<PAGE>   1

                                                                   EXHIBIT 10.10



              -----------------------------------------------------

                                WARRANT AGREEMENT

                                     BETWEEN

                           EPOCH PHARMACEUTICALS, INC.

                                       AND

                     AMERICAN STOCK TRANSFER & TRUST COMPANY

                           DATED AS OF APRIL 29, 1997

              ----------------------------------------------------

<PAGE>   2

                                TABLE OF CONTENTS
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                                       ARTICLE I

                          DISTRIBUTION OF WARRANT CERTIFICATES

1.1      Appointment of Warrant Agent.................................................1
1.2      Form of Warrant Certificates.................................................1
1.3      Execution of Warrant Certificates............................................2
1.4      Issuance and Distribution of Warrant Certificates............................2

                                       ARTICLE II

                    WARRANT EXERCISE PRICE AND EXERCISE OF WARRANTS

2.1      Exercise Price...............................................................2
2.2      Registration of Common Stock and Exercisability of Exchange Warrants.........2
2.3      Procedure for Exercise of Exchange Warrants..................................3
2.4      Issuance of Warrant Shares...................................................3
2.5      Certificates for Unexercised Exchange Warrants...............................3
2.6      Reservation of Shares........................................................4
2.7      Disposition of Proceeds......................................................4

                                      ARTICLE III

                                    CALL OF WARRANTS

3.1      Call Price and Trigger Price.................................................4
3.2      Payment of Call Price........................................................4

                                       ARTICLE IV

                           ADJUSTMENTS AND NOTICE PROVISIONS

4.1      Adjustment of Exercise Price.................................................4
4.2      Current Market Price.........................................................5
4.3      No Adjustments to Exercise Price.............................................5
4.4      Deferral of Adjustments to Exercise Price....................................5
4.5      Adjustment to Number of Shares...............................................6
4.6      Reorganizations..............................................................6
4.7      Reclassifications............................................................7
4.8      Adjustment of Call Trigger Price.............................................7
4.9      Verification of Computations.................................................7
4.10     Notice of Certain Actions....................................................7
4.11     Notice of Call...............................................................8
4.12     Notice of Adjustments........................................................8
4.13     Warrant Certificate Amendments...............................................8
4.14     Fractional Shares............................................................8

                                       ARTICLE V

                        OTHER PROVISIONS RELATING TO RIGHTS OF

                       REGISTERED HOLDERS OF WARRANT CERTIFICATES

5.1      Rights of Warrant Holders....................................................9
5.2      Lost, Stolen, Mutilated or Destroyed Warrant Certificates....................9
</TABLE>


                                        i
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                                TABLE OF CONTENTS
                                  (continued)
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                                       ARTICLE VI

                       SPLIT UP, COMBINATION, EXCHANGE, TRANSFER

                        AND CANCELLATION OF WARRANT CERTIFICATES

6.1      Split Up, Combination, Exchange and Transfer of Warrant Certificates.........9
6.2      Cancellation of Warrant Certificates........................................10
6.3      Agreement of Warrant Certificate Holders....................................10

                                      ARTICLE VII

                           PROVISIONS CONCERNING THE WARRANT

                                AGENT AND OTHER MATTERS

7.1      Payment of Taxes and Charges................................................11
7.2      Resignation or Removal of Warrant Agent.....................................11
7.3      Notice of Appointment.......................................................11
7.4      Merger of Warrant Agent.....................................................12
7.5      Company Responsibilities....................................................12
7.6      Certification for the Benefit of Warrant Agent..............................12
7.7      Books and Records...........................................................12
7.8      Liability of Warrant Agent..................................................12
7.9      Use of Attorneys, Agents and Employees......................................13
7.10     Indemnification.............................................................13
7.11     Acceptance of Agency........................................................13
7.12     Changes to Agreement........................................................13
7.13     Assignment..................................................................13
7.14     Successor to Company........................................................13
7.15     Notices.....................................................................14
7.16     Defects in Notice...........................................................14
7.17     Governing Law...............................................................14
7.18     Standing....................................................................14
7.19     Headings....................................................................14
7.20     Counterparts................................................................15
7.21     Conflict of Interest........................................................15
7.22     Availability of the Agreement...............................................15
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                                       ii

<PAGE>   4

                                WARRANT AGREEMENT



         WARRANT AGREEMENT dated as of April 29, 1997, between EPOCH
PHARMACEUTICALS, INC., a Delaware corporation (the "Company"), and AMERICAN
STOCK TRANSFER & TRUST COMPANY, a corporation organized under the banking laws
of the State of New York (the "Warrant Agent").

                              W I T N E S S E T H:

         WHEREAS, the Company has made a private placement (the "Offering") of
Redeemable Common Stock Purchase Warrants (the "Exchange Warrants") to exchange
for every two Redeemable Common Stock Purchase Warrants of the Company, which
were issued by the Company in its initial public offering on September 29, 1993
(the "Public Warrants"), one new Exchange Warrant to purchase one share of the
Company's Common Stock; and

         WHEREAS, the Company proposes to issue certificates evidencing the
Exchange Warrants (such Warrant certificates issued pursuant to this Agreement
being hereinafter called the "Warrant Certificates"); and

         WHEREAS, the Company desires the Warrant Agent, and the Warrant Agent
agrees, to act on behalf of the Company in connection with the issuance,
transfer, exchange, replacement, redemption and surrender of the Warrant
Certificates; and

         WHEREAS, the Company and the Warrant Agent desire to set forth in this
Warrant Agreement, among other things, the form and provisions of the Warrant
Certificates and the terms and conditions under which they may be issued,
transferred, exchanged, replaced, redeemed and surrendered in connection with
the exercise and redemption of the Warrants;

         NOW, THEREFORE, in consideration of the premises and of the mutual
agreements herein contained, the parties hereto agree as follows:

                                    ARTICLE I

                      DISTRIBUTION OF WARRANT CERTIFICATES

         1.1 Appointment of Warrant Agent. The Company hereby appoints the
Warrant Agent to act on behalf of the Company in accordance with the
instructions hereinafter set forth in this Agreement, and the Warrant Agent
hereby accepts such appointment.

