Document:

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                                                                     Exhibit 4.1

                               OMNIBUS AGREEMENT
                               -----------------

     OMNIBUS AGREEMENT (this "Agreement"), dated as of May 31, 2001, by and
between BOSTON LIFE SCIENCES, INC., a Delaware corporation (the "Company"), and
                                                                 -------
BROWN SIMPSON PARTNERS I, LTD., a Cayman Islands company (the "Holder").
                                                               ------

     Reference is made to each of the Series A and Series B Stock Purchase
Warrants set forth on Schedule I hereto (each a "Warrant", together the
                                                 -------
"Warrants") issued by the Company and held by the Holder, for the purchase of an
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aggregate of 1,690,000 shares of the Company's common stock, par value $.01 per
share (the "Common Stock"), subject to certain adjustments as set forth in the
            ------------
Warrants.  Capitalized terms used herein but not otherwise defined shall have
the meanings ascribed to such terms in the Warrants or the transaction documents
related thereto.

     The Company and the holder each hereby acknowledge and agree that Section
3(a) of each Warrant shall be null and void and of no further force and effect,
and replaced in its entirety with the following:

     "3.  Exercise Price.  The initial per share exercise price of this Warrant,
representing the price per share at which the shares of stock issuable upon
exercise of this Warrant may be purchased, is $4.625, subject to adjustment from
time to time pursuant to the provisions of Section 6 hereof (the "Exercise
Price")."

     The Company and the Holder each further hereby acknowledge and agree that
Section 6(i) of each Warrant only shall apply to situations where the Company
raises cash through the issuance of shares of its Common Stock or options,
warrants or other securities convertible or exchangeable therefore (other than
Excluded Services).  The Company and the Holder each further hereby acknowledge
and agree that Section 6(h)(i)(D)(V) ("Certain Events") shall be deleted and
shall have no force and effect.  All other provisions of the Warrants, except as
otherwise specifically set forth herein, shall remain in full force and effect.

     The current registration statement for the Warrants, which is presently
effective, shall remain effective in accordance with the terms of the
Registration Rights Agreement dated September 22, 1999, among the Company and
the Purchasers as set forth therein.

     The Company further acknowledges and agrees that, if requested by the
Holder at any time, it immediately will issue new warrants reflecting the
changes set forth herein, but acknowledges that such new warrants are not
necessary for the exercise of the Warrants in accordance with the provisions set
forth herein and therein.
<PAGE>

     In consideration of the foregoing, the Holder hereby acknowledges and
agrees that, through and including May 31, 2002, it only shall sell shares of
the Common Stock (including shares of the Common Stock issuable upon the
exercise of the Warrants) in accordance with the following:

     .    On any day when the Common Stock trades fewer than 100,001 shares, the
Holder may sell up to ten percent (10%) of the daily volume (on a net basis,
i.e., including sales and purchases) as traded on the Nasdaq or a Subsequent
----
Market (the "Daily Volume");
             ------------

     .    On any day when the Common Stock trades between 100,001 and 150,000
shares, the Holder may sell up to fifteen percent (15%) of the Daily Volume (on
a net basis);

     .    On any day when the Common Stock trades between 150,001 and 300,000
shares, the Holder may sell up to twenty percent (20%) of the Daily Volume (on a
net basis);

     .    On any day when the Common Stock trades between 300,001 and 700,000
shares, the Holder may sell up to twenty-five (25%) of the Daily Volume (on a
net basis); and

     .    On any day when the Common Stock trades in excess of 700,000 shares,
the Holder may sell up to thirty percent (30%) of the Daily Volume (on a net
basis).

