<PAGE>   1
 
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                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
 
                            ------------------------
 
                                   FORM 10-Q
                            ------------------------
 
     [X]   QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
        SECURITIES EXCHANGE ACT OF 1934
 
                    FOR THE PERIOD ENDED SEPTEMBER 30, 1998
 
                                       OR
 
     [ ]   TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
        SECURITIES EXCHANGE ACT OF 1934
 
         FOR THE TRANSITION PERIOD FROM ____________ TO ____________ .
 
                          COMMISSION FILE NO. 0-21905
 
                          COULTER PHARMACEUTICAL, INC.
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)
 
<TABLE>
<S>                                              <C>
                    DELWARE                                         94-3219075
        (STATE OR OTHER JURISDICTION OF                          (I.R.S. EMPLOYER
         INCORPORATION OR ORGANIZATION)                        IDENTIFICATION NO.)
 
   550 CALIFORNIA AVE., PALO ALTO, CALIFORNIA                         94306
     ADDRESS OF PRINCIPAL EXECUTIVE OFFICES                         (ZIP CODE)
</TABLE>
 
        REGISTRANT'S TELEPHONE NUMBER, INCLUDING AREA CODE: 650-849-7500
 
     Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 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  [ ]
 
     Number of shares outstanding of the issuer's Common Stock, par value $.001
per share, as of November 2, 1998: 16,402,537.
 
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<PAGE>   2
 
                          COULTER PHARMACEUTICAL, INC.
 
                                     INDEX
 
<TABLE>
<CAPTION>
                                                                        PAGE NO.
                                                                        --------
<S>       <C>                                                           <C>
                         PART I. FINANCIAL INFORMATION
 
Item 1.   Consolidated Financial Statements and Notes.................      3
          Consolidated Balance Sheets -- September 30, 1998 and
            December 31, 1997.........................................      3
          Consolidated Statements of Operations -- for the three
            months and nine months ended September 30, 1998 and 1997
            and for the period from inception (February 16, 1995) to
            September 30, 1998........................................      4
          Consolidated Statements of Cash Flows -- for the three
            months and nine months ended September 30, 1998 and 1997
            and for the period from inception (February 16, 1995) to
            September 30, 1998........................................      5
          Notes to Consolidated Financial Statements..................      6
 
Item 2.   Management's Discussion and Analysis of Financial Condition
            and Results of Operations.................................      8
 
                           PART II. OTHER INFORMATION
 
Item 6.   Exhibits and Reports on Form 8-K............................     11
 
SIGNATURES............................................................     12
</TABLE>
 
                                        2
<PAGE>   3
 
                         PART I. FINANCIAL INFORMATION
 
ITEM 1. CONSOLIDATED FINANCIAL STATEMENTS AND NOTES
 
                          COULTER PHARMACEUTICAL, INC.
                         (A DEVELOPMENT STAGE COMPANY)
 
                          CONSOLIDATED BALANCE SHEETS
               (IN THOUSANDS, EXCEPT SHARE AND PER SHARE AMOUNTS)
 
                                     ASSETS
 
<TABLE>
<CAPTION>
                                                              SEPTEMBER 30,    DECEMBER 31,
                                                                  1998             1997
                                                              -------------    ------------
                                                               (UNAUDITED)       (NOTE 1)
<S>                                                           <C>              <C>
Current assets:
  Cash and cash equivalents.................................    $ 49,332         $ 20,451
  Short-term investments....................................      58,967           54,994
  Prepaid expenses and other current assets.................         464              269
                                                                --------         --------
          Total current assets..............................     108,763           75,714
Property and equipment, net.................................       6,637            2,263
Employee loans receivable...................................         394              323
Other assets................................................         493              371
                                                                --------         --------
                                                                $116,287         $ 78,671
                                                                ========         ========
 