         1.2 Form of Warrant Certificates. The Warrant Certificates for the
Exchange Warrants shall be issued in registered form only and, together with the
purchase and assignment forms to be printed on the reverse thereof, shall be
substantially in the form of Exhibit A and Exhibit B attached hereto,
respectively, and, in addition, may have such letters, numbers or other marks of
identification or designation and such legends, summaries or endorsements
stamped, printed, lithographed or engraved thereon as the Company may deem
appropriate and as are not inconsistent with the provisions of this Agreement or
as, in any particular case, may be required, in the opinion of counsel 

<PAGE>   5

for the Company, to comply with any law or with any rule or regulation of any
regulatory authority or agency or to conform to customary usage.

         1.3 Execution of Warrant Certificates. The Warrant Certificates shall
be executed on behalf of the Company by its Chairman of the Board, Chief
Executive Officer or President or any Vice President, and by its Chief Financial
Officer or Treasurer or any Assistant Treasurer, or Secretary or any Assistant
Secretary, either manually or by facsimile signature printed thereon. The
Warrant Certificate shall be manually countersigned and dated the date of
countersignature by the Warrant Agent and shall not be valid for any purpose
unless so countersigned and dated. In case any authorized officer of the Company
who shall have signed any of the Warrant Certificates shall cease to be such
officer of the Company either before or after delivery thereof by the Company to
the Warrant Agent, the signature of such person on such Warrant Certificates,
nevertheless, shall be valid and such Warrant Certificates may be countersigned
by the Warrant Agent and issued and delivered to those persons entitled to
receive the Exchange Warrants represented thereby with the same force and effect
as though the person who signed such Warrant Certificates had not ceased to be
such officer of the Company.

         1.4 Issuance and Distribution of Warrant Certificates. Upon completion
of the Offering, the Company shall deliver to the Warrant Agent an adequate
supply of Warrant Certificates for the Exchange Warrants executed on behalf of
the Company as described in Section 1.3 hereof. Upon receipt of an order from
the Company, the Warrant Agent shall within three business days complete and
countersign Warrant Certificates representing the total number of Exchange
Warrants to be issued hereunder and shall deliver such Warrant Certificates
pursuant to written instructions of the Company.

                                   ARTICLE II

                 WARRANT EXERCISE PRICE AND EXERCISE OF WARRANTS

         2.1 Exercise Price. Each Warrant Certificate for the Exchange Warrants
shall, when signed by the Chairman, Chief Executive Officer or President or any
Vice President, and by the Chief Financial Officer or Treasurer or any Assistant
Treasurer, or Secretary or any Assistant Secretary, of the Company and
countersigned by the Warrant Agent, entitle the registered holder thereof,
subject to the provisions of Article III hereof, to purchase from the Company
one share of Common Stock for each Warrant evidenced thereby, at the purchase
Price of $2.50 per share (the "Initial Exercise Price"), or such adjusted number
of shares at such adjusted purchase price as may be established from time to
time pursuant to the provisions of Article IV hereof, payable in full at the
time of exercise of the Exchange Warrant. Except as the context otherwise
requires, the term "Exercise Price" as used in this Agreement shall mean the
purchase price of one share of Common Stock upon the exercise of an Exchange
Warrant, reflecting all appropriate adjustments made in accordance with the
provisions of Article IV hereof and Section 7.12 hereof.

         2.2 Registration of Common Stock and Exercisability of Exchange
Warrants. Each Exchange Warrant may be exercised at any time until 5:00 P.M.,
New York City time, on June 20, 2001. The term "Exercise Deadline" as used in
this Agreement shall mean the latest time and date at which the Exchange
Warrants may be exercised. The Company shall use its best efforts to maintain
the registration or qualification in effect of the Warrant Shares and to keep
available for delivery 


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<PAGE>   6

upon the exercise of the Exchange Warrants a prospectus that meets the
requirements of Section 10 of the Securities Act, until the earlier of the date
by which all the Exchange Warrants are exercised or the Exercise Deadline;
provided, however, that the Company shall have no obligation to maintain the
effectiveness of such registration or qualification or to keep available a
prospectus, as aforesaid, in the event that, by amendment to the Securities Act
or otherwise, such registration or qualification or the delivery of such
prospectus is not required at the time said Common Stock is to be issued; and
provided further, that in the event, by amendment to the Securities Act or
otherwise, some other or different requirement shall be imposed by act of the
Congress of the United States which shall relate to the issuance of Common Stock
upon exercise of the Exchange Warrants, the company shall use its best efforts
to comply with such requirements.

         2.3 Procedure for Exercise of Exchange Warrants. During the period
specified in and subject to the provisions of Section 2.2 hereof, the Exchange
Warrants may be exercised by surrendering the Warrant Certificates representing
such Exchange Warrants to the Warrant Agent at its principal office (the
"Principal Office"), which is presently located at 40 Wall Street, New York, New
York 10005, with the election to purchase form set forth on the Warrant
Certificate duly completed and executed, with signatures guaranteed by a member
firm of a national securities exchange, a commercial bank or trust company
located in the United States, a member of the National Association of Securities
Dealers, Inc. ("NASD") or other eligible guarantor institution which is a
participant in a signature guarantee program (as such terms are defined in Reg.
240. 17Ad-15 under the Securities Exchange Act of 1934, as amended) acceptable
to the Warrant Agent ("Signatures Guaranteed"), accompanied by payment in full
of the Exercise Price as provided in Section 2.1 in effect at the time of such
exercise, together with such taxes as are specified in Section 7.1 hereof, for
each share of Common Stock with respect to which such Exchange Warrants are
being exercised. Such Exercise Price and taxes shall be paid in full by
certified check or money order, payable in United States currency, to the
Warrant Agent for the account of the Company. The date on which the Exchange
Warrants are exercised in accordance with this Section 2.3 is sometimes referred
to herein as the Date of Exercise of such Exchange Warrants.

