transaction
which, if consummated, would constitute a Change in Control Transaction.

                  "PURCHASE AGREEMENT" shall have the meaning set forth in the
Preamble.

                  "REDEMPTION DATE" shall have the meaning set forth in the
definition of "Redemption Notice" below.

                  "REDEMPTION NOTICE" shall mean a written irrevocable notice
given by the Company to the Holder indicating its intention to redeem all or
part of this Debenture as may be provided herein. The Redemption Notice shall
(x) state that the Company seeks to redeem the Debenture, (y) set the date (the
"REDEMPTION DATE") for the Company's redemption of the Debenture and (z) state
the Outstanding Principal Amount of the Debentures that the Company seeks to
redeem and the redemption price for such Outstanding Principal Amount (plus
accrued but unpaid interest and default payments (not previously added to
principal)). Unless otherwise provided in the Redemption Notice, redemptions
shall occur at the offices of Holder's counsel.

                  "REDEMPTION PRICE" shall equal 100% of the Outstanding
Principal Amount of this Debenture to be redeemed (plus accrued but unpaid
interest and default payments (not previously added to principal)) and shall be
payable in cash only.
<PAGE>   7

                  "REGISTRATION RIGHTS AGREEMENT" shall have the meaning set
forth in the Preamble.

                  "RESTRICTED OWNERSHIP PERCENTAGE" shall have the meaning set
forth in Section 13.

                  "STOCK INTEREST" shall have the meaning set forth in the
Preamble.

                  "TRADING DAY" shall mean a day on which the Common Stock is
traded on the NASDAQ National Market System or principal exchange on which the
Common Stock has been listed (or any similar organization or agency succeeding
such market or exchange's functions of reporting prices).

         4.       CHANGE IN CONTROL, ETC.

                      (a) [INTENTIONALLY DELETED]

                      (b) If at any time there occurs a Public Announcement of a
pending Change in Control Transaction in which the public shareholders of the
Company are to receive consideration, a portion of which is capital stock or any
security convertible into capital stock of another entity in exchange for shares
of Common Stock ("CHANGE IN CONTROL CONSIDERATION"), then prompt provision shall
be made in a manner reasonably acceptable to the Holders so that each Holder
shall have the right (in addition to its rights hereunder) to:

                          (i) convert its Debentures (subject to Section 2(c) of
the Amendment Agreement), as part of the Change in Control Transaction and
thereafter, into the Change in Control Consideration that such Holder would have
been or would be entitled to receive had it converted all of its Debentures into
Common Stock (notwithstanding any restrictions imposed upon the Holder pursuant
to this Debenture, the Amendment Agreement or the Purchase Agreement in its
ability to do so) immediately prior to the Change in Control Transaction at the
Conversion Price (as defined below and as may be adjusted in accordance
herewith) in effect on the date of such conversion, and then acquired the Change
in Control Consideration as a shareholder of the Company.

                          (ii) [INTENTIONALLY DELETED]

                  (c) [INTENTIONALLY DELETED]

                  (d) This Debenture is subject to and entitled to the benefits
of the provisions of Section 2(c) and Section 6 of the Amendment Agreement in
the event of a Change in Control Transaction or any other transaction
constituting a Sale of the Company (as defined in the Amendment Agreement).

                      The rights set forth in this Section 4 are cumulative and
are in addition to any other rights or remedies that the Holder may have.
<PAGE>   8

                  5. CONVERSION AT THE OPTION OF THE HOLDER. The Holder of this
Debenture shall have the following conversion rights.

                      (a) Mechanism. (i) This Debenture shall be convertible, at
the option of the Holder, in whole or in part, from time to time, into fully
paid, validly issued and nonassessable shares of Common Stock, in accordance
with the terms set forth in this Debenture. If this Debenture is converted in
part, the remaining portion of this Debenture not so converted shall remain
entitled to the conversion rights as provided herein.

                          (ii) The Outstanding Principal Amount of this
Debenture that is converted into shares of Common Stock at the option of the
Holder shall be convertible into the number of shares of Common Stock which
results from application of the following formula:

                                    P + I + D
                              --------------------
                                Conversion Price

         P   = Outstanding Principal Amount of this Debenture submitted for
               conversion as of the Holder Conversion Date

         I   = accrued but unpaid interest (not previously added to
               principal) on P as of the Holder Conversion Date

         D   = default payments (not previously added to principal) on P as
               of the Holder Conversion Date

                           The number of shares of Common Stock into which each
$1,000 Outstanding Principal Amount of this Debenture hereto may be converted
pursuant to this paragraph hereof is hereafter referred to as the "CONVERSION
RATE."