                           LIABILITIES AND STOCKHOLDERS' EQUITY
 
Current liabilities:
  Accounts payable..........................................    $  3,733         $  1,838
  Accrued liabilities.......................................       7,958            7,959
  Current portion of equipment financing obligations and
     debt facility..........................................         902              715
                                                                --------         --------
          Total current liabilities.........................      12,593           10,512
Non current portion of equipment financing obligations and
  debt facility.............................................       1,967            2,298
Commitments
Stockholders' equity:
  Preferred stock, issuable in series, $.001 par value:
     3,000,000 shares authorized; no shares issued and
     outstanding at September 30, 1998 or December 31,
     1997...................................................          --               --
  Common stock, $.001 par value: 30,000,000 shares
     authorized; 16,396,334 shares and 13,570,224 shares
     issued and outstanding at September 30, 1998 and
     December 31, l997, respectively........................          16               14
  Additional paid-in capital................................     174,512          111,598
  Accumulated other comprehensive income....................         (12)              (7)
  Deferred compensation.....................................        (695)          (1,085)
  Deficit accumulated during the development stage..........     (72,094)         (44,659)
                                                                --------         --------
          Total stockholders' equity........................     101,727           65,861
                                                                --------         --------
                                                                $116,287         $ 78,671
                                                                ========         ========
</TABLE>
 
                            See accompanying notes.
                                        3
<PAGE>   4
 
                          COULTER PHARMACEUTICAL, INC.
                         (A DEVELOPMENT STAGE COMPANY)
 
                     CONSOLIDATED STATEMENTS OF OPERATIONS
                                  (UNAUDITED)
                     (IN THOUSANDS, EXCEPT PER SHARE DATA)
 
<TABLE>
<CAPTION>
                                        THREE MONTHS ENDED     NINE MONTHS ENDED       FOR THE PERIOD
                                           SEPTEMBER 30,         SEPTEMBER 30,         FROM INCEPTION
                                        -------------------   -------------------    (FEBRUARY 16, 1995)
                                          1998       1997       1998       1997     TO SEPTEMBER 30, 1998
                                        --------   --------   --------   --------   ---------------------
<S>                                     <C>        <C>        <C>        <C>        <C>
Operating expenses:
Research and development..............  $ 7,347    $ 5,227    $ 22,581   $ 11,810         $ 59,846
Selling, general and administrative...    2,643      2,146       7,721      5,326           18,321
                                        -------    -------    --------   --------         --------
Total operating expenses..............    9,990      7,373      30,302     17,136           78,167
Interest income and other, net........    1,168        454       2,867      1,417            6,073
                                        -------    -------    --------   --------         --------
Net loss..............................  $(8,822)   $(6,919)   $(27,435)  $(15,719)        $(72,094)
                                        =======    =======    ========   ========         ========
Basic and diluted net loss per
  share...............................  $ (0.58)   $ (0.69)   $  (1.96)  $  (1.76)
                                        =======    =======    ========   ========
Shares used in computing basic and
  diluted net loss per share..........   15,123     10,060      13,982      8,950
                                        =======    =======    ========   ========
</TABLE>
 
                            See accompanying notes.
                                        4
<PAGE>   5
 
                          COULTER PHARMACEUTICAL, INC.
                         (A DEVELOPMENT STAGE COMPANY)
 
                     CONSOLIDATED STATEMENTS OF CASH FLOWS
                INCREASE (DECREASE) IN CASH AND CASH EQUIVALENTS
                                  (UNAUDITED)
                                 (IN THOUSANDS)
 