         2.4 Issuance of Warrant Shares. As soon as practicable after the Date
of Exercise of any Exchange Warrants, the Company shall issue, or cause the
transfer agent for the Common Stock, if any, to issue a certificate or
certificates for the number of full shares of Common Stock to which such holder
is entitled, registered in accordance with the instructions set forth in the
election to purchase. All Warrant Shares shall be validly authorized and issued,
fully paid and nonassessable and free from all taxes, liens and charges created
by the Company in respect of the issue thereof, and shall be previously unissued
shares. Each person in whose name any such certificate for Warrant Shares is
issued shall for all purposes be deemed to have become the holder of record of
the Warrant Shares represented thereby on the Date of Exercise of the Exchange
Warrants resulting in the issuance of such shares, irrespective of the date of
issuance or delivery of such certificate for the Warrant Shares.

         2.5 Certificates for Unexercised Exchange Warrants. In the event that
less than all of the Exchange Warrants represented by a Warrant Certificate are
exercised, the Warrant Agent shall execute and mail, by first-class mail, within
30 days of the Date of Exercise, to the registered holder of such Warrant
Certificate, or such other person as shall be designated in the election to
purchase, a new Warrant Certificate representing the number of full Exchange
Warrants not exercised. In no event shall a fraction of an Exchange Warrant be
exercised, and the Warrant Agent shall distribute 


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<PAGE>   7

no Warrant Certificates representing fractions of Exchange Warrants under this
or any other section of this Agreement. Final fractions of shares shall be
treated as provided in Section 4.14.

         2.6 Reservation of Shares. The Company shall at all times reserve and
keep available for issuance upon the exercise of Exchange Warrants a number of
its authorized but unissued shares of Common Stock that will be sufficient to
permit the exercise in full of all outstanding Exchange Warrants.

         2.7 Disposition of Proceeds. The Warrant Agent shall account at least
monthly (or more frequently upon the request of the Company, provided that in no
event shall the Warrant Agent be required to account more frequently than
weekly) to the Company with respect to Exchange Warrants exercised and
concurrently deliver to the Company all funds.

                                   ARTICLE III

                                CALL OF WARRANTS

         3.1 Call Price and Trigger Price. The Company may, at its option, upon
30 days' notice, call for redemption all or any portion of the then outstanding
Warrants at a call price of $.05 per warrant (such price is hereinafter referred
to as the "Call Price"), at any time after the last sale price of the Company's
Common Stock, as determined pursuant to Section 4.2, has been at least 150% of
the then effective Exercise Price of the Warrants, as adjusted pursuant to
Section 4.8 (the "Call Trigger Price") but not giving effect to any decrease of
such Exercise Price as permitted by Section 7.12 hereof, for 20 consecutive
business days ending within 15 days of the date of the notice of such call shall
have been given to the Warrant Agent by the Company pursuant to Section 4.11,
and provided further that the Company has complied and continues to be in
compliance with the provisions of Section 2.2 hereof. In the event the Company
exercises its right to redeem the Warrants, such Warrants will be exercisable
until the close of business on the date fixed for redemption in such notice. If
any Warrant called for redemption is not exercised by such time, such Warrant
shall cease to be exercisable and the holder thereof shall be entitled only to
the redemption price.

         3.2 Payment of Call Price. On or prior to the opening of business on
the Call Date (as defined in Section 4.11), the Company will deposit with the
Warrant Agent funds in form satisfactory to the Warrant Agent sufficient to
purchase all the Exchange Warrants which are to be called. Payment of the Call
Price will be made by the Warrant Agent upon presentation and surrender of the
Warrant Certificates representing such Exchange Warrants to the Warrant Agent at
its Principal Office.

                                   ARTICLE IV

                        ADJUSTMENTS AND NOTICE PROVISIONS

         4.1 Adjustment of Exercise Price. Subject to the provisions of this
Article IV, the Exercise Price in effect from time to time shall be subject to
adjustment, as follows:

                  (a) In case the Company shall at any time after the date
hereof (i) declare a dividend on the outstanding Common Stock payable in shares
of its capital stock, (ii) subdivide the 


                                      -4-
<PAGE>   8

outstanding Common Stock, (iii) combine the outstanding Common Stock into a
smaller number of shares, or (iv) issue any shares of its capital stock by
reclassification of the Common Stock (including any such reclassification in
connection with a consolidation or merger in which the Company is the continuing
corporation), then, in each case, the Exercise Price in effect, and the number
of shares of Common Stock issuable upon exercise of the Exchange Warrants
outstanding, at the time of the record date for such dividend or of the
effective date of such subdivision, combination or reclassification, shall be
proportionately adjusted so that the holders of the Exchange Warrants after such
time shall be entitled to receive the aggregate number and kind of shares which,
if such Exchange Warrants had been exercised immediately prior to such time,
such holders would have owned upon such exercise and been entitled to receive by
virtue of such dividend, subdivision, combination or reclassification. Such
adjustment shall be made successively whenever any event listed above shall
occur.

                  (b) In case the Company shall distribute to all holders of
Common Stock (including any such distribution made to the shareholders of the
Company in connection with a consolidation or merger in which the Company is the
continuing corporation) evidences of its indebtedness, cash or assets (other
than distributions and dividends payable in shares of Common Stock), or rights,
options or warrants to subscribe for or purchase Common Stock, or securities
convertible into or exchangeable for shares of Common Stock, then, in each case,
the Exercise Price shall be adjusted by multiplying the Exercise Price in effect
immediately prior to the record date for the determination of shareholders
entitled to receive such distribution by a fraction, the numerator of which
shall be the Current Market Price (as determined pursuant to Section 4.2 hereof)
per share of Common Stock on such record date, less the fair market value (as
determined in good faith by the board of directors of the Company, whose
determination shall be conclusive absent manifest error) of the portion of the
evidences of indebtedness or assets so to be distributed, or of such rights,
options, or warrants or convertible or exchangeable securities, or the amount of
such cash, applicable to one share, and the denominator of which shall be such
Current Market Price per share of Common Stock. Such adjustment shall become
effective at the close of business on such record date.