                          (iii) In order to convert this Debenture, in
accordance with the terms of this Debenture, in whole or in part, into full
shares of Common Stock, the Holder (x) shall give written notice in the form of
Exhibit 2 hereto (the "CONVERSION NOTICE") by facsimile to the Company in
accordance with Section 24 hereof that the Holder elects to convert the
Outstanding Principal Amount (plus accrued but unpaid interest and default
payments (not previously added to principal)) specified therein, which such
notice and election shall be irrevocable (unless expressly provided herein to
the contrary) and shall be deemed received on the date given, and (y) shall
surrender this Debenture, duly endorsed, to the principal office of the Company,
on or before the Acceptable Delivery Date or indicate that it is effecting
delivery of this Debenture pursuant to Section 5(f). For the sake of clarity, a
Conversion Notice shall be delivered to the Company via facsimile and shall be
deemed received by the Company upon delivery thereof with electronic
confirmation of receipt having been received by the Holder.

                          (iv) Following its receipt of a Conversion Notice
submitted pursuant to the terms hereof, the Company shall be obligated to issue
certificates
<PAGE>   9
evidencing the shares of the Common Stock issuable upon such conversion on the
Acceptable Delivery Date only if either (x) the Debenture evidencing the
principal amount is delivered to the Company as provided above or (y) the Holder
notifies the Company that the Debenture has been lost, stolen or destroyed and
promptly executes an agreement reasonably satisfactory to the Company to
indemnify the Company from any loss incurred by it in connection with such lost,
stolen or destroyed Debenture or (z) the Holder elects to effect delivery of the
Debenture in accordance with Section 5(f). Subject to the foregoing, the Company
shall issue and deliver, on the relevant Acceptable Delivery Date, to the Holder
of the Debenture at the address of the Holder, or to its designee, a certificate
or certificates for the number of shares of Common Stock to which the Holder
shall be entitled as aforesaid, together with a calculation of the Conversion
Rate and a Debenture or Debentures for the principal amount of Debenture not
submitted for conversion. In the event that such Holder or its designee has not
received such certificate or certificates and the balance of the Debenture(s),
subject to Section 5(f), within ten (10) calendar days of the Acceptable
Delivery Date, the Holder may, in addition to any other rights or remedies it
may have, revoke its Conversion Notice.

                          (v) The conversion terms set forth herein are
supplemented, but not superceded, by the conversion terms set forth elsewhere in
this Debenture.

                     (b) Right of Holder to Convert at the Conversion Price.

                         (i) (A) Subject to adjustments pursuant to Section
5(b)(ii) and Section 8 hereof, the Holder shall have the right to convert this
Debenture, at any time and from time to time, at the Conversion Price (as
defined in this Debenture). The date on which the Conversion Notice is given
shall be the Holder Conversion Date. Unless otherwise specified by the Holder,
Debentures submitted for conversion shall be converted at the lowest Conversion
Price available to the Holder with respect to such Debentures.

                             (B) [INTENTIONALLY DELETED]

                             (C) [INTENTIONALLY DELETED]

                         (ii) In addition to the foregoing and in addition to
any other rights or remedies which may be available to the Holder in this
Debenture or under the Purchase Agreement, the Registration Rights Agreement,
the Amendment Agreement or the Security Agreement, if at any time the Company
fails for any reason to redeem the Debenture (or portion thereof, as applicable)
in cash and/or non-cash consideration pursuant to and in accordance with Section
6 of the Amendment Agreement or make any cash payment (other than interest
payments with respect to which the Holder has the right to require the Company,
or the Company has the right to elect and has elected, to pay PIK Interest in
lieu thereof) in accordance with the terms of this Debenture, the Purchase
Agreement, Registration Rights Agreement, the Amendment Agreement or the
Security Agreement and such failure remains uncured for at least two (2) Trading
Days after the Company's receipt of written notice of such failure from the
Holder, then the Conversion Price
<PAGE>   10
shall be subject to further adjustment (downwards only). The Conversion Price
shall thereafter be equal to the lesser of (x) the lowest Market Price for
Shares of Common Stock during any of the five (5) days prior to the date that
the Holder submits a Conversion Notice (as defined above) to the Company and (y)
the Conversion Price otherwise applicable at such time, in each case subject to
further adjustment pursuant hereto and Section 8.

         (c) [INTENTIONALLY DELETED]

         (d) [INTENTIONALLY DELETED]

         (e) Depository Trust Company. In lieu of delivering physical
certificates representing the Common Shares issuable upon conversion of
Debentures or the Warrant Shares (as defined in the Purchase Agreement)
deliverable upon exercise of Warrants (as defined in the Purchase Agreement),
provided the Company's transfer agent is participating in the Depository Trust
Company ("DTC") Fast Automated Securities Transfer ("FAST") program, upon
request of the holder, the Company shall use its best efforts to cause its
transfer agent to electronically transmit the Common Shares and Warrant Shares
issuable upon conversion or exercise to the Holder, by crediting the account of
Holder's prime broker with DTC through its Deposit Withdrawal Agent Commission
("DWAC") system. The time periods for delivery described above shall apply to
the electronic transmittals through the DWAC system. The parties agree to
coordinate with DTC to accomplish this objective. The conversions pursuant to
Section 5 shall be deemed to have been made immediately prior to the close of
business on the Holder Conversion Date. The person or persons entitled to
receive the Common Shares issuable upon such conversion shall be treated for all
purposes as the record holder or holders of such Common Shares at the close of
business on the Holder Conversion Date.

