<PAGE>   1

                     U.S. SECURITIES AND EXCHANGE COMMISSION
                              Washington D.C. 20549

                                   FORM 10-QSB

(Mark One)

[X]  QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15 OF THE SECURITIES 
     EXCHANGE ACT OF 1934 

     FOR THE QUARTERLY PERIOD ENDED MARCH 31, 1999

[ ]  TRANSITION REPORT PURSUANT TO SECTION 13 OR 15 OF THE SECURITIES 
     EXCHANGE ACT OF 1934 

     FOR THE TRANSITION PERIOD FROM ______________ TO ______________.


                         Commission file number 0-22170


                           EPOCH PHARMACEUTICALS, INC.
-------------------------------------------------------------------------------
        (Exact name of small business issuer as specified in its charter)


             Delaware                                      91-1311592
-------------------------------                        -------------------
(State or other jurisdiction of                         (I.R.S. Employer 
 incorporation or organization)                        Identification No.)


12277 134th Court N.E., Suite 110, Redmond, Washington         98052
------------------------------------------------------       ----------
      (Address of principal executive offices)               (Zip Code)


                                 (425) 821-7535
-------------------------------------------------------------------------------
                (Issuer's telephone number, including area code)


                                 Not Applicable
-------------------------------------------------------------------------------
              (Former name, former address and former fiscal year,
                          if changed since last report)

Check whether the issuer (1) filed all reports to be filed by Section 13 or
15(d) of the Exchange Act during the past 12 months (or for such shorter period
that the registrant was required to file such reports), and (2) has been subject
to such filing requirements for the past 90 days.

                                YES  X      NO
                                    ---         ---

State the number of shares outstanding of each of the issuer's classes of common
equity as of the latest practicable date.


          Class                                       Outstanding at May 4, 1999
----------------------------                          --------------------------
Common Stock, $.01 par value                                 14,837,464


                               Page 1 of 11 Pages

<PAGE>   2

                           EPOCH PHARMACEUTICALS, INC.

                              INDEX TO FORM 10-QSB

<TABLE>
<CAPTION>
                                                                                      Page Number
                                                                                      -----------
<S>                                                                                  <C>
Part I.  Financial Information

    Item 1. Financial Statements

               Balance Sheets as of December 31, 1998
               and March 31, 1999 (unaudited).......................................        3

               Statements of Operations (unaudited) for the three
               months ended March 31, 1998 and 1999.................................        4

               Statements of Cash Flows (unaudited) for the three months ended
               March 31, 1998 and 1999..............................................        5

               Notes to Financial Statements (unaudited)............................        6

    Item 2. Management's Discussion and Analysis of Financial
            Condition and Results of Operations.....................................        7

Part II. Other Information

    Item 6. Exhibits and Reports on Form 8-K........................................       10

    Note:  Items 1 - 5 are omitted, as they are not applicable.

Signature ..........................................................................       11
</TABLE>


                                       2

<PAGE>   3

                           EPOCH PHARMACEUTICALS, INC.

                                 BALANCE SHEETS

                                     ASSETS
<TABLE>
<CAPTION>
                                                                                             MARCH 31,
                                                                        DECEMBER 31,           1999
                                                                            1998            (UNAUDITED)
                                                                        ------------        ------------
<S>                                                                     <C>                 <C>       
Current assets:
   Cash and cash equivalents ....................................       $    658,363        $  1,724,207
   Receivables ..................................................             38,303             108,088
   Prepaid expenses .............................................             45,769              48,263
                                                                        ------------        ------------
      Total current assets ......................................            742,435           1,880,558

Equipment, net ..................................................            173,831             207,086

Other assets ....................................................             53,937              53,898
                                                                        ------------        ------------
      Total assets ..............................................       $    970,203        $  2,141,542
                                                                        ============        ============