         4.2 Current Market Price. For the purpose of any computation under
Section 3.1 and this Article IV, the Current Market Price per share of Common
Stock on any date shall be deemed to be the average of the daily closing prices
for the 20 consecutive trading days immediately preceding the date in question.
For the purpose of any computation hereunder or under Section 3.1, the closing
price for each day shall be the last reported sales price regular way or, in
case no such reported sale takes place on such day, the closing bid price
regular way, in either case on the principal national securities exchange
(including, for purposes hereof, the NASDAQ National Market System) on which the
Common Stock is listed or admitted to trading or, if the Common Stock is not
listed or admitted to trading on any national securities exchange, the highest
reported bid price for the Common Stock as furnished by the NASD through NASDAQ
or a similar organization if NASDAQ is no longer reporting such information. If
on any such date the Common Stock is not listed or admitted to trading on any
national securities exchange and is not quoted by NASDAQ or any similar
organization, the fair value of a share of Common Stock on such date as
determined in good faith by the board of directors of the Company, whose
determination shall be conclusive absent manifest error, shall be used.

         4.3 No Adjustments to Exercise Price. No adjustment in the Exercise
Price shall be required if such adjustment is less than $.05; provided, however,
that any adjustments which by 


                                      -5-
<PAGE>   9

reason of this Article IV are not required to be made shall be carried forward
and taken into account in any subsequent adjustment. All calculations under this
Article IV shall be made to the nearest cent or to the nearest one hundredth of
a share, as the case may be.

         4.4 Deferral of Adjustments to Exercise Price. In any case in which
this Article IV shall require that an adjustment in the Exercise Price be made
effective as of a record date for a specified event, the Company may elect to
defer, until the occurrence of such event, issuing to the holders of the
Exchange Warrants, if any holder has exercised an Exchange Warrant after such
record date, the shares of Common Stock, if any, issuable upon such exercise
over and above the shares of Common Stock, if any, issuable upon such exercise
on the basis of the Exercise Price in effect prior to such adjustment; provided,
however, that the Company shall deliver to such exercising holder a due bill or
other appropriate instrument evidencing such holder's right to receive such
additional shares upon the occurrence of the event requiring such adjustment.

         4.5 Adjustment to Number of Shares. Upon each adjustment of the
Exercise Price as a result of the calculations made in Section 4.1(b) hereof,
the Exchange Warrants shall thereafter evidence the right to purchase, at the
adjusted Exercise Price, that number of shares (calculated to the nearest
hundredth) obtained by dividing (A) the product obtained by multiplying the
number of shares purchasable upon exercise of the Exchange Warrants prior to
adjustment of the number of shares by the Exercise Price in effect prior to
adjustment of the Exercise Price by (B) the Exercise Price in effect after such
adjustment of the Exercise Price.

         4.6 Reorganizations. In case of any capital reorganization, other than
in the cases referred to in Section 4.1 hereof, or the consolidation or merger
of the Company with or into another corporation (other than a merger or
consolidation in which the Company is the continuing corporation and which does
not result in any reclassification of the outstanding shares of Common Stock or
the conversion of such outstanding shares of Common Stock into shares of other
stock or other securities or property), or in the case of any sale, lease or
conveyance to another corporation of the property and assets of any nature of
the Company as an entirety or substantially as an entirety (such actions being
hereinafter collectively referred to as "Reorganizations"), there shall
thereafter be deliverable upon exercise of any Exchange Warrant (in lieu of the
number of shares of Common Stock theretofore deliverable) the number of shares
of stock or other securities or property to which a holder of the number of
shares of Common Stock which would otherwise have been deliverable upon the
exercise of such Exchange Warrant would have been entitled upon such
Reorganization if such Exchange Warrant had been exercised in full immediately
prior to such Reorganization. In case of any Reorganization, appropriate
adjustment, as determined in good faith by the Board of Directors of the
Company, shall be made in the application of the provisions herein set forth
with respect to the rights and interests of Warrant holders so that the
provisions set forth herein shall thereafter be applicable, as nearly as
possible, in relation to any shares or other property thereafter deliverable
upon exercise of Exchange Warrants. Any such adjustment shall be made by and set
forth in a supplemental agreement between the Company, or any successor thereto,
and the Warrant Agent and shall for all purposes hereof conclusively be deemed
to be an appropriate adjustment. The Company shall not effect any such
Reorganization unless upon or prior to the consummation thereof the successor
corporation, or if the Company shall be the surviving corporation in any such
Reorganization and is not the issuer of the shares of stock or other securities
or property to be delivered to holders of shares of the Common Stock outstanding
at the effective time thereof, then such issuer, shall assume by written
instrument the obligation to deliver to the registered holder of 


                                      -6-
<PAGE>   10

any Warrant Certificate such shares of stock, securities, cash or other property
as such holder shall be entitled to purchase in accordance with the foregoing
provisions. In the event of sale, lease or conveyance or other transfer of all
or substantially all of the assets of the Company as part of a plan for
liquidation of the Company, all rights to exercise any Exchange Warrant shall
terminate 30 days after the Company gives written notice to each registered
holder of a Warrant Certificate that such sale or conveyance or other transfer
has been consummated.

         4.7 Reclassifications. In case of any reclassification or change of the
shares of Common Stock issuable upon exercise of the Exchange Warrants (other
than a change in par value or from no par value to a specified par value, or as
a result of a subdivision or combination, but including any change in the shares
into two or more classes or series of shares), or in case of any consolidation
or merger of another corporation into the Company in which the Company is the
continuing corporation and in which there is a reclassification or change
(including a change to the right to receive cash or other property) of the
shares of Common Stock (other than a change in par value, or from no par value
to a specified par value, or as a result of a subdivision or combination, but
including any change in the shares into two or more classes or series of
shares), the holders of the Exchange Warrants shall have the right thereafter to
receive upon exercise of the Exchange Warrants solely the kind and amount of
shares of stock and other securities, property, cash, or any combination thereof
receivable upon such reclassification, change, consolidation or merger by a
holder of the number of shares of Common Stock for which the Exchange Warrants
might have been exercised immediately prior to such reclassification, change,
consolidation or merger. Thereafter, appropriate provision shall be made for
adjustments which shall be as nearly equivalent as practicable to the
adjustments in Article IV. The above provisions of this Section 4.7 shall
similarly apply to successive reclassifications and changes of shares of Common
Stock.

         4.8 Adjustment of Call Trigger Price. Upon each adjustment of the
Exercise Price of the Exchange Warrants pursuant to Article IV hereof, the Call
Trigger Price shall be adjusted by multiplying such price as in effect prior to
such adjustment by a fraction, the numerator of which shall be the Exercise
Price subsequent to adjustment and the denominator of which shall be the
Exercise Price prior to such adjustment. All calculations under this Section 4.8
shall be made to the nearest cent.