         (f) Book Entry. The Holder shall not be required to physically
surrender this Debenture to the Company unless the full Outstanding Principal
Amount represented by this Debenture is being converted or redeemed. The Holder
and the Company shall maintain records showing the Outstanding Principal Amount
so converted or redeemed and the dates of such conversions and/or redemptions or
shall use such other method, reasonably satisfactory to the Holder and the
Company, so as not to require physical surrender of this Debenture upon each
such conversion or redemption. Notwithstanding the foregoing, if this Debenture
is converted or redeemed as aforesaid, the Holder may not transfer this
Debenture unless the Holder first physically surrenders this Debenture to the
Company, whereupon the Company will forthwith issue and deliver upon the order
of the Holder a new Debenture of like tenor, registered as the Holder may
request, representing in the aggregate the remaining Outstanding Principal
Amount represented by this Debenture and reflecting the use of the book entry
provisions set forth herein. The Holder and any assignee, by acceptance of this
Debenture or a new Debenture, acknowledge and agree that, by reason of the
provisions of this paragraph, following conversion or redemption of any portion
of this Debenture, the Outstanding Principal Amount represented by this
Debenture may be less than the principal amount and the accrued interest set
forth on the face hereof.
<PAGE>   11

         6. [INTENTIONALLY DELETED]

         7. [INTENTIONALLY DELETED]

         8. STOCK SPLITS; DIVIDENDS; ADJUSTMENTS; REORGANIZATIONS.

         (a) If the Company, at any time while the Debentures are outstanding,
shall (i) pay a stock dividend or otherwise make a distribution or distributions
on any equity securities (including investments or securities convertible into
or exchangeable for such equity securities) in shares of Common Stock, (ii)
subdivide the outstanding shares of Common Stock into a larger number of shares,
(iii) combine outstanding shares of Common Stock into a smaller number of
shares, then each Affected Conversion Price (as defined below) shall be
multiplied by a fraction of which the numerator shall be the number of shares of
Common Stock outstanding before such event and of which the denominator shall be
the number of shares of Common Stock outstanding after such event. Any
adjustment made pursuant to this Section 8(a) shall become effective immediately
after the record date for the determination of shareholders entitled to receive
such dividend or distribution and shall become effective immediately after the
effective date in the case of an issuance, a subdivision or a combination.

         As used herein, the Affected Conversion Prices (each an "AFFECTED
CONVERSION PRICE") shall refer to: (x) the Conversion Price; and (y) the Market
Price for Shares of Common Stock occurring on each Trading Day used to determine
the Conversion Price hereunder, provided that such Trading Day occurred before
the record date in the case of events referred to in the immediately preceding
paragraph and the effective date in the case of the events referred to in
clauses (ii) and (iii) of the immediately preceding paragraph.

         (b) In the event that the Company issues or sells any Common Stock or
securities which are convertible into or exchangeable for its Common Stock, or
any convertible securities, or any warrants or other rights to subscribe for or
to purchase or any options for the purchase of its Common Stock or any such
convertible securities at a per share of Common Stock selling price ("PER SHARE
SELLING PRICE") which is less than:

            (i) [INTENTIONALLY DELETED]

            (ii) 90% of the Market Price for Shares of Common Stock on the
Trading Day next preceding such issue or sale, then the Affected Conversion
Prices per share shall be reduced effective concurrently with such issue or sale
to an amount determined by multiplying the Affected Conversion Price then in
effect by a fraction, (A) the numerator of which shall be the sum of (1) the
number of shares of Common Stock outstanding immediately prior to such issue or
sale, plus (2) the number of shares of Common Stock which the aggregate
consideration received by the Company for such additional shares would purchase
at such Market Price for Shares of Common Stock and (B) the denominator of which
shall be the number of shares of Common Stock of the Company outstanding
immediately after such issue or sale.
<PAGE>   12

                  Notwithstanding the foregoing, this provision shall not apply
to (x) any issuances or sales of securities pursuant to employee or director
option plans of the Company approved by shareholders or pursuant to contracts
currently in effect and disclosed to the Holders, (y) arrangements with the
Holders and (z) the issuances or sales of securities in connection with
strategic acquisitions of other entities by the Company which engage in
businesses related or complementary to the Company's business and that is not
essentially a capital raising transaction on behalf of the Company.