<TABLE>
<CAPTION>
                                                           NINE MONTHS           FOR THE PERIOD
                                                       ENDED SEPTEMBER 30,       FROM INCEPTION
                                                       --------------------      (FEB. 16, 1995)
                                                         1998        1997     TO SEPTEMBER 30, 1998
                                                       --------    --------   ---------------------
<S>                                                    <C>         <C>        <C>
Cash flows from operating activities:
  Net loss...........................................  $(27,435)   $(15,719)        $(72,094)
  Adjustments to reconcile net loss to net cash
     provided by (used in) operating activities:
     Depreciation and amortization...................       454         110              765
     Amortization of deferred compensation...........       390         861            1,804
  Changes in operating assets and liabilities:
     Prepaid expenses and other current assets.......      (195)         41             (464)
     Employee loans receivable.......................       (71)        (93)            (395)
     Other assets....................................      (122)       (127)            (492)
     Accounts payable................................     1,895         968            3,733
     Accrued liabilities.............................        (1)     (2,606)           8,046
                                                       --------    --------         --------
          Net cash used in operating activities......   (25,085)    (16,565)         (59,097)
                                                       --------    --------         --------
Cash flows from investing activities:
  Purchases of short-term investments................   (68,231)    (33,003)        (140,635)
  Maturities of short-term investments...............    59,180      12,089           74,310
  Sales of short-term investments....................     5,073          --            7,343
  Purchases of property and equipment................    (4,828)     (1,038)          (7,398)
                                                       --------    --------         --------
          Net cash used in investing activities......    (8,806)    (21,952)         (66,380)
                                                       --------    --------         --------
Cash flows from financing activities:
  Payments of equipment financing obligations and
     debt facility...................................      (564)       (366)          (1,139)
  Borrowings under equipment financing obligations
     and debt facility...............................       420       1,700            3,920
  Proceeds from issuance of convertible preferred
     stock, net......................................        --          --           28,355
  Proceeds from issuance of common stock, net........    62,916      34,547          143,673
                                                       --------    --------         --------
          Net cash provided by financing
            activities...............................    62,772      35,881          174,809
                                                       --------    --------         --------
Net increase (decrease) in cash and cash
  equivalents........................................    28,881      (2,636)          49,332
Cash and cash equivalents at beginning of period.....    20,451       8,826               --
                                                       --------    --------         --------
Cash and cash equivalents at end of period...........  $ 49,332    $  6,190         $ 49,332
                                                       ========    ========         ========
Supplemental Schedule of Cash Flow Information
Interest Paid........................................       242         193              525
Schedule of non-cash investing and financing
  activities:
  Net exercise of warrants to purchase 37,785 shares
     of common stock.................................  $     --    $    453         $    453
  Acquisition of equipment pursuant to supplemental
     lease obligation................................  $     --    $     --         $     78
  Deferred compensation related to grant of certain
     stock options...................................  $    156    $    157         $  2,656
</TABLE>
 
                            See accompanying notes.
                                        5
<PAGE>   6
 
                          COULTER PHARMACEUTICAL, INC.
                         (A DEVELOPMENT STAGE COMPANY)
 
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                               SEPTEMBER 30, 1998
                                  (UNAUDITED)
 
 1. SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES
 
  Basis of Presentation
 
     The information at September 30, 1998 for the three and nine month periods
ended September 30, 1998 and 1997 and for the period from inception (February
16, 1995) to September 30, 1998 is unaudited but includes all adjustments
(consisting only of normal recurring adjustments) which, in the opinion of
management, are necessary to state fairly the financial information set forth
therein in accordance with generally accepted accounting principles. The
September 30, 1998 interim results are not necessarily indicative of results to
be expected for the full fiscal year. These financial statements should be read
in conjunction with the audited financial statements for the fiscal year ended
December 31, 1997 included in the Company's annual report to security holders
furnished to the Securities and Exchange Commission pursuant to Rule 14a-3(b) in
connection with the Company's 1998 Annual Meeting of Stockholders.
 
     The consolidated balance sheet at December 31, 1997 has been derived from
audited consolidated financial statements at that date but does not include all
of the information and footnotes required by generally accepted accounting
principles for complete financial statements.
 
  Net Loss Per Share
 
     Effective December 31, 1997 the Company adopted Statement of Financial
Accounting Standards No. 128 ("SFAS 128"), "Earnings Per Share," which modifies
the way in which earnings per share are calculated and disclosed.
 
     "Basic" net loss per share (as defined by SFAS 128) is computed using the
weighted average number of common shares outstanding less those shares subject
to the Company's right of repurchase. As the Company reported a loss for all
periods presented, there is no difference between basic and diluted net loss per
share amounts as prescribed by SFAS 128. Loss per share for the three and nine
month periods ended September 30, 1997 have been restated to conform to the
requirements of SFAS 128.
 
  New Accounting Standards
 
     As of January 1, 1998, the Company adopted Statement of Financial
Accounting Standards No. 130, "Reporting Comprehensive Income" ("SFAS 130").
SFAS 130 establishes new rules for the reporting and display of comprehensive
income and its components; however, the adoption of SFAS 130 had no impact on
the Company's net income or shareholders' equity. SFAS 130 requires unrealized
gains or losses on the Company's available-for-sale securities which, prior to
adoption, were reported separately in shareholders' equity, to be included in
other comprehensive income. Prior year financial statements have been
reclassified to conform to the requirements of SFAS 130. For the quarters ended
September 30, 1998 and 1997, total comprehensive loss amounted to $8.8 million
and $6.9 million, respectively. For the nine month periods ended September 30,
1998 and 1997, total comprehensive losses were $27.4 million and $15.7 million,
respectively.
 