                            LIABILITIES AND STOCKHOLDERS' DEFICIT
Current liabilities:
   Accounts payable .............................................       $    215,813        $    131,314
   Accrued interest on note payable to related party ............            208,804             272,507
   Accrued expenses for canceled relocation .....................            391,042             103,645
   Other accrued liabilities ....................................            356,033             403,784
   Deferred revenue - current portion ...........................                 --             350,000
   Note payable to related party ................................                 --           3,000,000
                                                                        ------------        ------------

      Total current liabilities .................................          1,171,692           4,261,250

Note payable to related party ...................................          3,000,000                  --
Deferred revenue ................................................                 --           1,950,000

Stockholders' deficit:
    Preferred stock, par value $.01; 10,000,000 shares
      authorized; no shares issued and outstanding ..............                 --                  --
    Common stock, par value $.01; 50,000,000 shares
      authorized; issued and outstanding: 14,824,227 at
      December 31, 1998 and 14,835,214 at March 31, 1999 ........            148,242             148,352
   Additional paid-in capital ...................................         54,460,706          54,470,102
   Deferred compensation expense ................................           (159,826)           (147,838)
   Deferred financing expense ...................................           (817,794)           (651,123)
   Accumulated deficit ..........................................        (56,832,817)        (57,889,201)
                                                                        ------------        ------------
      Total stockholders' deficit ...............................         (3,201,489)         (4,069,708)
                                                                        ------------        ------------
Contingency

Total liabilities and stockholders' deficit .....................       $    970,203        $  2,141,542
                                                                        ============        ============
</TABLE>

                 See accompanying notes to financial statements.

                                       3

<PAGE>   4

                           EPOCH PHARMACEUTICALS, INC.

                            STATEMENTS OF OPERATIONS
                                   (UNAUDITED)

<TABLE>
<CAPTION>
                                                          THREE MONTHS ENDED
                                                              MARCH 31,
                                                    ------------------------------
                                                        1998              1999
                                                    ------------      ------------
<S>                                                 <C>               <C>         
Research contract revenue .....................     $     40,783      $     95,092

Operating expenses:
   Research and development ...................          703,147           644,601
   General and administrative .................          375,485           334,865
                                                    ------------      ------------
      Total operating expenses ................        1,078,632           979,466
                                                    ------------      ------------

        Operating loss ........................       (1,037,849)         (884,374)

Other income (expense):
   Interest income ............................           26,448            18,553
   Interest and financing expense .............          (47,467)         (230,563)
   Other income ...............................           19,955                --
                                                    ------------      ------------
      Loss from continuing operations .........       (1,038,913)       (1,096,384)

Discontinued operations -
   gain on disposal of discontinued operations            30,000            40,000
                                                    ------------      ------------

      Net loss ................................     $ (1,008,913)     $ (1,056,384)
                                                    ============      ============

Loss per share from continuing operations -
   basic and diluted ..........................     $      (0.07)     $      (0.07)
Income per share from discontinued operations -
   basic and diluted ..........................               --                --
                                                    ============      ============
Net loss per share - basic and diluted ........     $      (0.07)     $      (0.07)
                                                    ============      ============
Weighted average number of common shares
   outstanding - basic and diluted ............       14,814,793        14,830,435
</TABLE>

                 See accompanying notes to financial statements.


                                       4
<PAGE>   5

                           EPOCH PHARMACEUTICALS, INC.

                            STATEMENTS OF CASH FLOWS
                                   (UNAUDITED)

<TABLE>
<CAPTION>
                                                                    THREE MONTHS ENDED
                                                                         MARCH 31,
                                                               -----------------------------
                                                                   1998             1999
                                                               ------------     ------------
<S>                                                            <C>              <C>         
Cash flows from operating activities:
   Net loss ..............................................     $(1,008,913)     $(1,056,384)