                  For the purposes of the foregoing adjustment, in the case of
the issuance of any convertible securities, warrants, options or other rights to
subscribe for or to purchase or exchange for, shares of Common Stock
("CONVERTIBLE SECURITIES"), the maximum number of shares of Common Stock
issuable upon exercise, exchange or conversion of such Convertible Securities
shall be deemed to be outstanding, provided that no further adjustment shall be
made upon the actual issuance of Common Stock upon exercise, exchange or
conversion of such Convertible Securities. With respect to Convertible
Securities, the Per Share Selling Price shall be equal to the lowest price at
which shares of Common Stock may be issued on conversion, exercise or exchange
of the Convertible Securities as of the issuance date of such Convertible
Securities or any subsequent date, whichever results in the lower Per Share
Selling Price. If such lowest price may change after issuance of the Convertible
Securities (for example, by reason adjustments or resets resulting from changes
in the market price for the Common Stock, or for any other reason) then this
adjustment shall be recomputed to reflect such new "lowest price".

                  In the event of any such issuance for a consideration which is
less than the Market Price for Shares of Common Stock on the Trading Day next
preceding such issue or sale and also less than the Conversion Price then in
effect, than there shall be only one such adjustment by reason of such issuance,
such adjustment to be that which results in the greatest reduction of the
Conversion Price computed as aforesaid.

                  (c) If the Company, at any time while the Debentures are
outstanding, shall distribute to all holders of shares of Common Stock evidences
of its indebtedness or assets or securities or rights or warrants to subscribe
for or purchase any security (excluding those referred to in Section 8(b) above)
("DISTRIBUTED PROPERTY"), then the prices referred to in (x) and (y) of the
definition of the Affected Conversion Prices set forth in Section 8(a) above
shall be reduced to equal the relevant Affected Conversion Price multiplied by a
fraction (i) the numerator of which is equal to (A) the Market Price for Shares
of Common Stock on the record date for the distribution minus (B) the price
allocable to one share of Common Stock of the value (as jointly determined in
good faith by the board of directors of the Company and the Holder) of any and
all such distributed property and (ii) the denominator of which is equal to the
Market Price for Shares of Common Stock on the record date for the distribution.

                  (d) In the event that at any time or from time to time after
the Closing Date, the Common Stock issuable upon the conversion of the
Debentures is changed into the same or a different number of shares of any class
or classes of stock, whether by merger, consolidation, recapitalization,
reclassification or otherwise (other than a subdivision or combination of shares
or stock dividend or reorganization provided for

<PAGE>   13
elsewhere in this Section 8), then and as a condition to each such event
provision shall be made in a manner reasonably acceptable to the Holders of
Debentures so that each Holder of Debentures shall have the right thereafter to
convert such Debenture into the kind of stock receivable upon such
recapitalization, reclassification or other change by holders of shares of
Common Stock, all subject to further adjustment, mutatis mutandis as provided
herein. In such event, the formulae set forth herein for conversion and
redemption shall be equitably adjusted to reflect such change in number of
shares or, if shares of a new class of stock are issued, to reflect the market
price of the class or classes of stock (applying the same factors used in
determining the Conversion Price) issued in connection with the above described
transaction.

                  (e) Whenever any element of the Conversion Price is adjusted
pursuant to Section 8, the Company shall promptly mail to each Holder of the
Debentures, a notice setting forth the Conversion Price after such adjustment
and setting forth a brief statement of the facts requiring such adjustment.

                  (f) In the event of any taking by the Company of a record date
of the holders of any class of securities for the purpose of determining the
holders thereof who are entitled to receive any dividend or other distribution,
any security or right convertible or exchangeable into or entitling the holder
thereof to receive additional shares of Common Stock, or 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 deliver
to each Holder of Debentures at least 20 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, security or right and the amount
and character of such dividend, distribution, security or right.

                  (g) If the Company, at any time while the Debentures are
outstanding, shall distribute to all holders of shares of Common Stock
distributed property then the Holder shall participate in such distribution on a
pro rata basis with the holders of shares of Common Stock entitled to receive
such distributed property as if the Holder held that number of shares of Common
Stock that the Holder would have been entitled to receive hereunder upon
conversion of the Debenture (without regard to Section 13) immediately prior to
the record date fixed for determination of shareholders entitled to receive such
distributed property, at the Conversion Price then in existence.

         9. FRACTIONAL SHARES. No fractional shares of Common Stock or scrip
representing fractional shares of Common Stock shall be issuable hereunder. The
number of shares of Common Stock that are issuable upon any conversion shall be
rounded up to the nearest whole share.
<PAGE>   14

         10. RESERVATION OF STOCK ISSUABLE UPON CONVERSION. The Company
covenants that it will at all times reserve from its authorized and unissued
Common Stock a sufficient number of shares, which shall not be less than the
number required by Section 3.10 of the Purchase Agreement, for the issuance of
shares of Common Stock upon conversion of the Debentures.