         4.9 Verification of Computations. Whenever the exercise price is
adjusted as provided in this Article IV, the Company will promptly obtain a
certificate of its Chief Financial Officer setting forth the exercise price as
so adjusted and a brief statement of the facts accounting for such adjustment,
and will make available a brief summary thereof to the holders of the Warrant
Certificates, at their addresses listed on the register maintained for that
purpose by the Warrant Agent (which summary may be included in any notice of
adjustment required by Section 4.12 hereof).

         4.10 Notice of Certain Actions. In case at any time the Company shall
propose:

                  (a) to pay any dividend or make any distribution on shares of
         Common Stock in shares of Common Stock or make any other distribution
         (other than regularly scheduled cash dividends which are not in a
         greater amount per share than the most recent such cash dividend) to
         all holders of Common Stock; or


                                      -7-
<PAGE>   11

                  (b) to issue any rights, warrants or other securities to all
         holders of Common Stock entitling them to purchase any additional
         shares of Common Stock or any other rights, warrants or other
         securities; or

                  (c) to effect any consolidation, merger, sale, lease, or
         conveyance of property, described in Section 4.6, or any
         reclassification or change of outstanding shares of Common Stock,
         described in Section 4.7; or

                  (d) to effect any liquidation, dissolution or winding-up of
         the Company; or

                  (e) to take any other action which would cause an adjustment
         to the Exercise Price;

then, in each such case, the Company shall cause notice of such proposed action
to be mailed to the Warrant Agent. Such notice shall specify the date on which
the books of the Company shall close, or a record shall be taken, for
determining holders of Common Stock entitled to receive such stock dividend or
other distribution or such rights or warrants, or the date on which such
reclassification, change, consolidation, merger, sale, lease, other disposition,
liquidation, dissolution, winding up or exchange or other action shall take
place or commence, as the case may be, and the date as of which it is expected
that holders of record of Common Stock shall be entitled to receive securities
or other property deliverable upon such action, if any such date has been fixed.
The Company shall cause copies of such notice to be mailed to each registered
holder of a Warrant Certificate. Such notice shall be mailed, in the case of any
action covered by Subsection 4.10(a) or 4.10(b) above, at least 15 days prior to
the record date for determining holders of the Common Stock for purposes of
receiving such payment or offer; in the case of any action covered by Subsection
4.10(c) or 4.10(d) above, at least 15 days prior to the earlier of the date upon
which such action is to take place or any record date to determine holders of
Common Stock entitled to receive such securities or other property; and in the
case of any action covered by Subsection 4.10(e) above, no more than 15 days
after such action.

         4.11 Notice of Call. Notice of any call for redemption shall be given
to the Warrant Agent by the Company upon not less than 30 days nor more than 60
days prior to the date established for such call (the "Call Date") and the
Company shall cause the Warrant Agent to mail such notice to all registered
holders of Warrant Certificates to be called promptly after the Company shall
have given such notice to the Warrant Agent. Each such notice of call will
specify the Call Date and the Call Price. The notice will state that payment of
the Call Price will be made by the Warrant Agent upon presentation and surrender
of the Warrant Certificates representing such Exchange Warrants to the Warrant
Agent at its Principal Office, and will also state that the right to exercise
the Exchange Warrants will terminate at 5:00 P.M., New York City time, on the
business day immediately preceding the Call Date. The Company will also make
prompt public announcement of such redemption by news release and by notice to
the NASD or any national securities exchange on which the Warrants are listed
for trading.

         4.12 Notice of Adjustments. Whenever any adjustment is made pursuant to
this Article IV, the Company shall cause written notice of such adjustment to be
sent by registered mail, postage prepaid to the Warrant Agent within 15 days
thereafter, such notice to include in reasonable detail (i) the events
precipitating the adjustment, (ii) the computation of any adjustments, and (iii)


                                      -8-
<PAGE>   12

the Exercise Price, the number of shares or the securities or other property
purchasable upon exercise of each Exchange Warrant and the Call Trigger Price
after giving effect to such adjustment. The Company shall cause the Warrant
Agent, within 15 days after receipt of such notice from the Company, to mail a
similar notice to be mailed to each registered holder of a Warrant Certificate.

         4.13 Warrant Certificate Amendments. Irrespective of any adjustments
pursuant to this Article IV, Warrant Certificates theretofore or thereafter
issued need not be amended or replaced but certificates thereafter issued shall
bear an appropriate legend or other notice of any adjustments.

         4.14 Fractional Shares. The Company shall not be required upon the
exercise of any Exchange Warrant to issue fractional shares of Common Stock
which may result from adjustments in accordance with this Article IV to the
Exercise Price or number of shares of Common Stock purchasable under each
Exchange Warrant. If more than one Exchange Warrant is exercised at one time by
the same registered holder, the number of full shares of Common Stock which
shall be deliverable shall be computed based on the number of shares deliverable
in exchange for the aggregate number of Exchange Warrants exercised. With
respect to any final fraction of a share called for upon the exercise of any
Exchange Warrant or Exchange Warrants, the Company shall pay a cash adjustment
in respect of such final fraction in an amount equal to the same fraction of the
Current Market Price of a share of Common Stock calculated in accordance with
Section 4.2.

                                    ARTICLE V

                          OTHER PROVISIONS RELATING TO
                          RIGHTS OF REGISTERED HOLDERS
                             OF WARRANT CERTIFICATES

         5.1 Rights of Warrant Holders. No Warrant Certificate shall entitle the
registered holder thereof to any of the rights of a shareholder of the Company,
including, without limitation, the right to vote, to receive dividends and other
distributions, or to receive any notice of, or to attend, meetings of
shareholders or any other proceedings of the Company.