     Effective January 1, 1998, the Company adopted Statement of Financial
Accounting Standards No. 131, "Disclosures About Segments of an Enterprise and
Related Information" ("SFAS 131"). SFAS 131 superseded SFAS 14, "Financial
Reporting for Segments of a Business Enterprise." SFAS 131 establishes standards
for the way that public business enterprises report selected information about
operating segments in annual financial statements, SFAS 131 also establishes
standards for related disclosures about products and services, geographic areas
and major customers. The adoption of SFAS 131 will have no impact on the
Company's results of operations, or financial position.
 
                                        6
<PAGE>   7
                          COULTER PHARMACEUTICAL, INC.
                         (A DEVELOPMENT STAGE COMPANY)
 
             NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (CONTINUED)
                               SEPTEMBER 30, 1998
                                  (UNAUDITED)
 
 2. INVESTMENTS
 
     Management determines the appropriate classification of debt securities at
the time of purchase and re-evaluates such designation as of each balance sheet
date. The Company's debt securities are classified as available-for-sale and are
carried at estimated fair value in cash equivalents and short-term investments.
Unrealized gains and losses are reported as accumulated other comprehensive
income in stockholders' equity. The amortized cost of debt securities in this
category is adjusted for amortization of premiums and accretion of discounts to
maturity. Such amortization is included in interest income. Realized gains and
losses on available-for-sale securities are included in interest income and
expense. The cost of securities sold is based on the specific identification
method. Interest and dividends on securities classified as available-for-sale
are included in interest income. The Company's cash equivalents and short-term
investments as of September 30, 1998 are as follows (in thousands):
 
<TABLE>
<CAPTION>
                                                              GROSS        GROSS
                                                AMORTIZED   UNREALIZED   UNREALIZED   ESTIMATED
                                                  COST        GAINS        LOSSES     FAIR VALUE
                                                ---------   ----------   ----------   ----------
<S>                                             <C>         <C>          <C>          <C>
Money market funds............................  $  1,157       $--          $ --       $  1,157
Commercial paper..............................    76,798        --           (23)        76,775
Corporate bond................................     9,252        10            --          9,262
Certificate of Deposits.......................    20,070         1            --         20,071
                                                --------       ---          ----       --------
          Total...............................   107,277        11           (23)       107,265
Less amounts classified as cash equivalents...   (48,319)       --            21        (48,298)
                                                --------       ---          ----       --------
Total short-term investments..................  $ 58,958       $11          $ (2)      $ 58,967
                                                ========       ===          ====       ========
</TABLE>
 
     Realized gains or losses on the sale of available-for-sale securities for
the quarters ended September 30, 1998 and September 30, 1997 were not material.
 
     At September 30, 1998 the contractual maturities of short term investments
were as follows (in thousands):
 
<TABLE>
<CAPTION>
                                                                              ESTIMATED FAIR
                                                             AMORTIZED COST       VALUE
                                                             --------------   --------------
<S>                                                          <C>              <C>
Due in one year or less....................................     $37,891          $37,889
Due after one year through two years.......................      21,067           21,078
                                                                -------          -------
                                                                $58,958          $58,967
                                                                =======          =======
</TABLE>
 
 3. STOCKHOLDER'S EQUITY
 
     On July 31, 1998, the Company completed a public offering of 2,400,000
shares of common stock at a price to the public of $25.00 per share, resulting
in net proceeds to the Company of $56.7 million. Also, in August 1998, the
underwriters of that offering purchased 245,000 additional shares of common
stock upon a partial exercise of their over-allotment option, raising additional
net proceeds of $5.8 million. The total net proceeds from this offering were
$62.5 million.
 
                                        7
<PAGE>   8
 
ITEM 2.MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
       OF OPERATIONS
 
     The following discussion contains, in addition to historical information,
forward-looking statements that involve risks and uncertainties. Actual results
may differ significantly from the results discussed in the forward-looking
statements. Factors that could cause or contribute to such differences include,
but are not limited to, those discussed below and in the Company's Registration
Statement on Form S-3, File No. 333-58829, declared effective on July 30, 1998.
 