         11. NO REISSUANCE OF THE DEBENTURE. No Debentures acquired by the
Company by reason of redemption, purchase, exchange or otherwise shall be
reissued, and all such Debentures shall be retired.

         12. NO IMPAIRMENT. The Company shall not intentionally take any action
which would impair the rights and privileges of the Debentures set forth herein
or the Holders thereof.

         13. LIMITATIONS ON HOLDER'S RIGHT TO CONVERT.

             (a) Notwithstanding anything to the contrary contained herein, the
number of shares of Common Stock that may be acquired by a Holder upon
conversion pursuant to the terms hereof at any time shall not exceed a number
that, when added to the total number of shares of Common Stock deemed
beneficially owned at such time by such Holder (other than by virtue of the
ownership of securities or rights to acquire securities (including the
Debentures) that have limitations on the Holder's right to convert, exercise or
purchase similar to the limitation set forth herein), together with all shares
of Common Stock deemed beneficially owned at such time (other than by virtue of
the ownership of securities or rights to acquire securities that have
limitations on the right to convert, exercise or purchase similar to the
limitation set forth herein) by the Holder's "affiliates" (as defined in Rule
144 of the Act) ("AGGREGATION PARTIES") that would be aggregated for purposes of
determining whether a group under Section 13(d) of the Securities Exchange Act
of 1934 as amended, exists, would exceed 9.99% of the total issued and
outstanding shares of the Common Stock (the "RESTRICTED OWNERSHIP PERCENTAGE").
Each Holder shall have the right (w) at any time and from time to time to reduce
its Restricted Ownership Percentage immediately upon notice to the Company and
(x) (subject to waiver) at any time and from time to time, to increase its
Restricted Ownership Percentage immediately upon notice to the Company in the
event of the announcement as pending or planned, of a transaction or event
referred to in Section 4 or Section 18(g) or (k) hereof. For this purpose, any
material modification of the terms of a Change in Control Transaction will be
deemed to result in a new Change in Control Transaction. The Company shall
provide all Holders with the later of (i) 20 days' prior written notice of any
such Change in Control Transaction, to the extent the Company has prior
knowledge of a Change in Control Transaction; or (ii) notice on the day
immediately following the Company's learning of any such transaction, but only
after, in the case of (i) and (ii), such Change in Control Transaction has been
publicly disclosed.

             (b) The Holder covenants at all times on each day (each such day
being referred to as a "COVENANT DAY") as follows: During the balance of such
Covenant Day and the succeeding sixty-one (61) days (the balance of such
Covenant Day and the succeeding 61 days being referred to as the "COVENANT
PERIOD") such Holder will not
<PAGE>   15
acquire shares of Common Stock pursuant to any right (including conversion of
Debentures) existing at the commencement of the Covenant Period to the extent
the number of shares so acquired by such Holder and its Aggregation Parties
(ignoring all dispositions) would exceed:

                          (x) the Restricted Ownership Percentage of the total
             number of shares of Common Stock outstanding at the commencement of
             the Covenant Period,

                           minus

                          (y) the number of shares of Common Stock actually
             owned by such Holder and its Aggregation Parties at the
             commencement of the Covenant Period.

                  A new and independent covenant will be deemed to be given by
the Holder as of each moment of each Covenant Day. No covenant will terminate,
diminish or modify any other covenant. The Holder agrees to comply with each
such covenant. This Section 13 controls in the case of any conflict with any
other provision of the Purchase Agreement or related documents.

                  (c) The Company's obligation to issue shares of Common Stock
which would exceed such limits referred to in this Section 13 shall be suspended
to the extent necessary until such time, if any, as shares of Common Stock may
be issued in compliance with such restrictions.

              14. OBLIGATIONS ABSOLUTE. No provision of this Debenture, the
Purchase Agreement, the Registration Rights Agreement, the Amendment Agreement
or the Security Agreement shall alter or impair the obligation of the Company,
which is absolute and unconditional, to pay the principal of, and interest and
default payments on, this Debenture or to issue shares of Common Stock in
response to a Conversion Notice at the time, place and rate, and in the manner,
herein prescribed.

              15. WAIVERS OF DEMAND, ETC. The Company hereby expressly and
irrevocably waives demand and presentment for payment, notice of nonpayment,
protest, notice of protest, notice of dishonor, notice of acceleration or intent
to accelerate, bringing of suit and diligence in taking any action to collect
amounts called for hereunder and will be directly and primarily liable for the
payment of all sums owing and to be owing hereon, regardless of and without any
notice, diligence, act or omission as or with respect to the collection of any
amount called for hereunder.

