<PAGE>

THESE SECURITIES HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933 OR
ANY APPLICABLE STATE SECURITES LAWS. THEY MAY NOT BE SOLD, OFFERED FOR SALE,
PLEDGED OR HYPOTHECATED OR OTHERWISE TRANSFERRED IN THE ABSENCE OF A
REGISTRATION STATEMENT IN EFFECT WITH RESPECT TO THE SECURITIES UNDER SUCH ACT
OR AN OPINION OF COUNSEL SATISFACTORY TO THE COMPANY THAT SUCH REGISTRATION IS
NOT REQUIRED OR UNLESS SOLD PURSUANT TO RULE 144 OF SUCH ACT. ANY SUCH TRANSFER
MAY ALSO BE SUBJECT TO APPLICABLE STATE SECURITIES LAWS.



                                 ENDOREX CORP.



                     Warrant for the Purchase of Shares of
                     -------------------------------------
                                 Common Stock
                                 ------------


No. 2                                                             650,000 Shares


     FOR VALUE RECEIVED, ENDOREX CORP., a Delaware corporation (the "Company"),
hereby certifies that ARIES FUND, a Cayman Islands Trust, or its permitted
assigns, is entitled to purchase from the Company, at any time or from time to
time commencing on May 19, 1997, and prior to 5:00 P.M., New York City time, on
May 19, 2002 (the "Termination Date"), six-hundred and fifty-thousand (650,000)
fully paid and non-assessable shares of the Common Stock, $.001 par value per
share, of the Company at an exercise price equal to the Offering Price (as
defined in the PPM) of the Common Stock of the Company issued in connection with
the Company's current private placement offering pursuant to the confidential
Term Sheet dated May 19, 1997 (as hereafter supplemented and amended, the "PPM")
(Hereinafter, (i) said Common Stock, together with any other equity securities
which may be issued by the Company with respect thereto or in substitution
therefor, is referred to as the "Common Stock", (ii) the shares of the Common
Stock purchasable hereunder or under any other Warrant (as hereinafter defined)
are referred to as the "Warrant Shares", (iii) the aggregate purchase price
payable for the Warrant Shares hereunder is referred to as the "Aggregate
Warrant Price", (iv) the price payable for each of the Warrant Shares hereunder
is referred to as the "Per Share Warrant Price", (v) this Warrant, all similar
Warrants issued on the date hereof and all warrants hereafter issued in exchange
or substitution for this Warrant or such similar warrants are referred to as the
"Warrants" and (vi) the holder of this Warrant is referred to as the "Holder"
and the holder of this Warrant and all other Warrants or Warrant Shares issued
upon the exercise of any Warrant are referred to as the "Holders"). The
Aggregate Warrant Price is not subject to adjustment. The Per Share Warrant
Price is subject to adjustment as hereinafter provided; in the event of any such
adjustment, the number of Warrant
                                       1
<PAGE>

Shares shall be adjusted by dividing the Aggregate Warrant Price by the Per
Share Warrant Price in effect immediately after such adjustment.


1.   Exercise of Warrant
     -------------------

     (a)  This Warrant may be exercised, in whole at any time or in part from
time to time, commencing on May 19, 1997 and prior to the Termination Date, by
the holder:

     (i) by the surrender of this Warrant (with the subscription form at the end
hereof duly executed) at the address set forth in Subsection 9 (a) hereof,
together with proper payment of the Aggregate Warrant Price, or the
proportionate part thereof if this Warrant is exercised in part, with payment
for Warrant Shares made by certified or official bank check payable to the order
of the Company; or

     (ii) by the surrender of this Warrant (with the cashless exercise form at
the end hereof duly executed) (a "Cashless Exercise") at the address set forth
in Subsection 9 (a) hereof. Such presentation and surrender shall be deemed a
waiver of the Holder's obligation to pay the Aggregate Warrant Price, or the
proportionate part thereof if this Warrant is exercised in part. In the event of
a Cashless Exercise, the Holder shall exchange its Warrant for that number of
Warrant Shares subject to such Cashless Exercise multiplied by a fraction, the
numerator of which shall be the difference between the then current Market Price
per share (as hereinafter defined) of Common Stock and the Per Share Warrant
Price, and the denominator of which shall be the then current Market Price per
share of Common Stock. The then current market price per share of the Common
Stock at any date (the "Market Price") shall be deemed to be the last sale price
of the Common Stock on the business day prior to the date of the Cashless
Exercise or, in case no such reported sales take place on such day, the average
of the last reported bid and asked prices of the Common Stock on such day, in
either case on the principal national securities exchange on which the Common
Stock is admitted to trading or listed, or if not listed or admitted to trading
on any such reported by the NASDAQ Bulletin Board ("NASDAQ"), or other similar
organization if NASDAQ is no longer reporting such information, or it not so
available, the fair market price of the Common Stock as determined in good faith
by the Board of Directors.