OVERVIEW
 
     Coulter Pharmaceutical is engaged in the development of novel drugs and
therapies for the treatment of people with cancer. The Company currently is
developing a family of cancer therapeutics based upon two drug discovery
programs, therapeutic antibodies and targeted oncologics. Within these broad
discovery programs, the Company is currently concentrating on two distinct
platform technologies: therapeutic antibodies based on conjugated antibody
technology and targeted oncologics based on tumor activated peptide pro-drugs
technology.
 
     The Company's most advanced product candidate, Bexxar(TM) (formerly known
as the "B-1 Therapy"), consists of a monoclonal antibody conjugated with a
radioisotope. The Company intends to seek initial approval of Bexxar for the
treatment of low-grade and transformed low-grade non-Hodgkin's lymphoma ("NHL")
in patients who have relapsed after, or are refractory to, chemotherapy. The
Company intends to seek expedited Biologics License Application ("BLA") review
and marketing approval for Bexxar, while simultaneously pursuing clinical trials
to expand the potential use of Bexxar to other indications. Bexxar is based upon
the antibody therapeutics program which originated at Coulter Corporation. In
1995 Coulter Pharmaceutical was incorporated and acquired worldwide rights to
Bexxar and related intellectual property, know-how and other assets from Coulter
Corporation. In 1997 Beckman Instruments, Inc. acquired Coulter Corporation,
which is now known as Beckman Coulter.
 
     To date, the Company has devoted substantially all of its resources to its
research and development programs, as well as selling, general and
administrative activities needed to support product development and potential
product sales. No revenues have been generated from product sales, and products
resulting from the Company's research and development efforts, if any, are not
expected to be available commercially for at least the next one to two years.
The Company has a limited history of operations and has experienced significant
operating losses to date. The Company expects that losses will fluctuate from
quarter to quarter and that such fluctuations may be substantial. There can be
no assurance that the Company will successfully develop, manufacture and
commercialize its products or ever achieve or sustain product revenues or
profitability. As of September 30, 1998, the Company's accumulated deficit
during the development stage was approximately $72.1 million.
 
RESULTS OF OPERATIONS
 
  Operating Costs and Expenses
 
     Research and development expenses were $7.3 million for the three months
ended September 30, 1998 compared to $5.2 million for the same period in 1997.
For the nine months ended September 30, 1998, research and development expenses
were $22.6 million compared to $11.8 million for the same period in 1997. These
increases were due primarily to increases in staffing and expenditures
associated with the development of Bexxar, including manufacturing expenses and
costs of clinical trials. These manufacturing expenses included certain expenses
associated with scaled-up production of monoclonal antibodies and the
establishment of a centralized scaled-up radiolabeling capability. The Company
expects its research and development expenses to continue to grow during the
remainder of 1998, reflecting anticipated increased costs related to additions
to staffing, preclinical studies, clinical trials and manufacturing.
 
     Selling, general and administrative expenses were $2.6 million for the
quarter ended September 30, 1998, compared to $2.1 million for the same period
in 1997, and were $7.7 million for the nine months ended
 
                                        8
<PAGE>   9
 
September 30, 1998 and $5.3 million for the same period in 1997. These increases
were incurred to support the Company's facilities and staffing expansion,
increased research and development efforts, increased pre-commercialization
activities, increased corporate development activities and related legal and
patent activities. The Company expects its selling, general and administrative
expenses to continue to increase during the remainder of 1998, in support of its
increased research and development, patent and corporate development activities,
as well as increasing commercialization efforts in anticipation of potential
product sales.
 
  Interest Income and Other, Net
 
     Interest income and other was $1.2 million for the quarter ended September
30, 1998, compared to $0.5 million for the same period in 1997, and was $2.9
million for the nine months ended September 30, 1998 and $1.4 million for the
same period in 1997. This increase was due to higher average cash, cash
equivalent and short-term investment balances as a result of the completion of
the Company's two public offerings of common stock in the quarters ended
December 31, 1997 and September 30, 1998. Interest expense is not material for
any period presented.
 