   Adjustments to reconcile net loss to net cash
     provided by (used in) operating activities:
      Depreciation and amortization ......................          13,627           18,873
      Amortization of deferred financing expense .........          25,576          166,671
      Amortization of deferred compensation expense ......              --           11,988
      Changes in operating assets and liabilities:
         Receivables .....................................           6,852          (69,785)
         Prepaid expenses and other assets ...............          (5,676)          (2,455)
         Accounts payable ................................         (79,766)         (84,499)
         Accrued interest on note payable to related party          21,708           63,703
         Accrued expenses for canceled relocation ........              --         (287,397)
         Deferred revenue ................................              --        2,300,000
         Other accrued liabilities .......................          99,577           47,751
                                                               -----------      -----------
           Net cash provided by (used in) operating
             activities ..................................        (927,015)       1,108,466
                                                               -----------      -----------
Cash used in investing activities - acquisition 
  of equipment ...........................................         (20,512)         (52,128)
                                                               -----------      -----------
Cash flows from financing activities:
   Proceeds from note payable ............................       3,000,000               --
   Exercise of stock options .............................              --            9,506
                                                               -----------      -----------
      Net cash provided by financing activities ..........       3,000,000            9,506
                                                               -----------      -----------

Net increase in cash and cash equivalents ................       2,052,473        1,065,844
Cash and cash equivalents at beginning of period .........       1,485,483          658,363
                                                               -----------      -----------
Cash and cash equivalents at end of period ...............     $ 3,537,956      $ 1,724,207
                                                               ===========      ===========
Supplemental disclosure of non-cash financing 
  activities - warrants issued in debt financing .........     $ 1,333,361      $        --
                                                               ===========      ===========
Supplemental disclosure of cash flow information - cash
  payments made during the period for interest ...........     $       183      $       189
                                                               ===========      ===========
</TABLE>

                 See accompanying notes to financial statements.

                                       5

<PAGE>   6

                           EPOCH PHARMACEUTICALS, INC.

                          NOTES TO FINANCIAL STATEMENTS
                                 MARCH 31, 1999
                                   (UNAUDITED)

NOTE (1) BASIS OF PRESENTATION

        Epoch Pharmaceuticals, Inc. ("Epoch" or the "Company") is a biomedical
company utilizing nucleoside and nucleotide chemistry to develop molecular tools
for genetic analysis. Utilizing unique and proprietary technology in the
rational design, synthesis and chemical modification of oligonucleotides, the
Company has positioned itself to provide products and techniques for high
throughput genetic sequence analysis that are in increasing demand in the
rapidly expanding field of genetic pharmacology.

        Previously, Epoch's therapeutic research and development program had
focused on the modification of gene expression by altering cellular genomic DNA
using oligonucleotide targeting technology combined with chemical reactivity.
The Company's technology is based on its expertise in designing and synthesizing
oligonucleotides bearing modifications that selectively bind to and interact
with the target genes.

        Recently, Epoch discovered that the compounds and techniques that were
being developed for its gene modification therapeutic program can be adapted to
several gene sequencing analysis systems currently in use or being developed by
others. The Company believes that this technology has broad application
potential in the developing fields of molecular diagnostics and genomics,
including the detection of infectious diseases, inheritable diseases through
prenatal testing, screening populations to identify genetic markers that
correlate with disease risk or drug response, as well as any other genetic
analysis based on DNA sequence determination.

        In January 1999, we licensed certain of our enabling genetic analysis
technology to the PE Biosystems Division of The Perkin-Elmer Corporation
("Perkin-Elmer"). Perkin-Elmer will use the technology in applications related
to its proprietary technology in the areas of biomedical research and certain
non-clinical applied fields. As part of the license agreement, Perkin-Elmer will
purchase our proprietary chemical intermediates. In addition to up-front license
fees and pre-payments for future purchases, we will receive a royalty on all
products that Perkin-Elmer sells which incorporate our technology.

        The unaudited financial statements have been prepared in accordance with
generally accepted accounting principles for interim financial information and
with the instructions to Form 10-QSB. Accordingly, they do not include all of
the information and footnotes required to be presented for complete financial
statements. The accompanying financial statements include all adjustments
(consisting only of normal recurring accruals) which are, in the opinion of
management, necessary for a fair presentation of the results for the interim
periods presented. Certain 1998 balances have been reclassified to conform with
the 1999 presentation.

