<PAGE>   1


                                 EXHIBIT 4.3

                              Warrant Agreement

      This Agreement (the "Agreement"), dated as of March 12, 1997, is entered
into among Alpha 1 Biomedicals, Inc., a Delaware corporation (the "Company"),
and the purchasers (the "Investors") of Units (as defined below) in a private
offering (the "Offering") by the Company in accordance with a Unit Purchase
Agreement, dated as of the date hereof (the "Unit Purchase Agreement").

                                 WITNESSETH:

      WHEREAS, the Company has issued in the Offering a total of 4.0 Units (the
"Units"), each Unit consisting of 500,000 shares of the common stock, par value
$.001 per share, of the Company (the "Common Stock") and 165,000 Class D
Warrants (the "Warrants"), each Warrant being exercisable to purchase one share
of Common Stock (the "Warrant Shares"); and

      WHEREAS, the Company desires to set forth herein the terms of the
Warrants and to provide for the issuance of certificates representing the
Warrants.   NOW, THEREFORE, in consideration of the above and foregoing
premises and the mutual promises and agreements hereinafter set forth, it is
agreed that:

      1.    WARRANT CERTIFICATES.

            (a) Each Warrant shall entitle the holder in whose name the
certificate shall be registered on the transfer books of the Company (a "Warrant
Holder") to purchase one share of Common Stock at the exercise price set forth
in Section 3(a), subject to modification and adjustment as provided in Section 8
hereof. The Warrant certificates shall be detached from certificates
representing shares of Common Stock comprising the Units and shall be
distributed to the purchasers thereof at the closing of the Offering (the
"Closing Date").

            (b) Warrants shall be issuable only in whole number denominations
both upon initial issuance and in connection with any exercise, transfer or
exchange.

      2.    FORM AND EXECUTION OF CERTIFICATES.

            (a) The Warrants shall be issued in registered form only. The form
of Warrant certificate shall be substantially as attached hereto as Exhibits A
and shall include any such other terms and legends as may be required to comply
with any applicable law or the rules and regulations of any stock exchange or
market.

            (b) Each Warrant certificate shall be sequentially numbered and
shall have set forth thereon the designation "WD." The Warrant certificates
shall be dated the date of their issuance.


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<PAGE>   2


            (c) The Company shall act as its own warrant agent in connection
with the issuance, registration, transfer, exchange and exercise of Warrants, or
in its sole discretion, upon notice to the Warrant Holders, may appoint an
entity that is registered as "transfer agent" under the Securities Exchange Act
of 1934, as amended (the "Exchange Act"), to perform any one or more of such
functions (the "Warrant Agent").

      (d)   The Warrant certificates shall be manually signed on behalf of the
Company by proper officers thereof (or, in the case of the appointment of a
Warrant Agent other than the Company, by the facsimile signatures of the proper
officers of the Company and countersigned by the Warrant Agent) and shall not be
valid for any purpose unless so signed. In the event any officer of the Company
who executed certificates (whether manually or by facsimile) shall cease to be
an officer of the Company, such certificates shall have the same force and
effect as though the person who signed such certificate had not ceased to be an
officer of the Company.

      3.    EXERCISE; EXPIRATION.

            (a) Subject to the provisions of this Agreement, each Warrant may be
exercised at a price (the "Exercise Price") of $.10 per Warrant Share, subject
to adjustment as provided herein, at any time during the period (the "Warrant
Exercise Period") commencing on the Closing Date and terminating on a date (the
"Warrant Expiration Date") that is the tenth anniversary of the Closing Date or
if the Warrant Expiration Date is a Saturday, Sunday, or a day on which banks in
New York are not open for business (a "Business Day"), then the Warrant
Expiration Date shall be the next Business Day. If an initial Warrant Holder is
the holder of a Warrant on the 90th day preceding the Warrant Expiration Date,
the Company will notify him no later than the 60th day prior to the Warrant
Expiration Date of the date on which the Warrant will expire.