     (b) If this Warrant is exercised in part, this Warrant must be exercised
for a number of whole shares of the Common Stock and the Holder is entitled to
receive a new Warrant covering the Warrant Shares which have not been exercised
and setting forth the proportionate part of the Aggregate Warrant Price
applicable to such Warrant Shares. Upon surrender of this Warrant, the Company
will (i) issue a certificate or certificates in the name of the Holder for the
largest number of whole shares of the Common Stock to which the Holder shall be
entitled and, if this Warrant is exercised in whole, in lieu of any fractional
share of the Common Stock to which the Holder shall be entitled, pay to the
Holder cash in an amount equal to the fair value of such fractional share
(determined in such reasonable manner as the Board of Directors of the Company
shall determine), and (ii) deliver the other securities and properties
receivable upon the exercise of this Warrant, if any, or the proportionate part
thereof if this Warrant is exercised in part, pursuant to the provisions of this
Warrant.

                                       2
<PAGE>

     2. Reservation of Warrant Share; Listing. The Company agrees that, prior to
the expiration of this Warrant, the Company will at all times (a) have
authorized and in reserve, and will keep available, solely for issuance or
delivery upon the exercise of this Warrant, the shares of the Common Stock and
other securities and properties as from time to time shall be receivable upon
the exercise of this Warrant, free and clear of all restrictions on sale or
transfer, except for the restrictions on sale or transfer set forth in the
Securities Act of 1933, as amended (the "Act"), and restrictions created by or
on behalf of the Holder, and free and clear of all preemptive rights and rights
of first refusal; and (b) when the Company prepares and files a registration
statement covering the shares of Common Stock issued or issuable upon exercise
of this Warrant with the Securities and Exchange Commission (the "SEC") which
registration statement is declared effective by the SEC under the Act and the
Company lists its Common Stock on any national securities exchange or other
quotation system, it will use its reasonable best efforts to cause the shares of
Common Stock subject to this Warrant to be listed on such exchange or quotation
system.

     3. Protection Against Dilution.
     ------------------------------

     (a) If, at any time or from time to time after the date of this Warrant,
the Company shall issue or distribute to the holders of shares of Common Stock
evidence of its indebtedness, any other securities of the Company or any cash,
property or other assets (excluding a subdivision, combination or
reclassification, or dividend or distribution payable in shares of Common Stock,
referred to in Subsection 3 (b), and also excluding cash dividends or cash
distributions paid out of net profits legally available therefor in the full
amount thereof, which together with the value of other dividends and
distributions made substantially concurrently therewith or pursuant to a plan
which includes payment thereof, is equivalent to not more than 5% of the
Company's net worth) (any such non-excluded event being herein called a "Special
Dividend"), the Per Share Warrant Price shall be adjusted by multiplying the Per
Share Warrant Price then in effect by a fraction, the numerator of which shall
be the then current Market Price of the Common Stock less the fair market value
(as determined in good faith by the Company's Board of Directors) of the
evidence of indebtedness, cash, securities or property, or other assets issued
or distributed in such Special Dividend applicable to one share of Common Stock
and the denominator of which shall be the then current Market Price of the
Common Stock. An adjustment made pursuant to this Subsection 3 (a) shall become
effective immediately after the record date of any such Special Dividend.

     (b) In case the Company shall hereafter (i) pay a dividend or make a
distribution on its capital stock in shares of Common Stock, (ii) subdivide its
outstanding shares of Common Stock into a greater number of shares, (iii)
combine its outstanding shares of Common Stock into a smaller number of shares
or (iv) issue by reclassification of its Common Stock any shares of capital
stock of the Company, the Per Share Warrant Price shall be adjusted to be equal
to a fraction, the numerator of which shall be the Aggregate Warrant Price and
the denominator of which shall be the number of shares of Common Stock or other
capital stock of the Company which he would have owned immediately following
such action had such Warrant been exercised immediately prior thereto. An
adjustment made pursuant to this Subsection 3 (b) shall become effective
immediately after the record date in the case of a dividend or distribution and
shall become effective immediately after the effective date in the case of a
subdivision, combination or reclassification.