        The financial statements and related disclosures have been prepared with
the presumption that users of the interim financial information have read or
have access to the audited financial statements for the preceding fiscal year.
Accordingly, these financial statements should be read in conjunction with the
audited financial statements and the related notes thereto included in the
Company's Annual Report on Form 10-KSB as filed with the Securities and Exchange
Commission on April 15, 1999.


                                       6


<PAGE>   7

NOTE (2) LOSS PER SHARE

        Basic earnings per share (EPS) is computed based on weighted average
shares outstanding and excludes any potential dilution. Diluted EPS reflects
potential dilution from the exercise or conversion of securities into common
stock or from other contracts to issue common stock. The capital structure of
the Company includes stock options and stock warrants. At March 31, 1999, there
were 1,458,999 options outstanding to purchase the common stock of the Company
with exercise prices ranging from $0.30 to $5.88. Also outstanding at March 31,
1999 were 7,798,875 warrants to purchase the common stock of the Company with
exercise prices ranging from $0.30 to $9.21 per share. At March 31, 1998, there
were 1,116,450 options outstanding to purchase the common stock of the Company
with exercise prices ranging from $0.30 to $10.00. Also outstanding at March 31,
1998 were 8,470,016 warrants to purchase the common stock of the Company with
exercise prices ranging from $0.30 to $9.21 per share. The assumed conversion
and exercise of these securities have been excluded from Diluted EPS as their
effect is anti-dilutive.

NOTE (3) LIQUIDITY

        The Company has experienced recurring losses from operations and has a
total stockholders' deficit of approximately $4,070,000 at March 31, 1998 and
cash of approximately $1,724,000, which management estimates will be sufficient
to operate until the third quarter 1999. Additionally, the note payable of
$3,000,000 is due in February 2000, at which time the Company will be required
to retire or refinance the debt.

        To continue operations, the Company will be required to sell additional
equity securities, borrow additional funds, or obtain additional financing
through licensing, joint venture, or other collaborative arrangements. The
Company is pursuing other financing arrangements but has no commitments for such
financing and there can be no assurance that such financing will be available on
satisfactory terms, if at all. If additional funds are not available, the
Company will be required to delay, reduce, or eliminate expenditures for certain
or all of its programs or products.

NOTE (4) DEFERRED REVENUE

        Deferred revenue represents unrecognized license and technology fees,
prepaid royalties, and prepayments for product purchases related to the license
and supply agreement with Perkin-Elmer. License fees, technology fees, and
prepayments for product purchases will be recognized based upon sales of
products as sold. Prepaid royalties will be recognized based upon sales of the
licensed product by Perkin-Elmer.

ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
        OF OPERATIONS; PLAN OF OPERATIONS

        This Quarterly Report on Form 10-QSB contains certain forward-looking
statements that are based on current expectations. In light of the important
factors that can materially affect results, including those set forth below and
elsewhere in this Quarterly Report on Form 10-QSB, the inclusion of
forward-looking information herein should not be regarded as a representation by
the Company or any other person that the objectives or plans of the Company will
be achieved. The Company may encounter competitive, technological, financial and
business challenges making it more difficult than expected to continue to
develop therapeutic technologies and products; the market may not accept the
Company's therapeutic products; the Company may be unable to retain existing key
management personnel; and


                                       7

<PAGE>   8

there may be other material adverse changes in the Company's operations or
business. Certain important factors affecting the forward-looking statements
made herein include, but are not limited to (i) the successful development of
viable therapeutic technologies and products, (ii) accurately forecasting
capital expenditures, and (iii) obtaining new sources of external financing.
Assumptions relating to budgeting, product development and other management
decisions are subjective in many respects and thus susceptible to
interpretations and periodic revisions based on actual experience and business
developments, the impact of which may cause the Company to alter its operating,
capital expenditure or other budgets, which may in turn affect the Company's
financial position and results of operations.