         5.2 Lost, Stolen, Mutilated or Destroyed Warrant Certificates. If any
Warrant Certificate shall be mutilated, lost, stolen or destroyed, the Company
shall direct the Warrant Agent to execute and deliver, in exchange and
substitution for and upon cancellation of a mutilated Warrant Certificate, or in
lieu of or in substitution for a lost, stolen or destroyed Warrant Certificate,
a new Warrant Certificate for the number of Exchange Warrants represented by the
Warrant Certificate so mutilated, lost, stolen or destroyed but only upon
receipt of evidence of such loss, theft or destruction of such Warrant
Certificate, and of the ownership thereof, and indemnity, if requested, all
satisfactory to the Company and the Warrant Agent. Applicants for such
substitute Warrant Certificates shall also comply with such other reasonable
regulations and pay such other reasonable charges incidental thereto as the
Company or Warrant Agent may prescribe. Any such new Warrant Certificate shall
constitute an original contractual obligation of the Company, whether or not the
allegedly lost, stolen, mutilated or destroyed Warrant Certificate shall be at
any time enforceable by anyone.


                                      -9-
<PAGE>   13

                                   ARTICLE VI

                    SPLIT UP, COMBINATION, EXCHANGE, TRANSFER
                    AND CANCELLATION OF WARRANT CERTIFICATES

         6.1 Split Up, Combination, Exchange and Transfer of Warrant
Certificates. Prior to the Exercise Deadline, Warrant Certificates, subject to
the provisions of Section 6.2, may be split up, combined or exchanged for other
Warrant Certificates representing a like aggregate number of Exchange Warrants
or may be transferred in whole or in part. Any holder desiring to split up,
combine or exchange a Warrant Certificate or Warrant Certificates shall make
such request in writing delivered to the Warrant Agent at its Principal Office
and shall surrender the Warrant Certificate or Warrant Certificates so to be
split up, combined or exchanged at said office. Subject to any applicable laws,
rules or regulations restricting transferability, any restriction on
transferability that may appear on a Warrant Certificate in accordance with the
terms hereof, or any "stop-transfer" instructions the Company may give to the
Warrant Agent to implement any such restrictions (which instructions the Company
is expressly authorized to give), transfer of outstanding Warrant Certificates
may be effected by the Warrant Agent from time to time upon the books of the
Company to be maintained by the Warrant Agent for that purpose, upon a surrender
of the Warrant Certificate to the Warrant Agent at its Principal Office, with
the assignment form set forth in the Warrant Certificate duly executed and with
Signatures Guaranteed. Upon any such surrender for split up, combination,
exchange or transfer, the Warrant Agent shall execute and deliver to the person
entitled thereto a Warrant Certificate or Warrant Certificates, as the case may
be, as so requested. The Warrant Agent may require the holder to pay a sum
sufficient to cover any tax or governmental charge that may be imposed in
connection with any split up, combination, exchange or transfer of Warrant
Certificates prior to the issuance of any new Warrant Certificate.

         6.2 Cancellation of Warrant Certificates. Any Warrant Certificate
surrendered upon the exercise of Exchange Warrants or for split up, combination,
exchange or transfer, or purchased or otherwise acquired by the Company, shall
be cancelled and shall not be reissued by the Company; and, except as provided
(i) in Section 2.5, in case of the exercise of less than all of the Exchange
Warrants evidenced by a Warrant Certificate, or (ii) in Section 6.1, in case of
a split up, combination, exchange or transfer of the Exchange Warrants evidenced
by a Warrant Certificate, no Warrant Certificate shall be issued hereunder in
lieu of such cancelled Warrant Certificate. Any Warrant Certificate so cancelled
shall be destroyed by the Warrant Agent unless otherwise directed by the
Company.

         6.3 Agreement of Warrant Certificate Holders. Every holder of a Warrant
Certificate by accepting the same consents and agrees with the Company and the
Warrant Agent and with every other holder of a Warrant Certificate that:

                  (a) transfer of the Warrant Certificates shall be registered
on the books of the Company maintained for that purpose by the Warrant Agent
only if surrendered at the Principal Office of the Warrant Agent, duly endorsed
or accompanied by a proper instrument of transfer, with Signatures Guaranteed;
and

                  (b) prior to due presentment for registration of transfer, the
Company and the Warrant Agent may deem and treat the person in whose name the
Warrant Certificate is registered as 


                                      -10-
<PAGE>   14

the absolute owner thereof and of the Exchange Warrants evidenced thereby
(notwithstanding any notations of ownership or writing on the Warrant
Certificates made by anyone other than the Company or the Warrant Agent) for all
purposes whatsoever, and neither the Company nor the Warrant Agent shall be
affected by any notice to the contrary.

                                   ARTICLE VII

                     PROVISIONS CONCERNING THE WARRANT AGENT
                                AND OTHER MATTERS

         7.1 Payment of Taxes and Charges. The Company will from time to time
promptly pay to the Warrant Agent, or make provisions satisfactory to the
Warrant Agent for the payment of, all taxes and charges that may be imposed by
the United States or any state upon the Company or the Warrant Agent in
connection with the issuance or delivery of shares of Common Stock upon the
exercise of any Exchange Warrants, but any transfer taxes in connection with the
issuance of Warrant Certificates or certificates for shares of Common Stock in
any name other than that of the registered holder of the Warrant Certificate
surrendered shall be paid by such registered holder; and, in such case, the
Company shall not be required to issue or deliver any Warrant Certificate or
certificate for shares of Common Stock until such taxes shall have been paid or
it has been established to the Company's satisfaction that no tax is due.

         7.2 Resignation or Removal of Warrant Agent. The Warrant Agent may
resign its duties and be discharged from all further duties and liabilities
hereunder after giving 30 days' notice in writing to the Company, except that
such shorter notice may be given as the Company shall, in writing, accept as
sufficient. Upon comparable notice to the Warrant Agent, the Company may remove
the Warrant Agent; provided, however, that in such event the Company shall
appoint a new Warrant Agent, as hereinafter provided, and the removal of the
Warrant Agent shall not be effective until a new Warrant Agent has been
appointed and has accepted such appointment. If the office of Warrant Agent
becomes vacant by resignation or incapacity to act or otherwise, the Company
shall appoint in writing a new Warrant Agent. If the Company shall fail to make
such appointment within a period of 30 days after it has been notified in
writing of such resignation or incapacity by the resigning or incapacitated
Warrant Agent or by the registered holder of any Warrant Certificate, then the
registered holder of any Warrant Certificate may apply to any court of competent
jurisdiction for the appointment of a new Warrant Agent. Any successor Warrant
Agent, whether appointed by the Company or any such court, shall be a registered
transfer agent, bank or trust company in good standing and incorporated under
the United States banking laws or under the laws of any State within the United
States, having its principal office within the United States. Any new Warrant
Agent appointed hereunder shall execute, acknowledge and deliver to the former
Warrant Agent last in office and to the Company, an instrument accepting such
appointment under substantially the same terms and conditions as are contained
herein and thereupon such new Warrant Agent, without any further act or deed,
shall become vested with the rights, powers, duties and responsibilities of the
Warrant Agent and the former Warrant Agent shall cease to be the Warrant Agent;
but if for any reason it becomes necessary or expedient to have the former
Warrant Agent execute and deliver any further assurance, conveyance, act or
deed, the same shall be done at the expense of the Company and shall be legally
and validly executed and delivered by the former Warrant Agent.