            (b) A Warrant shall be deemed to have been exercised immediately
prior to the close of business on the date (an "Exercise Date") that the Warrant
Holder has delivered to the Company at its corporate offices located at 6707
Democracy Boulevard, Suite 111, Bethesda, MD 20817 (the "Corporate Office"), or
at any such other office or agency as the Company may designate, (i) the Warrant
certificate with the Election to Purchase certification duly executed, which
shall include, if at the time of exercise the Warrant Shares deliverable upon
exercise of a Warrant have not been registered for sale by the Company under the
Securities Act of 1933, as amended (the "Act"), a written representation of the
Warrant Holder to the effect that (A) the Holder is an "accredited investor" as
defined by Rule 501 under the Act (or such other reasonable representations as
shall be necessary for the Company to conclude that the sale of the Warrant
Shares to the Warrant Holder is an exempt transaction under the Securities Act),
(B) the Warrant Shares being acquired upon exercise are being purchased for
investment and not for distribution in violation of the Act, (C) acknowledging
that such Warrant Shares have not been registered under the Act and (D) agreeing
that such Warrant Shares may not be sold or transferred unless there is an
effective registration statement relating thereto under the Act or such sale or
transfer is not in violation of the Act (the "Exercise Form"), and (ii) payment
in full of the aggregate Exercise Price. An Exercise Form shall be executed by
the Warrant Holder thereof or his attorney duly authorized in writing. Payment
of


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the Exercise Price of each Warrant shall be in cash or by official bank or
certified check, money order or wire transfer of an amount equal to the Exercise
Price then in effect, in lawful money of the United States of America. The
person entitled to receive the Warrant Shares deliverable on exercise shall be
treated for all purposes as the holder of such Warrant Shares as of the close of
business on the Exercise Date.

            (c) The Company shall not be obligated to issue any fractional
shares of Common Stock in connection with the exercise of any Warrant. In lieu
of issuing any fractional Warrant Shares, the Company shall pay to any Warrant
Holder who otherwise would have been entitled to a fractional Warrant Share cash
(without interest) in an amount determined by multiplying the fractional
interest to which such Warrant Holder would otherwise be entitled by the closing
sale price of the Common Stock as reported on the NASDAQ National Market (or, if
the Common Stock is not then listed for trading thereon, on such other principal
market or exchange on which the Common Stock is then traded or, if no closing
sale price is reported by the principal market or exchange on which the Common
Stock is then traded, then the average of the closing bid and asked prices as
reported) on the day immediately prior to (but not including) the Exercise Date
(or if no bid and asked prices are reported, then the fair market value of the
Common Stock as determined in good faith by the Board of Directors of the
Company (as so determined, the "Market Price").

            (d) Within two Business Days after the Exercise Date, the Company,
at its own expense, shall cause to be issued and sent for next Business Day
delivery to the person or persons entitled to receive the same, a certificate or
certificates in the name of the Warrant Holder for the number of Warrant Shares
deliverable on such exercise. All Warrant Shares delivered upon the exercise of
the Warrants shall be validly issued, fully paid and nonassessable.

            (e) The Company may deem and treat the Warrant Holder as the
absolute owner thereof for all purposes, and the Company shall not be affected
by any notice to the contrary. No Warrant shall entitle the holder thereof to
any of the rights of shareholders or to any dividend declared on the Common
Stock unless such holder shall have exercised the Warrant on or prior to the
record date fixed by the Board of Directors for the determination of holders of
Common Stock entitled to such rights or dividends.

      4.    REGISTRATION RIGHTS.

            The holders of Warrant Shares shall have the registration rights
provided for in the Registration Rights Agreement executed by the Company and
the Investors on the date hereof (the "Registration Rights Agreement").

      5.    RESERVATION OF SHARES AND PAYMENT OF TAXES.

            (a) The Company covenants that it shall at all times reserve and
have available from its authorized Common Stock such number of shares of Common
Stock as shall then be issuable on the exercise of all outstanding Warrants. The
Company covenants that all Warrant Shares shall be free from all taxes, liens
and charges with respect to the issuance thereof.