                                       3
<PAGE>

     (c) Except as provided in Subsections 3 (a) and 3 (d), in case the Company
shall hereafter issue or sell any Common Stock, any securities convertible into
Common Stock or any rights, options or warrants to purchase Common Stock or
securities convertible into Common Stock, in each case for a price per share or
entitling the holders thereof to purchase Common Stock at a price per share
(determined by dividing (i) the total amount, if any, received or receivable by
the Company in consideration of the issuance or sale of such securities plus the
total consideration, if any, payable to the Company upon exercise or conversion
thereof (the "Total Consideration") by (ii) the number of additional shares of
Common Stock issuable upon exercise or conversion of such securities) less than
the then either the current Market Price of the Common Stock or the current Per
Share Warrant Price in effect on the date of such issuance or sale, the Per
Share Warrant Price shall be adjusted by multiplying the Per Share Warrant Price
then in effect by a fraction, the numerator of which shall be (x) the sum of (A)
the number of shares of Common Stock outstanding on the date of such issuance or
sale plus (B) the Total Consideration divided by either the current Market Price
of the Common Stock or the current Per Share Warrant Price, whichever is
greater, and the denominator of which shall be (y) the number of shares of
Common Stock outstanding on the date of such issuance or sale plus the maximum
number of additional shares of Common Stock issued, sold or issuable upon
exercise or conversion of such securities.

     (d) No adjustment in the Per Share Warrant Price shall be required in the
case of the issuance by the Company of (i) Common Stock pursuant to the exercise
or conversion of any Warrant or any other options, warrants or any convertible
securities currently outstanding or outstanding as a result of securities issued
pursuant to the PPM; provided, that the exercise price or conversion price at
which such options, warrants or convertible securities are exercised or
converted, as the case may be, is equal to the exercise price or conversion
price in effect as of the date of this Warrant or as of the date of issuance
with respect to securities issued pursuant to the PPM (except for standard anti-
dilution adjustments) and (ii) shares of Common Stock issued or sold pursuant to
stock purchase or stock option plans or other similar arrangements that are
approved by the Company's Board of Directors.

     (e) In case of any capital reorganization or reclassification, or any
consolidation or merger to which the Company is a party other than a merger or
consolidation in which the Company is the continuing corporation, or in case of
any sale or conveyance to another entity of the property of the Company as an
entirety or substantially as an entirety, or in the case of any statutory
exchange of securities with another corporation (including any exchange effected
in connection with a merger of a third corporation into the Company), the Holder
of this Warrant shall have the right thereafter to receive on the exercise of
this Warrant the kind and amount of securities, cash or other property which the
Holder would have owned or have been entitled to receive immediately after such
reorganization, reclassification, consolidation, merger, statutory exchange,
sale or conveyance had this Warrant been exercised immediately prior to the
effective date of such reorganization, reclassification, consolidation, merger,
statutory exchange, sale or conveyance and in any such case, if necessary,
appropriate adjustment shall be made in the application of the provisions set
forth in this Section 3 with respect to the rights and interests thereafter of
the Holder of this Warrant to the end that the provisions set forth in this
Section 3 shall thereafter correspondingly be made applicable, as nearly as may
reasonably be, in relation to any shares of stock or other securities or
property thereafter deliverable on the exercise of this Warrant. The above
provisions of this Subsection 3 (e) shall similarly apply to successive
reorganizations, reclassifications, consolidations, mergers,

                                       4
<PAGE>

statutory exchanges, sales or conveyances. The issuer of any shares of stock or
other securities or property thereafter deliverable on the exercise of this
Warrant shall be responsible for all of the agreements and obligations of the
Company hereunder. Notice of any such reorganization, reclassification,
consolidation, merger, statutory exchange, sale or conveyance and of said
provisions so proposed to be made, shall be mailed to the Holders of the
Warrants not less than 30 days prior to such event. A sale of all or
substantially all of the assets of the Company for a consideration consisting
primarily of securities shall be deemed a consolidation or merger for the
foregoing purposes.

     (f) In case any event shall occur as to which the other provisions of this
Section 3 are not strictly applicable but as to which the failure to make any
adjustment would not fairly protect the purchase rights represented by this
Warrant in accordance with the essential intent and principles hereof then, in
each such case, the Holders of Warrants representing the right to purchase a
majority of the Warrant Shares subject to all outstanding Warrants may appoint a
firm of independent public accountants of recognized national standing
reasonably acceptable to the Company, which shall give their opinion as to the
adjustment, if any, on a basis consistent with the essential intent and
principles established herein, necessary to preserve the purchase rights
represented by the Warrants. Upon receipt of such opinion, the Company will
promptly mail a copy thereof to the Holder of this Warrant and shall make the
adjustments described therein. The fees and expenses of such independent public
accountants shall be borne by the Company.