LIQUIDITY AND CAPITAL RESOURCES
 
     Since its inception through September 30, 1998, the Company has financed
its operations primarily through private placements and public offerings of
equity securities totaling $172.3 million. In addition, the Company entered into
a $3.8 million equipment lease financing and debt facility in December 1996,
none of which is available at September 30, 1998. Cash, cash equivalents and
short-term investments totaled $108.3 million at September 30, 1998.
 
     The negative cash flow from operations results primarily from the Company's
net operating losses and is expected to continue and to accelerate in the next
several years. The Company expects to incur substantial and increasing research
and development expenses, including expenses related to additions to personnel,
preclinical studies, clinical trials, manufacturing and commercialization
efforts. The Company may need to raise substantial additional capital to fund
its operations. The Company may seek such additional funding through public or
private equity or debt financings from time to time, as market conditions permit
or through collaborative arrangements. There can be no assurance that additional
financing will be available on acceptable terms, if at all. If adequate funds
are not available, the Company may be required to delay, reduce the scope of, or
eliminate one or more of its research and development programs or obtain funds
through arrangements with collaborative partners or others that may require the
Company to relinquish rights to certain of its technologies, product candidates
or products that the Company would otherwise seek to develop or commercialize.
 
     Net cash used in operations was $25.1 million for the nine month period
ended September 30, 1998, compared to $16.6 million for the same period in 1997.
This $8.5 million increase is primarily the result of the increased net loss for
the nine month period ended September 30, 1998, partially offset by an increase
in accounts payable. Net cash used in investing activities was $8.8 million for
the nine month period ended September 30, 1998 compared to $22.0 million for the
same period in 1997. This decrease primarily resulted from purchases of
short-term investments exceeding maturities and sales of such investments by
$4.0 million in the 1998 period compared to $21.9 million in 1997. Property and
equipment purchases of $4.8 million in the nine months ended September 30, 1998
were in support of the Company's facilities expansion and staffing growth. Net
cash provided by financing activities increased to $62.8 million for the nine
month period ended September 30, 1998 from $35.9 million for the same period in
1997 primarily resulting from the completion of the Company's public offering of
common stock in the quarter ended September 30, 1998.
 
     The Company expects that its existing capital resources, including the net
proceeds of its public offering of common stock completed in the quarter ended
September 30, 1998 and interest thereon, will be adequate to satisfy the
requirements of its current and planned operations into 2000. At September 30,
1998, the Company had entered into a long-term lease obligation for office and
laboratory space that will require material commitments for capital expenditures
of approximately $5.0 million through the end of 1998 which the Company may
elect to offset by bank or other borrowings. The Company's future capital
requirements will depend on a number of factors, including: the scope and
results of preclinical studies and clinical trials; the cost, timing and outcome
of
 
                                        9
<PAGE>   10
 
regulatory approvals; the expenses of establishing a sales and marketing force;
continued progress of the Company's research and development of potential
products; the timing and cost of establishment or procurement of requisite
production, radiolabeling and other manufacturing capacities; the adequacy of
facilities, the cost involved in preparing, filing, prosecuting, maintaining,
defending and enforcing patent claims; the need to acquire licenses to new
technology; the status of competitive products; the availability of other
financing, and the ability to achieve profitability.
 
YEAR 2000 READINESS
 
     The Company uses and relies on a wide variety of information technologies,
computer systems and scientific equipment containing computer related
components. Some of the Company's older computer software programs and equipment
use two digit fields rather than four digit fields to define the applicable year
(i.e., "98" in the computer code refers to the year "1998"). As a result,
time-sensitive functions of those software programs and equipment may
misinterpret dates after January 1, 2000, to refer to the twentieth century
rather than the twenty-first century (i.e., "02" could be interpreted as "1902"
rather than "2002"). This could cause system or equipment shutdowns, failures or
miscalculations resulting in inaccuracies in computer output or disruptions of
operations, including, among other things, inaccurate processing of financial
information and/or temporary inability's to process transactions or engage in
other normal business activities.
 