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<PAGE>   4

            (b) The Company shall pay all documentary, stamp or similar taxes
and other government charges that may be imposed with respect to the issuance of
the Warrants, and the issuance or delivery of any Warrant Shares upon the
exercise of the Warrants, except that in the event that the Warrant Shares are
to be delivered in a name other than the name of the Warrant Holder reflected on
the certificate for the Warrant, no such delivery shall be made unless the
person requesting the same has paid to the Company the amount of any such taxes,
charges or transfer fees incident thereto.

      6.    REGISTRATION OF TRANSFER.

            (a) The Warrant certificates may, subject to provisions of the
Federal securities and state securities laws and the provisions of this
Agreement, be transferred in whole or in part. Certificates to be transferred
shall be surrendered to the Company at its Corporate Office or such other office
or agency as the Company may designate.

            (b) The Company shall keep transfer books which shall register
Warrant certificates and the transfer thereof. On due presentment for
registration of transfer of any Warrant certificate, the Company shall execute,
issue and deliver to the transferee or transferees a new certificate or
certificates representing an equal aggregate number of Warrants. All such
Warrant certificates shall be duly endorsed or be accompanied by a written
instrument or instruments of transfer in form reasonably satisfactory to the
Company, together with an opinion of counsel, reasonably satisfactory in form
and substance to counsel for the Company, that an exemption from registration
under the Act for the transfer exists and a written representation from the
transferee that (i) the Warrants are being acquired for investment and not for
distribution otherwise than in compliance with the Act, (ii) acknowledging that
the Warrants have not been registered under the Act and (iii) agreeing that the
Warrants, if not registered under the Act, may not be transferred unless there
is an effective registration statement with respect thereto or in the opinion of
counsel, which shall be reasonably satisfactory in form and substance to counsel
for the Company, that such transfer is an exempt transaction under the Act.

            (c) Prior to due presentment for registration of transfer thereof,
the Company may treat the Warrant Holder as the absolute owner thereof
(notwithstanding any notations of ownership or writing thereon made by anyone),
and the Company shall not be affected by any notice to the contrary.

      7.    LOSS OR MUTILATION.

            On receipt by the Company of satisfactory evidence of the loss,
theft, destruction or mutilation of any Warrant certificate, the Company shall
execute and deliver to a Warrant Holder in lieu thereof a new Warrant
certificate representing an equal number of Warrants. In the case of loss, theft
or destruction of any certificate, the Warrant Holder shall be required to
indemnify the Company and to post an indemnity bond as a condition to the
issuance of a replacement certificate. In the event a certificate is mutilated,
such certificates shall be surrendered and canceled by the Company prior to
delivery of a new certificate. The Warrant Holder shall also comply with such
other regulations and pay such other reasonable charges as the Company may
prescribe.

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<PAGE>   5

      8.    ADJUSTMENT OF EXERCISE PRICE AND NUMBER OF SHARES PURCHASABLE.

            (a)   (i) Except as otherwise provided in Section 8(b) and subject
to the exceptions set forth in Section 8(c), in the event the Company shall, at
any time or from time to time after the date hereof, (A) sell or issue for cash
any shares of Common Stock for a consideration per share that is less than
either (x) the Market Price of the Common Stock (as defined in Section 3(c)) on
the last trading day preceding the date of such sale or issuance or (y) at any
time prior to the first anniversary of the date of this Agreement, for a price
per share that is less than the then-applicable Exercise Price on the last
trading day preceding the date of such sale or issuance, (B) issue any shares of
Common Stock as a stock dividend to the holders of shares of Common Stock, or
(C) subdivide or combine the outstanding shares of Common Stock into a greater
or lesser number of shares of Common Stock, then in each such case the Exercise
Price in effect immediately prior to such event shall be changed to the Exercise
Price (calculated to the nearest cent) determined by multiplying the Exercise
Price in effect immediately prior thereto by a fraction, (1) the numerator of
which shall be the sum of the number of shares of Common Stock outstanding
immediately prior to the issuance of such additional shares and the number of
shares of Common Stock that the aggregate consideration received (determined as
provided in Section 8(b)) for the issuance of such additional shares would
purchase at the Market Price and (2) the denominator of which shall be the sum
of the number of shares of Common Stock outstanding immediately after the
issuance of such additional shares; provided, however, if a sale or issuance
satisfies conditions of both A(x) and A(y), only the adjustment that produces
the greater change in the Exercise Price shall be made. Such adjustment shall be
made successively whenever such an issuance is made.