     (g) No adjustment in the Per Share Warrant Price shall be required unless
such adjustment would require an increase or decrease of at least $0.05 per
share of Common Stock; provided, however, that any adjustments which by reason
of this Subsection 3 (g) are not required to be made shall be carried forward
and taken into account in any subsequent adjustment; provided, further, however,
that adjustments shall be required and made in accordance with the provisions of
this Section 3 (other than this Subsection 3 (g)) not later than such time as
may be required in order to preserve the tax-free nature of a distribution to
the Holder of this Warrant or Common Stock issuable upon the exercise hereof.
All calculations under this Section 3 shall be made to the nearest cent or to
the nearest 1/100th of a share, as the case may be. Anything in this Section 3
to the contrary notwithstanding, the Company shall be entitled to make such
reductions in the Per Share Warrant Price, in addition to those required by this
Section 3, as it in its discretion shall deem to be advisable in order that any
stock dividend, subdivision of shares or distribution of rights to purchase
stock or securities convertible or exchangeable for stock hereafter made by the
Company to its stockholders shall not be taxable.

     (h) Whenever the Per Share Warrant Price is adjusted as provided in this
Section 3 and upon any modification of the rights of a Holder of Warrants in
accordance with this Section 3, the Chief Financial Officer of the Company shall
promptly prepare a certificate setting forth the Per Share Warrant Price and the
number of Warrant Shares after such adjustment or the effect of such
modification and a brief statement of the facts requiring such adjustment or
modification and the manner of computing the same and cause copies of such
certificate to be mailed to the Holders of the Warrants. In the event of a
dispute with respect to any adjustment required pursuant to Section 3, the
Holder may appoint, at the Company's expense, an independent financial advisor
(e.g. an investment banking or accounting firm) reasonably acceptable to the
Company to calculate such adjustment. Such determination shall be binding upon
the Holder and the Company.

                                       5
<PAGE>

     (i) If the Board of Directors of the Company shall declare any dividend or
other distribution with respect to the Common Stock, the Company shall mail
notice thereof to the Holders of the Warrants not less than 15 days prior to the
record date fixed for determining stockholders entitled to participate in such
dividend or other distribution.

     (j) If, as a result of an adjustment made pursuant to this Section 3, the
Holder of any Warrant thereafter surrendered for exercise shall become entitled
to receive shares of two or more classes of capital stock or shares of Common
Stock and other capital stock of the Company, the Board of Directors (whose
determination shall be conclusive and shall be described in a written notice to
the Holder of any Warrant promptly after such adjustment) shall determine the
allocation of the adjusted Per Share Warrant Price between or among shares or
such classes of capital stock or shares of Common Stock and other capital stock.

     4. Fully Paid Stock; Taxes. The Company agrees that the shares of the
Common Stock represented by each and every certificate of Warrant Shares
delivered on the exercise of this Warrant be validly issued and outstanding,
fully paid and nonassessable, and not subject to preemptive rights or rights of
first refusal, and the Company will take all such actions as may be necessary to
assure that the par value or stated value, if any, per share of the Common Stock
is at all times equal to or less than the then Per Share Warrant Price. The
Company further covenants and agrees that it will pay, when due and payable, any
and all Federal and state stamp, original issue or similar taxes which may be
payable in respect of the issue of any Warrant Share or any certificate thereof.

     5. Registration Under Securities Act of 1933.
        -----------------------------------------

     (a) The Company shall include the Warrant Shares on the Shelf Registration
Statement (as defined in the PPM) and the Holder shall otherwise have the
registration rights set forth in Section 5 of the subscription agreement (the
"Subscription Agreement") to be entered into between the purchasers of units (as
described in the PPM) and the Company. By acceptance of this Warrant, the Holder
agrees that it shall have the same obligations, and otherwise comply with, the
provisions in such Section 5 of the Subscription Agreement to same extent as if
it were a party thereto. To the extent that no Final Closing Date (as defined in
the Subscription Agreement) occurs or the Offering is terminated, the rights
granted to Holder hereunder to have its shares registered shall begin as of
November 19, 1997 on the same terms as provided in Section 5 of the Subscription
Agreement.

     (b) Until all Warrant Shares have been sold under a Registration Statement
or pursuant to Rule 144, the Company shall use its reasonable best efforts to
file with the Securities and Exchange Commission all current reports and the
information as may be necessary to enable the Holder to effect sales of its
shares in reliance upon Rule 144 promulgated under the Act.