                                      -11-
<PAGE>   15

         7.3 Notice of Appointment. Not later than the effective date of the
appointment of a new Warrant Agent, the Company shall cause notice thereof to be
mailed to the former Warrant Agent and the transfer agent, if any, for the
Common Stock and shall forthwith cause a copy of such notice to be mailed to
each registered holder of a Warrant Certificate. Failure to mail such notice, or
any defect contained therein, shall not affect the legality or validity of the
appointment of the successor Warrant Agent.

         7.4 Merger of Warrant Agent. Any company into which the Warrant Agent
may be merged or with which it may be consolidated, or any company resulting
from any merger or consolidation to which the Warrant Agent shall be a party,
shall be the successor Warrant Agent under this Agreement without further act,
provided that such company would be eligible for appointment as a successor
Warrant Agent under the provisions of Section 7.2 hereof. Any such successor
Warrant Agent may adopt the prior countersignature of any predecessor Warrant
Agent and distribute Warrant Certificates countersigned but not distributed by
such predecessor Warrant Agent, or may countersign the Warrant Certificates in
its own name.

         7.5 Company Responsibilities. The Company agrees that it shall (i) pay
the Warrant Agent reasonable remuneration for its services as Warrant Agent
hereunder and will reimburse the Warrant Agent upon demand for all expenses,
advances and expenditures that the Warrant Agent may reasonably incur in the
execution of its duties hereunder (including fees and expenses of its counsel);
(ii) provide the Warrant Agent, upon request, with sufficient funds to pay any
cash due pursuant to Section 4.14 upon exercise of the Exchange Warrants; and
(iii) perform, execute, acknowledge and deliver or cause to be performed,
executed, acknowledged and delivered all further and other acts, instruments and
assurances as may reasonably be required by the Warrant Agent for the carrying
out or performing by the Warrant Agent of the provisions of this Agreement.

         7.6 Certification for the Benefit of Warrant Agent. Whenever in the
performance of its duties under this Agreement the Warrant Agent shall deem it
necessary or desirable that any matter be proved or established or that any
instructions with respect to the performance of its duties hereunder be given by
the Company prior to taking or suffering any action hereunder, such matter
(unless other evidence in respect thereof be herein specifically prescribed) may
be deemed to be conclusively proved and established, or such instructions may be
given, by a certificate or instrument signed by the Chairman, the Chief
Executive Officer, the President, a Vice President, the Secretary or the
Treasurer of the Company and delivered to the Warrant Agent. Such certificate or
instrument may be relied upon by the Warrant Agent for any action taken or
suffered in good faith by it under the provisions of this Agreement; but in its
discretion the Warrant Agent may in lieu thereof accept other evidence of such
matter or may require such further or additional evidence as it may deem
reasonable.

         7.7 Books and Records. The Warrant Agent shall maintain the Company's
books and records for registration and registration of transfer of the Warrant
Certificates issued hereunder. Such books and records shall show the names and
addresses of the respective holders of the Warrant Certificates, the number of
Exchange Warrants evidenced on its face by each Warrant Certificate and the date
of each Warrant Certificate.

         7.8 Liability of Warrant Agent. The Warrant Agent shall be liable
hereunder for its own negligence or willful misconduct. The Warrant Agent shall
act hereunder solely as an agent for the 


                                      -12-
<PAGE>   16

Company and its duties shall be determined solely by the provisions hereof. The
Warrant Agent shall not be liable for or by reason of any of the statements of
fact or recitals contained in this Agreement or in the Warrant Certificates
(except its counter-signature thereof) or be required to verify the same, but
all such statements and recitals are and shall be deemed to have been made by
the Company only. The Warrant Agent will not incur any liability or
responsibility to the Company or to any holder of any Warrant Certificate for
any action taken, or any failure to take action, in reliance on any notice,
resolution, waiver, consent, order, certificate or other paper, document or
instrument reasonably believed by the Warrant Agent to be genuine and to have
been signed, sent or presented by the proper party or parties. The Warrant Agent
shall not be under any responsibility in respect of the validity of this
Agreement or the execution and delivery hereof by the Company or in respect of
the validity or execution of any Warrant Certificate (except its
counter-signature thereof); nor shall it be responsible for any breach by the
Company of any covenant or condition contained in this Agreement or in any
Warrant Certificate; nor shall it be responsible for the making of any
adjustment required under the provisions of Article IV hereof or responsible for
the manner, method or amount of any such adjustment or the facts that would
require any such adjustment; nor shall it by any act hereunder be deemed to make
any representation or warranty as to the authorization or reservation of any
shares of Common Stock or other securities to be issues pursuant to this
Agreement or any Warrant Certificate or as to whether any shares of Common Stock
or other securities will, when issued, be validly authorized and issued and
fully paid and nonassessable.

         7.9 Use of Attorneys, Agents and Employees. The Warrant Agent may
execute and exercise any of the rights or powers hereby vested in it or perform
any duty hereunder either itself or by or through its attorneys, agents or
employees.

         7.10 Indemnification. The Company agrees to indemnify the Warrant Agent
and save it harmless against any and all losses, expenses or liabilities,
including judgments, costs and counsel fees arising out of or in connection with
its agency under this Agreement, except as a result of the negligence or willful
misconduct of the Warrant Agent.