provided further, however, that on any Trading Day when the Common Stock closes
-------- -------  -------
above $8.00 per share, each of the above percentages shall be increased by five
percent (5%) for that Trading Day; provided further, however, that on any
                                   -------- -------  -------
Trading Day when the Common Stock closes above $10.00 per share, each of the
above percentages shall be increased by ten percent (10%) for that Trading Day;
provided further, however, that on any Trading Day when the Common Stock closes
-------- -------  -------
above $12.00 per share, there shall be no restriction on the number of shares of
Common Stock that the Holder may sell on that Trading Day.  (The trading
activity set forth in the foregoing five bullet points hereinafter shall be
referred to as the "Permitted Sales").  Notwithstanding the foregoing, the
Holder may not sell Common Stock constituting 25% or more of the Daily Volume
for more than two (2) consecutive Trading Days; provided, however,  that the
                                                --------  -------
restriction contained in the immediately preceding clause shall not apply if the
Common Stock closes above $8.00 per share.  Nothing contained herein shall
restrict the ability of the Holder to sell any number of shares of Common Stock
in a direct placement with a single purchaser or group of purchasers, such as
direct placement to be made on an off-market basis.

     The Holder hereby agrees that, without the prior written consent of the
Company, neither it nor its affiliates will through and including May 31, 2002,
in excess of the Permitted Sales, (i) offer, pledge, sell, contract to sell,
sell any option or contract to purchase, purchase any option or contract to
sell, grant any option, right or warrant to purchase, lend, or otherwise
transfer or dispose of, directly or indirectly, any shares of the Common Stock
or any securities convertible into or exercisable or exchangeable for shares of
the Common Stock (including, inter alia, the Warrants) or (ii) enter into any
                             ----- ----
swap or other arrangement that transfers to another, in whole or in part, any of
the economic consequences of ownership of shares of the Common Stock, whether
any such transaction described in clause (i) or (ii) above is to be settled by
delivery of shares of the Common Stock or other securities, in cash or
otherwise.  The foregoing sentence shall not apply to, or in any way affect,
(a) the Permitted Sales or (b) transfers to the Holder's investors, partners
(general or
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limited), shareholders, members, or affiliates, provided, however, that in the
                                                -----------------
case of (b), the transferee must agree to be bound by the restrictions set forth
in this Agreement.

     Any copy of this Agreement containing a facsimile signature page shall be
deemed an original. This Agreement shall be governed by and construed in
accordance with the laws of the State of New York applicable to agreements made
and to be performed within that State, without regard to the conflicts of laws
principles thereof.

     At the sole option of the Holder, the Company will be obligated to issue an
additional 50,000 common shares (with piggyback rights of registration) to the
Holder, provided the Holder elects to restrict its sale of stock at prices over
$12 not to exceed the amounts permitted (as above described) for the $10 price
level. This option to give up unrestricted sales over the $12 price level will
apply only if at the time of such election (made through notification to the
Company by the Holder) prior to January 1, 2002, the Holder still owns at least
one million shares in the aggregate counting both common stock and unexercised
warrants.

BOSTON LIFE SCIENCES, INC.

/s/ David Hillson
----------------------------
Name:  David Hillson
Title:  Chairman & CEO

Acknowledged and Agreed:

BROWN SIMPSON PARTNERS I, LTD.

/s/ Peter D. Greene
----------------------------
Peter D. Greene
Attorney-In-Fact
<PAGE>

                                  SCHEDULE I
                                  ----------

Warrant Series/No.           Registered Owner         Number of Shares
-----------------            ----------------         ----------------

A/1                   Brown Simpson Partners I, Ltd.           776,000

A/2                   Brown Simpson Partners I, Ltd.           194,000

B/1                   Brown Simpson Partners I, Ltd.           576,000

B/2                   Brown Simpson Partners I, Ltd.           144,000<PAGE>

                                                                     Exhibit 4.2

                              FIRST AMENDMENT TO
                          BOSTON LIFE SCIENCES, INC.
              WARRANTS FOR THE PURCHASE OF SHARES OF COMMON STOCK
                         NOS. BLSI - J-146 AND - J-147

     FIRST AMENDMENT TO WARRANTS (the "First Amendment") made and entered into
as of May 27, 2001, by and among Boston Life Sciences, Inc., a Delaware
corporation (the "Company"), and Pictet Global Sector-Fund Biotech (the
"Holder").