                  (ii) Upon the adjustment of the Exercise Price pursuant to
this Section 8, the total number of shares of Common Stock purchasable upon
exercise of each Warrant shall be such number of shares (calculated to the
nearest one-tenth of a share) purchasable at the Exercise Price in effect
immediately prior to such adjustment multiplied by a fraction, (1) the numerator
of which shall be the Exercise Price in effect immediately prior to such
adjustment and (2) the denominator of which shall be the Exercise Price in
effect immediately after such adjustment.

            (b)   For purposes of Section 8(a), the following provisions shall
be applicable:

                  (i) The number of shares of Common Stock outstanding at any
given time shall not include shares of Common Stock owned or held by or for the
account of the Company, and the sale of such shares shall be a sale for purposes
of Section 9(a).

                  (ii) No adjustment of the Exercise Price shall be made unless
such adjustment would require an increase or decrease of at least $.01 in the
Exercise Price; provided that any adjustments that by reason of this clause (ii)
are not required to be made shall be carried forward and shall be made at the
time of and together with the next subsequent adjustment that, together with all
adjustments so carried forward, require an increase or decrease of at least $.01
in the Exercise Price.

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            (iii) In the event of (A) the sale by the Company (or as a component
of a unit being sold) for cash of any rights or warrants to subscribe for or
purchase, or any options for the purchase of, either Common Stock or any
securities that are convertible into or exchangeable for Common Stock (such
securities convertible or exchangeable into Common Stock being herein referred
to as "Convertible Securities") or (B) the issuance by the Company, without the
receipt by the Company of any consideration therefor, of any rights or warrants
to subscribe for or purchase, or any options for the purchase of, Common Stock
or Convertible Securities (in either case whether or not such rights, warrants
or options, or the right to convert or exchange such Convertible Securities, are
immediately exercisable), and the price per share for which Common Stock is
issuable upon the exercise of such rights, warrants or options or upon the
conversion or exchange of such Convertible Securities (determined by dividing
(1) the minimum aggregate consideration payable to the Company upon the exercise
of such rights, warrants or options, plus the consideration, if any, received by
the Company for the issuance or sale of such rights, warrants or options, plus,
in the case of such Convertible Securities, the minimum aggregate amount of
additional consideration, if any (other than the surrender of such Convertible
Securities), payable upon the conversion or exchange thereof, by (2) the total
maximum number of shares of Common Stock issuable upon the exercise of such
rights, warrants or options or upon the conversion or exchange of the
Convertible Securities issuable upon the exercise of such rights, warrants or
options) is less than either (x) the Market Price of the Common Stock on the
last trading day preceding the date of the issuance or sale of such rights,
warrants or options or (y) at any time prior to the first anniversary of the
date of this Agreement, for a price per share that is less than the
then-applicable Exercise Price on the last trading day preceding the date of
such sale or issuance, then for purposes of Section 8(a) the total maximum
number of shares of Common Stock issuable upon the exercise of such rights,
warrants, or options and upon the conversion or exchange of such Convertible
Securities shall be deemed to be outstanding shares of Common Stock as of the
date of the issuance or sale of such rights, warrants or options and shall be
deemed to have been sold for cash in an amount equal to such price per share.