              16. REPLACEMENT DEBENTURE. In the event that any Holder notifies
the Company that its Debenture(s) have been lost, stolen or destroyed,
replacement Debenture(s) identical in all respects to the original Debenture(s)
(except for registration number and Outstanding Principal Amount, if different
than that shown on the original Debenture(s)), shall be issued to the Holder,
provided that the Holder executes and
<PAGE>   16
delivers to the Company an agreement reasonably satisfactory to the Company to
indemnify the Company from any loss incurred by it in connection with such
Debenture.

              17. PAYMENT OF EXPENSES; ISSUE TAXES. The Company agrees to pay
all debts and expenses, including attorneys' fees, which may be incurred by the
Holder in enforcing the provisions of this Debenture and/or collecting any
amount due under this Debenture, any of the other New Transaction Documents or
any of the other July 2001 Transaction Documents. The Company shall pay any and
all issue and other taxes (excluding any income, franchise or similar taxes)
that maybe payable in respect of any issue or delivery of shares of Common Stock
on conversion of any Debenture pursuant hereto.

              18. DEFAULTS. If one or more of the following described "EVENTS OF
DEFAULT" shall occur:

                  (a) the Company shall default in the payment of (i) interest
on this Debenture or any other Debenture issued pursuant to the Purchase
Agreement (subject to the Company's option to pay PIK Interest), and such
default shall continue for five (5) business days after the due date thereof, or
(ii) the principal of this Debenture or any other Debenture issued pursuant to
the Purchase Agreement; or

                  (b) any of the representations or warranties made by the
Company herein, in the Purchase Agreement, the Registration Rights Agreement or
in any certificate or financial or other statements heretofore or hereafter
furnished by or on behalf of the Company in connection with the execution and
delivery of this Debenture or such other documents shall be false or misleading
at the time made; or

                  (c) the Company shall fail to materially perform or observe
any covenant or agreement in the Purchase Agreement or the Registration Rights
Agreement, or any other covenant, term, provision, condition, agreement or
obligation of the Company under this Debenture and such failure shall continue
uncured for a period of ten (10) business days after notice of such failure; or

                  (d) the Company shall (1) become insolvent; (2) admit in
writing its inability to pay its debts generally as they mature; (3) make an
assignment for the benefit of creditors or commence proceedings for its
dissolution; or (4) apply for or consent to the appointment of a trustee,
liquidator or receiver for it or for a substantial part of its property or
business; or

                  (e) a trustee, liquidator or receiver shall be appointed for
the Company or for a substantial part of its property or business without its
consent and shall not be discharged within forty-five (45) days after such
appointment; or

                  (f) any governmental agency or any court of competent
jurisdiction at the instance of any governmental agency shall assume custody or
control of the whole or any substantial portion of the properties or assets of
the Company and shall not be dismissed within forty-five (45) days thereafter;
or
<PAGE>   17

                  (g) the Company shall sell or otherwise transfer all or
substantially all of its assets and either (i) a material portion of the
consideration received by the Company is cash or (ii) the public shareholders of
the Company did not receive Change in Control Consideration; or

                  (h) bankruptcy, reorganization, insolvency or liquidation
proceedings or other proceedings, or relief under any bankruptcy law or any law
for the relief of debt shall be instituted by or against the Company and, if
instituted against the Company shall not be dismissed within forty-five (45)
days after such institution, or the Company shall by any action or answer
approve of, consent to, or acquiesce in any such proceedings or admit to any
material allegations of, or default in answering a petition filed in any such
proceeding; or

                  (i) the Company shall be in default of any other of its
indebtedness exceeding $1,000,000, or any other event shall have occurred, and
as a result thereof the holders thereof shall have accelerated or shall have the
right (upon the giving of notice, the passage of time, or both) to accelerate
such indebtedness; or

                  (j) a "going private" transaction under Rule 13e-3 promulgated
pursuant to the Exchange Act shall have been announced; or

                  (k) a tender offer by the Company under Rule 13e-4 promulgated
pursuant to the Exchange Act shall have been announced (i) on or before the
eighteen (18) month anniversary of the Closing Date, and/or (ii) to which the
Company is or will be required to dedicate more than 10% of its available cash
and marketable securities; or

                  (l) [INTENTIONALLY DELETED]; or

                  (m) the Company shall be in default under any of the July 2001
Transaction Documents (including, without limitation, breach of any of the
representations, warranties or covenants contained therein) and such default
continues beyond the applicable cure period provided therefor (if any); or