        Future operating results may be impacted by a number of factors that
could cause actual results to differ materially from those stated herein, which
reflect management's current expectations. These factors include industry
specific factors, the Company's ability to maintain access to external financing
sources and its financial liquidity, the Company's ability to timely develop and
produce commercially viable therapeutic products and the Company's ability to
manage expense levels.

RESULTS OF OPERATIONS

        RESEARCH CONTRACT REVENUE. Research contract revenue reflects revenue
from U.S. government grants and contracts, and subcontracts.

        RESEARCH AND DEVELOPMENT. Research and development expenses for the
three months ended March 31, 1999 totaled $645,000, which is $58,000 less than
the prior year. This decrease is primarily the result of reduced rent expense in
the first quarter of 1999, as the new facility is smaller than the previous
facility. Additional variations in research and development expense are the
result of normal business fluctuations.

        GENERAL AND ADMINISTRATIVE. General and administrative expenses of
$335,000 in the first quarter of 1999, are $40,000 less than in the first
quarter of 1998. This variation is the result of normal business fluctuations.

        INTEREST INCOME. Interest income in the first quarter of 1999 is less
than the 1998 comparable period due to lower cash balances available for
investment.

        INTEREST AND FINANCING EXPENSE. Interest and financing expense
represents the costs associated with the $3,000,000 note payable to a related
party which was funded at the end of February 1998. The increases in 1999
represents three months of expenses versus one month in 1998.

        OTHER INCOME. Other income in the first quarter of 1998 represents
payments received from a sublease and administrative support agreement. As of
April 1998, this agreement was terminated and, consequently, there is no further
income from this source beyond April 1998.

        GAIN ON DISPOSAL. The gain on disposal of discontinued operations
represents only that portion of the gain for which cash payments were received
during the reporting periods.

LIQUIDITY AND CAPITAL RESOURCES

        At March 31, 1999, the Company had cash and cash equivalents of
$1,724,000, which resulted primarily from $2,300,000 received in January and
February of 1999 under a license and supply agreement with Perkin-Elmer less
normal expenditures for operations. Under the agreement, the Company will
receive an ongoing royalty stream based on licensee sales and earn revenues from
the sale of chemical intermediates to Perkin-Elmer. Management estimates that
its existing cash balance provides sufficient working capital to operate until
the third quarter of 1999.


                                       8

<PAGE>   9

        Using the proceeds of the Perkin-Elmer licensing agreement and any
future financing, the Company plans to further develop and verify applicability
of its compounds and techniques in the developing fields of molecular
diagnostics and genomics and to determine how its technology may be exploited.

        The Company is focused on the development of its products with the goal
of entering into corporate partnering arrangements to further commercialize the
technology. Our primary future needs for capital are for continued research and
development, repayment of the note payable due in February 2000 and relocation
expenses anticipated to be incurred in a move to new facilities, if our Company
is unable to negotiate a new lease at its existing facility. The Company's
working capital requirements may vary depending upon numerous factors including
the progress of our research and development, competitive and technological
advances, possible relocation expenses and other factors. We anticipate
operating with approximately 25 employees.

        To continue operations, the Company will be required to sell additional
equity securities, borrow additional funds, or obtain additional financing
through licensing, joint venture, or other collaborative arrangements. The
Company is pursuing other financing arrangements but has no commitments for such
financing and there can be no assurance that such financing will be available on
satisfactory terms, if at all. If additional funds are not available, the
Company will be required to delay, reduce, or eliminate expenditures for certain
or all of its programs or products.

        Cash increased by $1,066,000 during the quarter as a result of
$2,300,000 received from Perkin-Elmer offset by normal expenditures on the
Company's operations and payment of $287,000 on the canceled building facility
project discussed below. The comparable period of the prior year had a cash
increase of $2,052,000, the net result of proceeds from a $3,000,000 note
payable offset by normal operating expenditures on the Company's operations.