     REFERENCE is hereby made to the Boston Life Sciences, Inc. Warrant for the
Purchase of Shares of Common Stock Nos. BLSI - J-146 and - J-147 issued pursuant
to that certain Purchase Agreement among the Company and the Holder dated as of
May 26, 2000 (the "Warrants").

     WHEREAS, the Holder and the Company are in the process of negotiating in
good faith potential mutually beneficial amendments to the Warrants, which
negotiations have not yet concluded;

     WHEREAS, in consideration of and in order to provide additional time for
completion of such negotiations, the Holder and the Company desire to amend
certain time-sensitive provisions of each of the Warrants as set forth herein.

     NOW, THEREFORE, the parties to this Amendment agree as follows:

     1.   Amendment to Warrant No. BLSI - J-146.  The second sentence of the
          -------------------------------------
introductory paragraph of Warrant No. BLSI - J-146  (which sentence begins "If
the weighted average sales price per share") is hereby deleted and replaced in
its entirety with the following:

          "If the weighted average sales price per share of common stock of the
     company (as reported by Bloomberg Financial Services) for the 20 trading
     days ending on June 1, 2001 is less than $8.00 per share, then the exercise
     price of the warrant will be adjusted to the lower of (x) the weighted
                                                  --------
     average sales price per share of common stock of the company (as reported
     by Bloomberg Financial Services) for the 20 trading days ending on June 1,
     2001 and (y) the weighted average sales price per share of common stock of
     the company (as reported by Bloomberg Financial Services) for the 20
     trading days ending on June 15, 2001 (such lower price, the "Reset Price"),
     any such adjustment to be calculated and become effective as of June 16,
     2001."

     2.   Amendment to Warrant No. BLSI - J-147.  The second sentence of the
          -------------------------------------
introductory paragraph of Warrant No. BLSI - J-147  (which sentence begins "If
the weighted average sales price per share") is hereby deleted and replaced in
its entirety with the following:

          "If the weighted average sales price per share of common stock of the
     company (as reported by Bloomberg Financial Services) for the 20 trading
     days ending on June 1, 2001 is less than $10.00 per share, then the
     exercise price of the warrant will be adjusted to the lower of (x) the
                                                           --------
     weighted average sales price per share of common stock of the company (as
     reported by Bloomberg Financial Services) for the 20 trading days ending on
     June 1, 2001 and (y) the weighted average sales price per share of common
     stock of the company (as reported by
<PAGE>

     Bloomberg Financial Services) for the 20 trading days ending on June 15,
     2001 (such lower price, the "Reset Price"), any such adjustment to be
     calculated and become effective as of June 16, 2001."

     3.   Parties in Interest. All the terms and provisions of this First
          -------------------
Amendment shall be binding upon and inure to the benefit of and be enforceable
by the respective successors and permitted assigns of the parties hereto, and,
in particular, shall inure to the benefit of and be enforceable by any holder of
the Warrants, or its permitted assigns. This First Amendment shall be treated
for all purposes as having been incorporated into and become a part of each of
the Warrants and any party furnishing a copy of a Warrant to any person shall
furnish a copy of this First Amendment therewith.

     4.   Headings; Governing Law.  Sections 10 and 11 of the Warrants are
          -----------------------
incorporated herein by reference and shall govern this First Amendment in the
same manner as if set forth in its entirety herein.

     5.   Counterparts. This First Amendment may be executed concurrently in two
          ------------
or more counterparts, each of which shall be deemed an original, but all of
which together shall constitute one and the same instrument.

     6.   No Other Change. Except to the extent specifically amended hereby, the
          ---------------
provisions of the Warrants shall remain unmodified and the Warrants as amended
hereby are hereby confirmed as being in full force and effect.
<PAGE>

     IN WITNESS WHEREOF, the Company and the Holder have executed this First
Amendment as of the date and year first above written.

BOSTON LIFE SCIENCES, INC.

By: /s/ S. David Hillson
---------------------------------
Name:  S. David Hillson
Title:  Chairman, President and
Chief Executive Officer

PICTET GLOBAL SECTOR FUND-BIOTECH

By: /s/ Yves Martignier
---------------------------------
Name:  Yves Martignier
Title: Director

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