                  (iv) In the event of the sale by the Company for cash of any
Convertible Securities, whether or not the right of conversion or exchange
thereunder is immediately exercisable, and the price per share for which Common
Stock is issuable upon the conversion or exchange of such Convertible Securities
(determined by dividing (1) the total amount of consideration received by the
Company for the sale of such Convertible Securities, plus the minimum aggregate
amount of additional consideration, if any (other than the surrender of such
Convertible Securities), payable upon the conversion or exchange thereof, by (2)
the total maximum number of shares of Common Stock issuable upon the conversion
or exchange of such Convertible Securities) is less than either (x) the Market
Price of the Common Stock on the last trading day preceding the date of the sale
of such Convertible Securities or (y) at any time prior to the first anniversary
of the date of this Agreement, for a price per share that is less than the
then-applicable Exercise Price on the last trading day preceding the date of
such sale or issuance, then for purposes of Section 8(a) the total maximum
number of shares of Common Stock issuable upon the conversion or exchange of
such Convertible Securities shall be deemed to be outstanding shares of Common
Stock as of the date of the sale


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of such Convertible Securities and shall be deemed to have been sold for cash in
an amount equal to such price per share.


                  (v) On the expiration of any rights or warrants to subscribe
for or purchase, or any options for the purchase of, Common Stock or Convertible
Securities, or the termination of any right to convert or exchange Convertible
Securities, in respect of which any adjustments previously shall have been made
in accordance with clause (iii) or (iv) of this Section 8(b), the Exercise Price
in effect immediately prior to the time of such expiration or termination shall
be adjusted to such Exercise Price as would be applicable had such adjustments
not been made with respect to (A) the issuance of or the adjustment of the
Exercise Price of such rights, warrants or options which have expired or (B) the
issuance of or the adjustment of the conversion or exercise price of such
Convertible Securities the rights under which to convert or exchange have
terminated.

                  (vi) In case of the sale or issuance of any shares of Common
Stock, any Convertible Securities, any rights or warrants to subscribe for or
purchase, or any options for the purchase of, Common Stock or Convertible
Securities, the consideration received by the Company therefor shall be deemed
to be the gross sales price therefor without deducting therefrom any expense
paid or incurred by the Company or any underwriting discounts or commissions or
concessions paid or allowed by the Company in connection therewith.

            (c)   No adjustment to the Exercise Price of the Warrants or to the
number of shares of Common Stock purchasable upon the exercise of each Warrant
will be made:
                  (i)   upon the issuance or sale of any securities (including
stock options) of the Company that are issued pursuant to any stock option or
stock bonus plan or arrangement of the Company for the benefit of directors,
officers or employees of the Company; or

                  (ii)  upon the sale or exercise of the Warrants or any
adjustment to the Exercise Price thereof; or

                  (iii) upon the issuance or sale of Common Stock or Convertible
Securities as the result of the exercise of any rights or warrants to subscribe
for or purchase, or any options for the purchase of, Common Stock or Convertible
Securities, whether or not such rights, warrants or options were outstanding on
the date of this Agreement or were thereafter issued or sold; or

                  (iv)  upon the issuance or sale of Common Stock as the result
of the conversion or exchange of any Convertible Securities, whether or not such
Convertible Securities were outstanding on the date of this Agreement or were
thereafter issued or sold.

            (d)   As used in this Section 8, the term "Common Stock" shall mean
the Common Stock as designated in the Company's Certificate of Incorporation on
the date hereof and shall also include any capital stock of any class of the
Company hereafter authorized that shall not be limited to a fixed sum or
percentage in respect of the rights of the holders thereof to

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<PAGE>   8

participate in dividends and in the distribution of assets upon the voluntary
liquidation, dissolution or winding up of the Company; provided, however, that
the shares issuable upon exercise of the Warrants shall be the shares so
designated as Common Stock on the date hereof or (i) in the case of any
reclassification, change, consolidation, merger, sale or conveyance of the
character referred to in Section 8(e), the stock, securities or property
provided for in such section, or (ii) in the case of any reclassification or
change in the outstanding shares of Common Stock issuable upon exercise of the
Warrants consisting of a change in par value, or from par value to no par value,
or from no par value to par value, such shares of Common Stock as so
reclassified or changed.