     The Company has developed a strategy to address the potential exposures
related to the impact on its computer systems for the Year 2000 and beyond. An
inventory of key financial, informational and operational systems is being
completed. Detailed plans for implementation and testing of any necessary
modifications to these key computer systems and equipment to ensure they are
Year 2000 compliant are being developed by a cross functional team to address
computer system and equipment problems as required by December 31, 1999. The
Company believes that with these plans and completed modifications, the Year
2000 issue will not pose significant operational problems for its computer
systems and equipment. However, if such modifications and conversions are not
made, or are not completed in a timely fashion, the Year 2000 issue could have a
material impact on the operations of the Company, the precise degree of which
cannot be known at this time. The Company currently has no contingency plans to
deal with major Year 2000 failures, though such plans will be developed over the
coming months.
 
     In addition to risks associated with the Company's own computer systems and
equipment, the Company has relationships with, and is to varying degrees
dependent upon, a large number of third parties that provide information, goods
and services to the Company. These include financial institutions, suppliers,
vendors, research partners and governmental entities. If significant numbers of
these third parties experience failures in their computer systems or equipment
due to Year 2000 non-compliance, it could affect the Company's ability to
process transactions, develop, manufacture and distribute products, or engage in
similar normal business activities. While some of these risks are outside the
control of the Company, the Company has instituted programs, including internal
records review and use of external questionnaires, to identify key third
parties, assess their level of Year 2000 compliance, update contracts and
address any non-compliance issues.
 
     The total cost of the Year 2000 systems assessments and conversions is
funded through operating cash flows, and the Company is expensing these costs.
The financial impact of making the required systems changes cannot be known
precisely at this time, but it is currently expected to be less than $1.0
million. The amount of the cost incurred to date is not material. The actual
financial impact could, however, exceed this estimate. These costs are not
expected to be material to the Company's financial position, results of
operations or cash flows.
 
BUSINESS RISKS
 
     Except for the historical information contained herein, the matters
discussed in this filing are forward-looking statements that involve risks and
uncertainties, including uncertainties related to product development,
uncertainties related to the need for regulatory and other government approvals,
dependence on proprietary technology, uncertainty of market acceptance of Bexxar
or the Company's other product candidates and other risks, including those
detailed in the Company's other filings with the Securities and
 
                                       10
<PAGE>   11
 
Exchange Commission. In particular, see "Risk Factors," referenced in the
Company's Registration Statement on Form S-3, File No. 333-58829, declared
effective on July 30, 1998.
 
                           PART II. OTHER INFORMATION
 
ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K
 
(a) Exhibits
 
<TABLE>
<CAPTION>
    EXHIBIT
    NUMBER                       DESCRIPTION OF DOCUMENT
    -------                      -----------------------
    <S>        <C>
    10.19+     Supply agreement, dated August 31, 1998 by and between MDS
               Nordion, Inc. and the Registrant.
    10.20+     Facilities agreement, dated August 31, 1998 by and between
               MDS Nordion, Inc. and the Registrant.
    27.0       Financial data Schedule
</TABLE>
 
(b) Reports on Form 8-K
 
     There were no reports on Form 8-K during the quarter ended September 30,
1998.
---------------
+ Portions omitted pursuant to a request of confidentiality filed separately
  with the Commission.
 
                                       11
<PAGE>   12
 
                                   SIGNATURES
 
     Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.
 
                                          COULTER PHARMACEUTICAL, INC.
 
<TABLE>
<S>                                            <C>
Date: November 13, 1998                                    /s/ MICHAEL F. BIGHAM
                                               ----------------------------------------------
                                                             Michael F. Bigham
                                                   President and Chief Executive Officer
 
Date: November 13, 1998                                    /s/ WILLIAM G. HARRIS
                                               ----------------------------------------------
                                                             William G. Harris
                                                 Vice President and Chief Financial Officer
</TABLE>
 
                                       12
<PAGE>   13
 
                                 EXHIBIT INDEX
 
<TABLE>
<CAPTION>
EXHIBIT
NUMBER                     DESCRIPTION OF DOCUMENT
-------                    -----------------------
<S>      <C>
10.19+   Supply agreement, dated August 31, 1998 by and between MDS
         Nordion, Inc. and the Registrant.
10.20+   Facilities agreement, dated August 31, 1998 by and between
         MDS Nordion, Inc. and the Registrant.
27.0     Financial data Schedule
</TABLE>
 
---------------
 
+ Portions omitted pursuant to a request of confidentiality filed separately
  with the Commission.