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                                                                    Exhibit 4.11


                                  AGREEMENT


        AGREEMENT (this "Agreement"), dated as of October 29, 1997, between
Southbrook International Investments, Ltd., a corporation organized and
existing under the laws of the British Virgin Islands ("Southbrook"), Brown
Simpson Strategic Growth Fund, LP, a limited partnership existing under the
laws of Delaware ("Brown Simpson"), and Illinois Superconductor Corporation, a
corporation organized and existing under the laws of Delaware (the "Company").

        WHEREAS, Southbrook and the Company entered into a Convertible
Preferred Stock Purchase Agreement, dated as of June 6, 1997 (the "Purchase
AGreement"), providing for, among other things, the issuance and sale to
Southbrook of shares of its Series C Convertible Preferred Stock (the "Series C
Stock") and a registration rights agreement, dated as of June 6, 1997 (the
"Registration Rights Agreement"), with respect to the registration of the
Series C Stock, among other things;

        WHEREAS, the parties desire to modify the terms of the Purchase
Agreement and the Registration Rights Agreement as follows:

        1.      Capitalized terms used and not otherwise deffined herein shall
have the respective meanings set forth in the Purchase Agreement.

        2.      Notwithstanding anything to the contrary contained in the
Purchase Agreement, the parties agree that shares of Series C Stock shall be
issued in consideration for the purchase price per share of $5,000 as follows:

                (a)   The Company shall issue to Southbrook two-hundred, ninety
(290) shares registered in the name of Southbrook of Series C Stock on the
closing date for the transactions contemplated hereby; and

                (b)   The Company shall issue to Brown Simpson ten (10) shares
of Series C Stock registered in the name of Brown Simpson (the "Brown Simpson
Shares").

        3.      Brown Simpson hereby represents and warrants to the Company as
follows:

                (a)   Brown Simpson is acquiring the Brown Simpson Shares and
the Underlying Shares relating thereto for its own account for investment
purposes only and not with a view to or for distributing or reselling such
Brown Simpson Shares or Underlying Shares or any part thereof or interest
therein, without prejudice, however, to Brown Simpson's right, subject to the
provisions of the Purchase Agreement, at all times to sell or otherwise to
dispose of all or any part of the Brown Simpson Shares and the Underlying
Shares pursuant to an effective registration statement under the Securities Act
and in compliance with applicable State securites laws or under an exemption
from such registration.


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                (b)  At the time Brown Simpson was offered the Brown Simpson
Shares, it was, and at the date hereof, it is, an "accredited investor", as
defined in Rule 501(a):(1), (2), (3) or (7) under the Securities Act.

                (c)  Brown Simpson, either alone or together with its
representatives, has such knowledge, sophistication and experience in business
and financial matters so as to be capable of evaluating the merits and risks of
the prospective investment in the Brown Simpson Shares and the Underlying
Shares, and has so evaluated the merits and risks of such investment.

                (d)  Brown Simpson is able to bear the economic risk of an
investment in the Brown Simpson Shares and the Underlying Shares and, at the
present time, is able to afford a complete loss of such investment.

                (e)  The Brown Simpson Shares to be purchased by Brown Simpson
are not being acquired, directly or indirectly, with the assets of any
"employee benefit plan," within the meaning of Section 3(3) of the Employee
Retirement Income Security Act of 1974, as amended.

                (f)  Brown Simpson acknowledges that it has been afforded (i)
the opportunity to ask such questions as it has deemed necessary of, and to
receive answers from representatives of the Company concerning the terms and
conditions of the offering of the Brown Simpson Shares; (ii) access to
information about the Company and the Company's financial condition, results of
operations, business, properties, management and prospects sufficient to enable
it to evaluate its investment; and (iii) the opportunity to obtain such
additional information which the Company possesses or can acquire without
unreasonable effort or expense that is necessary to make an informed investment
decision with respect to the investment and to verify the accuracy and
completeness of the information contained in the Disclosure Materials.

                (g)  Brown Simpson understands and acknowledges that (i) the
Brown Simpson Shares are being offered and sold to it without registration
under the Securities Act in a private placement that is exempt from the
registration provisions of the Securities Act under Regulation D promulgated
thereunder and (ii) the availability of such exemption depends in part on, and
the Company will rely upon the accuracy and truthfulness of, the foregoing
representations and Brown Simpson hereby consents to such reliance.

        4.      Brown Simpson and the Company agree to comply with the terms
and conditions of Section 3.1 of the Purchase Agreement with respect to the
Brown Simpson Shares and the Underlying Shares.

        5.      Brown Simpson shall be deemed a party to the Registration
Rights Agreement solely with respect to the registration of the Underlying
Shares issuable upon conversion of the Brown Simpson Shares issued to Brown
Simpson hereunder.


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        6.      Except as modified herein, the Purchase Agreement and the
Registration Rights Agreement shall remain in full force and effect.

        7.      The address for notice to Brown Simpson is 152 West 57th
Street, 4th Floor, New York, New York 10019, Attn: Matthew C. Brown.

        IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be
duly executed by their respective authorized person as of the date first
indicated above.

                                              ILLINOIS SUPERCONDUCTOR
                                               CORPORATION



                                              By: /s/ Stephen G. Wasko       
                                                 ------------------------------ 
                                                 Name: Stephen G. Wasko 
                                                 Title: Senior Vice President &
                                                        Chief Financial Officer



                                              SOUTHBROOK INTERNATIONAL
                                              INVESTMENTS, LTD.



                                              By: /s/ Kenneth Henderson
                                                 ------------------------------ 
                                                 Kenneth L. Henderson 
                                                 Assistant Secretary



                                              BROWN SIMPSON STRATEGIC
                                              GROWTH FUND, LP



                                              By: /s/ MCB
                                                 ------------------------------ 
                                                 Name:                      
                                                 Title:                     
                                                
                                                

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