                  (n) the Company and/or one or more of its affiliates shall be
in default of any of its indebtedness or other obligations (including, without
limitation, obligations consisting of one or more covenants or agreements)
currently owed, or owing in the future, by the Company and/or any of its
affiliates to one or more Lenders (as defined in the Security Agreement and
expressly including their successors and/or assigns), and such default continues
beyond the applicable cure period provided therefor (if any) other than an Event
of Default solely arising under Section 8.1(8) of the Revolving Credit Agreement
(as defined in the Security Agreement); or

                  (o) the Company and/or one or more of its affiliates shall be
in default of any indebtedness or other obligation currently owed, or owing in
the future, by the Company and/or any of its affiliates provided that such
obligation involves an amount equal to or greater than $100,000, and such
default continues beyond the applicable cure period provided therefor (if any);
<PAGE>   18

         then, or at any time thereafter, and in each and every such case,
unless such Event of Default shall have been waived in writing by the Holder
(which waiver shall not be deemed to be a waiver of any subsequent default) at
the option of the Holder and in the Holder's sole discretion, the Holder may
consider the Debenture immediately due and payable, without presentment, demand,
protest or notice of any kind, all of which are hereby expressly waived,
anything herein or in any other instruments contained to the contrary
notwithstanding, and the Holder may immediately, and without expiration of any
period of grace, enforce any and all of the Holder's rights and remedies
provided herein or any other rights or remedies afforded by law. In such event,
the Debenture shall be redeemed at the greater of (i) 115% of the Redemption
Price and (ii) the cash value that the Holder would be entitled to receive upon
conversion of the Debenture at the Conversion Price in existence on such date,
without regard to Section 13, and the subsequent sale of the Common Stock at the
Market Price for Shares of Common Stock then existing.

         19. SAVINGS CLAUSE. In case any provision of this Debenture is held by
a court of competent jurisdiction to be excessive in scope or otherwise invalid
or unenforceable, such provision shall be adjusted rather than voided, if
possible, so that it is enforceable to the maximum extent possible, and the
validity and enforceability of the remaining provisions of this Debenture will
not in any way be affected or impaired thereby, and such provision shall remain
effective in all other jurisdictions.

         20. ENTIRE AGREEMENT. This Debenture, the other July 2001 Transaction
Documents, the other New Transaction Documents and the agreements referred to in
this Debenture and in such other documents constitute the full and entire
understanding and agreement between the Company and the Holder with respect to
the subject hereof. Neither this Debenture nor any term hereof may be amended,
waived, discharged or terminated other than by a written instrument signed by
the Company and the Holder.

         21. ASSIGNMENT, ETC. The Holder (but not the Company) may without
notice, transfer or assign this Debenture or any interest herein and may
mortgage, encumber or transfer any of its rights or interest in and to this
Debenture or any part hereof and, without limitation, each assignee, transferee
and mortgagee (which may include any affiliate of the Holder) shall have the
right to transfer or assign its interest. Each such assignee, transferee and
mortgagee shall have all of the rights of the Holder under this Debenture. The
Company agrees that, subject to compliance with the Purchase Agreement, after
receipt by the Company of written notice of assignment from the Holder or from
the Holder's assignee, all principal, interest and other amounts which are then
and thereafter become due under this Debenture shall be paid to such assignee at
the place of payment designated in such notice. This Debenture shall be binding
upon the Company and its successors and affiliates and shall inure to the
benefit of the Holder and its successors and assigns.

         22. NO WAIVER. No failure on the part of the Holder to exercise, and no
delay in exercising any right, remedy or power hereunder shall operate as a
waiver thereof, nor shall any single or partial exercise by the Holder of any
right, remedy or power hereunder preclude any other or future exercise of any
other right, remedy or power. Each and
<PAGE>   19

every right, remedy or power hereby granted to the Holder or allowed it by law
or other agreement shall be cumulative and not exclusive of any other, and may
be exercised by the Holder from time to time.

         23. CERTIFICATE. The Company shall, upon the written request at any
time of any Holder of Debentures, furnish or cause to be furnished to such
Holder a certificate prepared by the chief financial officer of Company setting
forth any adjustments or readjustments of the Conversion Price pursuant to this
Debenture and any right of the Holder to receive additional shares of Common
Stock or any other equity or debt security pursuant to Section 8.

         24. NOTICES.


             (a) The Company shall distribute to the Holders of Debentures
copies of all notices, materials, annual and quarterly reports, proxy
statements, information statements and any other documents distributed generally
to the holders of shares of Common Stock of the Company, at such times and by
such method as such documents are distributed to such holders of such Common
Stock, but shall not directly or indirectly provide material non-public
information to the Holder without such Holder's prior written consent.