            (e)   In case of any reclassification, capital reorganization or
other change in the Common Stock, or in case of any consolidation or merger of
the Company with or into another corporation (other than a consolidation or
merger in which the Company is the continuing corporation and which does not
result in any reclassification, capital reorganization or other change in the
Common Stock), or in case of any sale or conveyance to another corporation of
the property of the Company as, or substantially as, an entirety, the Company
shall cause effective provision to be made so that each registered holder of a
Warrant then outstanding shall have the right thereafter, by exercising such
Warrant, to purchase the kind and number of shares of stock or other securities
or property (including cash) receivable upon such reclassification, capital
reorganization or other change, consolidation, merger, sale or conveyance by a
holder of the number of shares of Common Stock that could have been purchased
upon the exercise of such Warrant immediately prior to such reclassification,
capital reorganization or other change, consolidation, merger, sale or
conveyance, and in any such case appropriate adjustments shall be made in the
application of the provisions of this Section 8 with respect to rights and
interests thereafter of the holder to the end that the provisions of this
Section 8 shall thereafter be applicable, as near as reasonably practicable, in
relation to any shares or other property thereafter purchasable upon the
exercise of a Warrant. The Company shall not effect any such consolidation,
merger or sale unless prior to, or simultaneously with, the consummation thereof
the successor (if other than the Company) resulting from such consolidation or
merger or the corporation purchasing the property of the Company shall assume,
by written instrument executed and delivered to the Company, the obligation to
deliver to the holder of each Warrant such shares of stock, securities or
property as, in accordance with the foregoing provisions, such holder shall be
entitled to purchase (and the other obligations of the Company under this
Agreement). The foregoing provisions shall similarly apply to successive
reclassifications, capital reorganizations and other changes in the Common Stock
and to successive consolidations, mergers, sales or conveyances.

            (f)   After each adjustment of the Exercise Price pursuant to this
Section 8, the Company promptly will prepare a statement, certified by its
Chairman or President and by its Treasurer or Assistant Treasurer, setting
forth: (i) in reasonable detail the computation of the Exercise Price, as so
adjusted, and the computation of the number of shares of Common Stock
purchasable upon exercise of each Warrant, as so adjusted, and (ii) a brief
description of the circumstances giving rise to the adjustment. The Company
shall deliver a copy of such statement to each Warrant Holder. The Company

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<PAGE>   9

will allow any Warrant Holder or its representative to inspect the books and
records of the Company to the extent necessary to verify any such computation.

            (g)   Irrespective of any adjustments in the Exercise Price or the
number of shares of Common Stock purchasable upon exercise of the Warrants, the
Warrant certificates theretofore and thereafter issued shall, unless the Company
in its sole discretion shall determine to issue new Warrant certificates,
continue to express the Exercise Price per share and the number of shares
purchasable thereunder as were expressed in the Warrant certificates when the
same were originally issued.

            (h)   The Company will not, by amendment of its Certificate of
Incorporation or through any consolidation, merger, reorganization, transfer of
assets, dissolution, issue or sale of securities or any other voluntary action,
avoid or seek to avoid the observance or performance of any of the terms of the
Warrants, but will at all times in good faith assist in the carrying out of all
such terms and in the taking of all such action as reasonably may be necessary
or appropriate (including, if necessary or appropriate, making equitable
adjustments to the kind and amount of securities issuable upon the exercise of
the Warrants and the Exercise Price) in order to protect the rights of the
holders of the Warrants against dilution or other impairment.

            (i)   In case the Company shall take a record of the holders of its
Common Stock for the purpose of (i) entitling them to receive a dividend or any
other distribution in respect of the Common Stock payable in cash or other
property, (ii) entitling them to subscribe for or purchase any shares of stock
of any class or to receive any other rights, (iii) any classification,
reclassification or other reorganization of the capital stock of the Company,
any consolidation or merger of the Company with or into another corporation, or
any conveyance of all or substantially all of the assets of the Company, or (iv)
the voluntary or involuntary dissolution, liquidation or winding up of the
Company, then, and in any such case, the Company shall mail to each Warrant
Holder in the manner provided for in Section 10, at least 20 days prior to such
record date, a notice stating the date or expected date on which a record is to
be taken for the purpose of such dividend, distribution of rights, or the date
on which such classification, reclassification, reorganization, consolidation,
merger, conveyance, dissolution, liquidation or winding up, as the case may be,
is to take place. Such notice shall also specify the date or expected date, if
any is to be fixed, on which said dividend, distribution of rights, or an
exchange of shares of Common Stock for securities or other property deliverable
upon such classification, reclassification, reorganization, consolidation,
merger, conveyance, dissolution, liquidation or winding up, as the case may be,
is expected to occur, provided, however, that the failure to give such notice
shall not affect the validity of any such proceeding or transaction.