        Prior to September 1998, the Company had been in negotiations for a
lease on approximately 21,000 square feet in the general vicinity of its then
current facility in Bothell, Washington. A design build team had been selected
and was working on plans for the new space. In September 1998, the project was
canceled in favor of an already existing space. Costs for architectural fees and
long lead equipment items incurred prior to cancellation of the project are
estimated at $472,000, which were included in general and administrative
expenses in the year ended 1998. Cash payments of $287,000 were distributed
during the first quarter of 1999 and $104,000 remained in accrued liabilities at
the end of the quarter. The remaining liability is expected to be resolved by
the end of third quarter of 1999.

        Receivables are $70,000 higher at the end of the first quarter 1999 than
in the prior year primarily as a result of increased revenues from grant work.

        Variances in accounts payable and other accrued liabilities in 1999 and
1998 are the result of normal business fluctuations.

        The note payable to related party is due in February 2000, at which time
the balance will need to be repaid or refinanced.


                                       9


<PAGE>   10

YEAR 2000 COMPLIANCE

        Many existing information technology (IT) systems, such as computer
systems and software products, as well as non-IT systems that include embedded
technology, were not designed to correctly process dates after December 31,
1999. We have assessed the impact of such "Year 2000" issues on our products,
our internal IT and non-IT systems, as well as on our suppliers and service
providers. We have determined that our business systems are not Year 2000 ready.
We have developed a plan to replace these systems in a timely fashion at a cost
of approximately $30,000. We are also discussing with our significant suppliers
and service providers their plans to investigate, identify and fix their Year
2000 issues. We believe that most of our significant suppliers and service
providers will cooperate in resolving any Year 2000 problems. However, we are
also dependent on certain utility companies, telecommunication service companies
and other service providers that are outside our control. Therefore, it may be
difficult for us to obtain assurances of Year 2000 readiness from such third
parties. We believe that we will have identified all of our material Year 2000
issues. However, given the pervasiveness of Year 2000 issues and the complex
interrelationships among Year 2000 issues both internal and external to us, we
cannot guarantee that we will be able to identify and accurately evaluate all
such issues.

        If any supplier or service provider fails to appropriately address their
Year 2000 issues, our business, financial condition and operating results could
be significantly hurt. For example, if a supplier or service provider
experiences a Year 2000 problem which results in or contributes to delays or
interruptions in delivering products or services to us, our business, financial
condition and operating results could be significantly hurt. Finally, general
economic disruption resulting from Year 2000 issues could also significantly
hurt us.

        In preparation for the Year 2000, we are developing contingency plans in
case we fail to complete our remediation programs in a timely manner and in the
event that any third party who provides goods or services essential to our
business, fails to appropriately address their Year 2000 issues. We expect to
finish developing these contingency plans by mid-1999. Even if we complete these
plans on time and put them in place, we cannot guarantee that such plans will be
sufficient to address any third party failures or that unresolved or undetected
internal and external Year 2000 issues will not significantly hurt our business,
financial condition and operating results.

PART II. OTHER INFORMATION

ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K

        (a) EXHIBITS

            27.1 -- Financial Data Schedule

        (b) REPORTS ON FORM 8K

            None


                                       10

<PAGE>   11

                                   SIGNATURES

        In accordance with the requirements of the Exchange Act, the registrant
caused this report to be signed on its behalf by the undersigned, thereunto duly
authorized.


                                       Epoch Pharmaceuticals, Inc.


Date:  May 17, 1999                    By: /s/ Sanford S. Zweifach
                                           ---------------------------------
                                               Sanford S. Zweifach
                                               President/Chief Financial Officer




                                       11


<PAGE>   12

                                 EXHIBIT INDEX


EXHIBIT NUMBER                  DESCRIPTION
--------------                  -----------

  27.1                    Financial Data Schedule