             (b) Except as set forth above, any notice or other communication
required or permitted to be given hereunder shall be in writing by facsimile,
mail or personal delivery and shall be effective upon delivery of such notice.
Notices may (and, as may expressly be provided herein or in the Purchase
Agreement, in some cases, shall) also be delivered via e-mail in addition to the
foregoing. The addresses for such communications shall be:

                  to the Company:

                           224 Harrison Street, 8th Floor
                           Syracuse, NY  13202
                           Attn:  Chief Executive Officer
                           Facsimile: (212) 398-4142

                  with copies to:
<PAGE>   20

                           224 Harrison Street, 8th Floor
                           Syracuse, NY  13202
                           Attn:  Chief Financial Officer
                           Facsimile: (315) 479-0824

                  and with copies to:

                           224 Harrison Street, 8th Floor
                           Syracuse, NY  13202
                           Attn:  General Counsel
                           Facsimile: (315) 479-0824
                           E-mail:  rmechur@appliedtheory.com

                  to the Holder:

                          at the address and/or fax number set forth on Schedule
                          I to the Purchase Agreement.

                  with copies to:

                           Kleinberg, Kaplan, Wolff & Cohen, P.C.
                           551 Fifth Avenue
                           New York, New York 10176
                           Attention:       Stephen M. Schultz
                           Facsimile:       (212) 986-8866
                           E-mail:          sschultz@kkwc.com

                  Any party hereto may from time to time change its address for
notices by giving at least 10 days' written notice of such changed address to
the other parties hereto.

             25. SPECIFIC ENFORCEMENT. The Company agrees that irreparable
damage would occur in the event that any of the provisions of this Debenture
were not performed in accordance with their specific terms or were otherwise
breached. It is accordingly agreed that the Holders of Debentures shall be
entitled to swift specific performance, injunctive relief or other equitable
remedies to prevent or cure breaches of the provisions of this Debenture and to
enforce specifically the terms and provisions hereof, this being in addition to
any other remedy to which any of them may be entitled under agreement, at law or
in equity.

             26. MISCELLANEOUS. Unless otherwise provided herein, any notice or
other communication to a party hereunder shall be sufficiently given if in
writing and personally delivered, facsimiled or mailed to said party by
certified mail, return receipt requested, at its address set forth herein or
such other address as either may designate for itself in such notice to the
other and communications shall be deemed to have been received when delivered
personally or, if sent by mail or facsimile, then when actually received by the
party to whom it is addressed. Whenever the sense of this Debenture requires,
words in the singular shall be deemed to include the plural and words in the

<PAGE>   21

plural shall be deemed to include the singular. Paragraph headings are for
convenience only and shall not affect the meaning of this document.

             27. GOVERNING LAW; CONSENT TO JURISDICTION. THIS DEBENTURE SHALL BE
GOVERNED BY AND CONSTRUED AND ENFORCED IN ACCORDANCE WITH THE LAWS OF THE STATE
OF NEW YORK APPLICABLE TO CONTRACTS TO BE EXECUTED AND PERFORMED ENTIRELY WITHIN
SUCH STATE. THE COMPANY (I) HEREBY IRREVOCABLY SUBMITS TO THE EXCLUSIVE
JURISDICTION OF THE STATE AND FEDERAL COURT LOCATED IN NEW YORK COUNTY, NEW YORK
FOR THE PURPOSES OF ANY SUIT, ACTION OR PROCEEDING ARISING OUT OF OR RELATED TO
THIS DEBENTURE AND (II) HEREBY WAIVES, AND AGREES NOT TO ASSERT IN ANY SUCH
SUIT, ACTION OR PROCEEDING, ANY CLAIM THAT IT IS NOT PERSONALLY SUBJECT TO THE
JURISDICTION OF SUCH COURT, THAT THE SUIT, ACTION OR PROCEEDING IS BROUGHT IN AN
INCONVENIENT FORUM OR THAT THE VENUE OF THE SUIT, ACTION OR PROCEEDING IS
IMPROPER. THE COMPANY CONSENTS TO PROCESS BEING SERVED IN ANY SUCH SUIT, ACTION
OR PROCEEDING BY MAILING A COPY THEREOF TO SUCH PARTY AS PROVIDED HEREIN AND
AGREES THAT SUCH SERVICE SHALL CONSTITUTE GOOD AND SUFFICIENT SERVICE OF PROCESS
AND NOTICE THEREOF. NOTHING IN THIS PARAGRAPH SHALL AFFECT OR LIMIT ANY RIGHT TO
SERVE PROCESS IN ANY OTHER MANNER PERMITTED BY LAW.

                             SIGNATURE PAGE FOLLOWS


<PAGE>   22

         IN WITNESS WHEREOF, the Company has caused this instrument to be duly
executed by an officer thereunto duly authorized.



                         APPLIEDTHEORY CORPORATION



                         By:
                            -----------------------------------------------
                            Name:
                            Title:



             Signature page to 5% Convertible Debenture of APPLIEDTHEORY
CORPORATION