      9.    OBTAINING OF GOVERNMENTAL APPROVALS AND STOCK EXCHANGE LISTINGS.

            The Company will use its best efforts (a), except that the
Company is not obligated to register the Warrant Shares for sale by the Company
under the Securities Act or any state securities laws, to obtain and keep
effective any and all permits, consents and approvals of governmental agencies
and authorities and make any necessary filings under federal or state securities


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laws, which may be or become requisite in connection with the issuance, sale and
delivery of the Warrant certificates, the exercise of the Warrants and the
issuance, sale, transfer and delivery of the Warrant Shares and (b) to cause the
Warrant Shares, prior to their sale pursuant to any registration statement filed
in accordance with the Registration Rights Agreement or other transfer which is
not restricted under the federal securities laws, to be listed on the NASDAQ
National Market or the principal securities exchange or market within the United
States of America on which the Common Stock is then listed.

      10.   NOTICES.

            All notices, demands, elections, opinions or requests (however
characterized or described) required or authorized hereunder shall be in writing
and shall be delivered by hand or sent by registered or certified mail, return
receipt requested and postage prepaid, or by facsimile transmission to, in the
case of the Company:

                  Alpha 1 Biomedicals, Inc.
                  6707 Democracy Boulevard
                  Suite 111
                  Bethesda, MD  20817-1129
                  Telecopier number: (301) 564-4424
                  Attention:  Michael Berman

and if to the Warrant Holder at the address of such holder as set forth on the
transfer books maintained by or on behalf of the Company.

            All such notices and communications shall be deemed to have been
duly given when delivered by hand, if personally delivered; five business days
after being deposited in the mail, postage prepaid; upon receipt, if sent by
facsimile, except that in the case of Roger H. Samet, no notice or communication
shall be deemed given unless (x) actually received by Roger H. Samet or (y)
given in the manner provided above to the person to whom copies are to be
delivered as identified in the Unit Purchase Agreement.

      11.   THIRD PARTY BENEFICIARIES.

            Each registered holder of a Warrant, whether or not such holder is a
party to this Agreement, is an intended beneficiary of this Agreement, and this
Agreement may be enforced by such registered holder. Nothing in this Agreement
shall be construed to give any person or entity, other than the Company and the
registered holders of the Warrants, any legal or equitable right, remedy or
claim under this Agreement.

      12.   FURTHER INSTRUMENTS.

            The parties shall execute and deliver any and all such other
instruments and take any and all other actions as may be reasonably necessary to
carry out the intention of this Agreement.

      13.   NO INCONSISTENT AGREEMENTS.

            The Company has not, as of the date hereof, and the Company shall
not, after the date of this Agreement, enter into any agreement with respect

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<PAGE>   11

to any of its securities that is inconsistent with the rights granted to the
Warrant Holders in this Agreement or otherwise conflicts with the provisions
hereof. The Company will not enter into any agreement which will grant any such
rights that are in conflict with the rights afforded by this Agreement.

      14.   AMENDMENTS AND WAIVERS.

            The Company may, without the consent or concurrence of the holders
of the Warrants, make any changes or corrections in this Agreement that are
necessary or desirable to cure any ambiguity or to correct any defective
provision, mistake or manifest error herein contained; provided that such
changes do not adversely affect the rights or interests of the holders of the
Warrants. Otherwise, the provisions of this Agreement may not be amended,
modified or supplemented, and waivers or consents to departures from the
provisions hereof may not be given, (i) as related to the rights or obligations
of Roger H. Samet, except with the prior written consent of the Company and
Roger H. Samet, and (ii) as related to the rights or obligations of the holders
of Warrants other than Roger H. Samet, otherwise than with the prior written
consent of the Company and the registered holders of not less than a majority of
the then-outstanding Warrants; provided, however, that no change in the number
of the Warrant Shares purchasable upon the exercise of any Warrant, no increase
in the Exercise Price and no acceleration of the Warrant Expiration Date shall
be made without the consent in writing of each Warrant Holder.