     6. Limited Transferability. This Warrant may not be sold, transferred,
assigned or hypothecated by the Holder except in compliance with the provisions
of the Act and the applicable state securities "blue sky" laws. The Company may
treat the registered Holder of this Warrant as he or it appears on the Company's
books at any time as the Holder for all purposes. The Company shall permit any
Holder of a Warrant or his duly authorized attorney, upon written request during
ordinary business hours, to inspect and copy or make extracts from

                                       6
<PAGE>

its books showing the registered holders of Warrants. All warrants issued upon
the transfer or assignment of this Warrant will be dated the same date as this
Warrant, and all rights of the holder thereof shall be identical to those of the
Holder.

     7. Loss, etc., of Warrant. Upon receipt of evidence satisfactory to the
Company of the loss, theft, destruction or mutilation of this Warrant, and of
indemnity reasonably satisfactory to the Company, if lost, stolen or destroyed,
and upon surrender and cancellation of this Warrant, if mutilated, the Company
shall execute and deliver to the Holder a new Warrant of like date, tenor and
denomination.

     8. Warrant Holder Not Shareholder. Except as otherwise provided herein,
this Warrant does not confer upon the Holder any right to vote or to consent to
or receive notice as a stockholder of the Company, as such, in respect of any
matters whatsoever, or any other rights or liabilities as a stockholder, prior
to the exercise hereof.

     9. Communication. No notice or other communication under this Warrant shall
be effective unless, but any notice or other communication shall be effective
and shall be deemed to have been given if, the same is in writing and is mailed
by first-class mail, postage prepaid, addressed to:

     (a) the Company at 900 North Shore Drive, Lake Bluff, IL, 60044, Attention:
Chief Executive Officer or other address as the Company has designated in
writing to the Holder, or

     (b) the Holder at c/o Paramount Capital Asset Management, Inc., 787 Seventh
Avenue, New York, NY, 10019, Attn: Lindsay A. Rosenwald, M.D. or other such
address as the Holder has designated in writing to the Company.

     10. Headings. The headings of this Warrant have been inserted as a matter
of convenience and shall not affect the construction hereof.

     11. Applicable Law. This Warrant shall be governed by and construed in
accordance with the law of the State of New York without giving effect to the
principles of conflicts of law thereof.

                                       7
<PAGE>

          IN WITNESS WHEREOF, the Company has caused this Warrant to be signed
by its President and its corporate seal to be hereunto affixed and attested by
its Secretary this 19th day of May 1997.


                                                ENDOREX CORP.



                                    By:     ___________________________________
                                            Michael S. Rosen
                                            President & Chief Executive Officer



ATTEST:



__________________________
Treasurer

[Corporate Seal]

                                       8
<PAGE>

                                 SUBSCRIPTION
                                 ------------

          The undersigned, ___________________, pursuant to the provisions of
the foregoing Warrant, hereby agrees to subscribe for and purchase
______________________ shares of the Common Stock, par value $.00l per share, of
Endorex, Corp. covered by said Warrant, and makes payment therefor in full at
the price per share provided by said Warrant.

Dated: ___________________                 Signature:___________________

                                           Address: ____________________

                                       9
<PAGE>

                               CASHLESS EXERCISE
                               -----------------

          The undersigned, ____________________, pursuant to the provisions of
the foregoing Warrant, hereby elects to exchange its Warrant for ______________
shares of Common Stock, par value $.001 per share, of Endorex Corp. pursuant to
the Cashless Exercise provisions of the Warrant.

Dated:____________________                  Signature: ___________________

                                            Address: _____________________

                                      10
<PAGE>

                                  ASSIGNMENT
                                  ----------

          FOR VALUE RECEIVED ___________________ hereby sells, assigns and
transfers unto______________________ the foregoing Warrant and all rights
evidenced thereby, and does irrevocably constitute and appoint
___________________________, attorney, to transfer said Warrant on the books of
Endorex Corp.

Dated:____________________                  Signature: ____________________

                                            Address: ______________________

                                      11
<PAGE>

                              PARTIAL ASSIGNMENT
                              ------------------

          FOR VALUE RECEIVED ____________________ hereby assigns and transfers
unto ______________________ the right to purchase ___________ shares of the
Common Stock, par value $.001 per share, of Endorex, Inc. covered by the
foregoing Warrant, and a proportionate part of said Warrant and the rights
evidenced thereby, and does irrevocably constitute and appoint
______________________, attorney, to transfer that part of said Warrant on the
books of Endorex, Inc.

Dated: ______________________                 Signature: ___________________

                                              Address: _____________________

                                      12