         7.11 Acceptance of Agency. The Warrant Agent hereby accepts the agency
established by this Agreement and agrees to perform the same upon the terms and
conditions herein set forth.

         7.12 Changes to Agreement. The Warrant Agent may, without the consent
or concurrence of any registered holder of a Warrant Certificate, by
supplemental agreement or otherwise, join with the Company in making any changes
or corrections in this Agreement that they shall have been advised by counsel
(i) are required to cure any ambiguity or to correct any defective or
inconsistent provision or clerical omission or mistake or manifest error herein
contained, (ii) add to the covenants and agreements of the Company or the
Warrant Agent in this Agreement such further covenants and agreements thereafter
to be observed, or (iii) result in the surrender or modification of any right or
power reserved to or conferred upon the Company or the Warrant Agent in this
Agreement, including, without limitation, the reduction of the Exercise Price
(except for purposes of Article III hereof), but which changes or corrections do
not or will not adversely affect, alter or change the rights, privileges or
immunities of the registered holders of Warrant Certificates.

         7.13 Assignment. All the covenants and provisions of this Agreement by
or for the benefit of the Company or the Warrant Agent shall bind and inure to
the benefit of their respective successors and assigns.


                                      -13-
<PAGE>   17

         7.14 Successor to Company. The Company will not merge or consolidate
with or into any other corporation or sell or otherwise transfer its property,
assets and business substantially as an entirety to a successor corporation,
unless the corporation resulting from such merger, consolidation, sale or
transfer (if not the Company) shall expressly assume, by supplemental agreement
satisfactory in form and substance to the Warrant Agent and delivered to the
Warrant Agent, the due and punctual performance and observance of each and every
covenant and condition of this Agreement to be performed and observed by the
Company.

         7.15 Notices. Any notice or demand required by this Agreement to be
given or made by the Warrant Agent or by the registered holder of any Warrant
Certificate to or on the Company shall be sufficiently given or made if sent by
first-class or registered mail, postage prepaid, addressed (until another
address is filed in writing with the Warrant Agent by the Company) as follows:

                           Epoch Pharmaceuticals, Inc.
                           1725 220th Street, S.E., No. 104
                           Bothell, Washington 98021
                           Attention:  Chief Financial Officer

Any notice or demand required by this Agreement to be given or made by the
registered holder of any Warrant Certificate or by the Company to or on the
Warrant Agent shall be sufficiently given or made if sent by first-class or
registered mail, postage prepaid, addressed (until another address is filed in
writing with the Company by the Warrant Agent), as follows:

                           American Stock Transfer & Trust Company
                           40 Wall Street
                           New York, New York 10005
                           Attention:  George Karfunkel

Any notice or demand required by this Agreement to be given or made by the
Company or the Warrant Agent to or on the registered holder of any Warrant
Certificate shall be sufficiently given or made, whether or not such holder
receives the notice, if sent by first-class or registered mail, postage prepaid,
addressed to such registered holder at his last address as shown on the books of
the Company maintained by the Warrant Agent. Otherwise such notice or demand
shall be deemed given when received by the party entitled thereto.

         7.16 Defects in Notice. Failure to file any certificate or notice or to
mail any notice, or any defect in any certificate or notice pursuant to this
Agreement, shall not affect in any way the rights of any registered holder of a
Warrant Certificate or the legality or validity of any adjustment made pursuant
to Article IV hereof, or any transaction giving rise to any such adjustment, or
the legality or validity of any action taken or to be taken by the Company.

         7.17 Governing Law. The laws of the State of New York shall govern this
Warrant Agreement and the Warrant Certificates.

         7.18 Standing. Nothing in this Agreement expressed and nothing that may
be implied from any of the provisions hereof is intended, or shall be construed,
to confer upon, or give to, any person or corporation other than the Company,
the Warrant Agent, and the registered holders of the 


                                      -14-
<PAGE>   18

Warrant Certificates any right, remedy or claim under or by reason of this
Agreement or of any covenant, condition, stipulation, promise or agreement
contained herein; and all covenants, conditions, stipulations, promises and
agreements contained in this Agreement shall be for the sole and exclusive
benefit of the Company and the Warrant Agent and their respective successors and
assigns, and the registered holders of the Warrant Certificates.

         7.19 Headings. The descriptive headings of the articles and sections of
this Agreement are inserted for convenience only and shall not control or affect
the meaning or construction of any of the provisions hereof.

         7.20 Counterparts. This Agreement may be executed in any number of
counterparts, each of which so executed shall be deemed to be an original; but
such counterparts shall together constitute but one and the same instrument.

         7.21 Conflict of Interest. The Warrant Agent and any shareholder,
director, officer or employee of the Warrant Agent may buy, sell or deal in any
of the Warrant Certificates or other securities of the Company or become
pecuniarily interested in any transaction in which the Company may be
interested, or contract with or lend money to the Company or otherwise act as
fully and freely as though the Warrant Agent were not Warrant Agent under this
Agreement. Nothing herein shall preclude the Warrant Agent from acting in any
other capacity for the Company, including, without limitation, as trustee under
any indenture or as transfer agent for the Common Stock or any other securities
of the Company, or for any other legal entity.

         7.22 Availability of the Agreement. The Warrant Agent shall keep copies
of this Agreement available for inspection by holders of Exchange Warrants
during normal business hours at its Principal Office. Copies of this Agreement
may be obtained upon written request addressed to:

                  Epoch Pharmaceuticals, Inc.
                  1725 220th Street, S.E., No. 104
                  Bothell, Washington 98021
                  Attention:  Chief Financial Officer


                                      -15-
<PAGE>   19

         IN WITNESS WHEREOF, this Agreement has been duly executed by the
parties hereto as of the day and year first above written.

                                         EPOCH PHARMACEUTICALS, INC.


                                         By: /s/ Sanford Zweifach
                                             -----------------------------------
                                             Name:  Sanford Zweifach
                                             Title: President and Chief 
                                             Financial Officer


                                         AMERICAN STOCK TRANSFER & TRUST COMPANY


                                         By: /s/ Herbert J. Lemmer
                                             -----------------------------------
                                             Name: Herbert J. Lemmer
                                             Title:  Vice President



                                      -16-