      15.   SUCCESSORS AND ASSIGNS.

            This Agreement shall inure to the benefit of and be binding upon the
successors and permitted assigns of each of the parties hereto.

      16.   COUNTERPARTS.

            This Agreement may be executed in any number of counterparts, each
of which when so executed shall be deemed to be an original and all of which
taken together shall constitute one and the same agreement.

      17.   HEADINGS.

            The headings in this Agreement are for convenience of reference only
and shall not limit or otherwise affect the meaning hereof.

      18.   GOVERNING LAW.

            THIS AGREEMENT SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH
THE LAWS OF THE STATE OF MARYLAND, AS APPLIED TO CONTRACTS MADE AND PERFORMED
WHOLLY WITHIN THE STATE OF MARYLAND, WITHOUT REGARD TO PRINCIPLES OF CONFLICTS
OF LAW. EACH OF THE PARTIES HERETO AGREES, AND EACH BENEFICIARY HEREOF SHALL BE
BOUND, TO SUBMIT TO THE JURISDICTION OF ANY STATE OR FEDERAL COURT LOCATED IN
THE STATE OF MARYLAND IN ANY ACTION OR PROCEEDING ARISING OUT OF OR RELATING TO
THIS AGREEMENT.

      19.   SEVERABILITY.

                                       56
<PAGE>   12

            If any term, provision, covenant or restriction of this Agreement is
held by a court of competent jurisdiction to be invalid, illegal, void or
unenforceable, the remainder of the terms, provisions, covenants and
restrictions set forth herein shall, to the extent permitted by law, remain in
full force and effect and shall in no way be affected, impaired or invalidated,
and the parties hereto shall use their best efforts to find and employ an
alternative means to achieve the same or substantially the same result as that
contemplated by such invalid, illegal, void or unenforceable term, provision,
covenant or restriction. It is hereby stipulated and declared to be the
intention of the parties that they would have executed the remaining terms,
provisions, covenants and restrictions without including any term, provision,
covenant or restriction that may be hereafter declared invalid, illegal, void or
unenforceable.

      20.   ENTIRE AGREEMENT.

            This Agreement, together with the Registration Rights Agreement and
the Unit Purchase Agreement, is intended by the parties hereto as a final
expression of their agreement and intended to be a complete and exclusive
statement of the agreement and understanding of the parties hereto in respect of
the subject matter contained herein, and supersede all prior agreements between
the parties with respect to such subject matter. There are no representations,
promises, warranties or undertakings between the parties hereto with respect to
the subject matter hereof, other than those set forth or referred to herein and
therein.

      IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be
duly executed on the date first set forth above.

                                    ALPHA 1 BIOMEDICALS, INC.


                                    By:   /s/ Michael L. Berman
                                        --------------------------
                                          Michael Berman
                                          President



                       [additional signature pages follow]


                                       57
<PAGE>   13


                              WARRANT AGREEMENT

                                SIGNATURE PAGE
                          FOR INDIVIDUAL PURCHASERS



      By    /s/ Michael L. Berman
        ----------------------------
            Michael Berman
            President and Chief
              Executive Officer


            /s/ Roger H. Samet
      -----------------------------------
      ROGER H. SAMET



            /s/ Joseph C. McNay
      -----------------------------------
      JOSEPH C. MCNAY


            /s/ Stephen C. Lampl
      -----------------------------------
      STEPHEN C. LAMPL
      ANNE B. SHUMADINE TTEE V/A
      STEPHEN C. LAMPL TRUST DTD 4/16/87


            /s/ C.L. Kaufman, Jr.
      -----------------------------------
      C. L. KAUFMAN, JR.


            /s/ Michael L. Berman
      -----------------------------------
      MICHAEL L. BERMAN


            /s/ R.J. Lanham
      -----------------------------------
      R.J. LANHAM




                                       58