<PAGE>   1
 
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
 
                       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 JUNE 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>
                   DELAWARE                                      94-3219075
       (STATE OR OTHER JURISDICTION OF                        (I.R.S. EMPLOYER
        INCORPORATION OR ORGANIZATION)                      IDENTIFICATION NO.)
  550 CALIFORNIA AVE., PALO ALTO, CALIFORNIA                       94036
   (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 July 31, 1998: 16,120,147.
 
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
<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 -- June 30, 1998 and December
         31, 1997....................................................      3
         Consolidated Statements of Operations -- for the three
         months and six months ended June 30, 1998 and 1997 and for
         the period from inception (February 16, 1995) to June 30,
         1998........................................................      4
         Consolidated Statements of Cash Flows -- for the three
         months and six months ended June 30, 1998 and 1997 and for
         the period from inception (February 16, 1995) to June 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 4.  Submission of Matters to a Vote of Security Holders.........     11
Item 5.  Other Information...........................................     11
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>
                                                               JUNE 30,      DECEMBER 31,
                                                                 1998            1997
                                                              -----------    ------------
                                                              (UNAUDITED)      (NOTE 1)
<S>                                                           <C>            <C>
Cash assets:
  Cash and cash equivalents.................................   $ 11,882        $ 20,451
  Short-term investments....................................     43,827          54,994
  Prepaid expenses and other current assets.................        424             269
                                                               --------        --------
          Total current assets..............................     56,133          75,714
Property and equipment, net.................................      3,903           2,263
Employee loans receivable...................................        318             323
Other assets................................................        405             371
                                                               --------        --------
                                                               $ 60,759        $ 78,671
                                                               ========        ========
 
LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
  Accounts payable..........................................   $  2,460        $  1,838
  Accrued liabilities.......................................      7,518           7,959
  Current portion of equipment financing obligations and
     debt facility..........................................        779             715
                                                               --------        --------
          Total current liabilities.........................     10,757          10,512
Non current portion of equipment financing obligations and
  debt facility.............................................      1,913           2,298
Commitments
Stockholders' equity:
  Preferred stock, issuable in series, $.001 par value:
     3,000,000 shares authorized; no shares issued and
     outstanding at June 30, 1998 or December 31, 1997......         --              --
  Common stock, $.001 par value: 30,000,000 shares
     authorized; 13,714,731 shares and 13,570,224 shares
     issued and outstanding at June 30, 1998 and December
     31, l997, respectively.................................         14              14
  Additional paid-in capital................................    112,254         111,598
  Accumulated other comprehensive income....................        (36)             (7)
  Deferred compensation.....................................       (871)         (1,085)
  Deficit accumulated during the development stage..........    (63,272)        (44,659)
                                                               --------        --------
          Total stockholders' equity........................     48,089          65,861
                                                               --------        --------
                                                               $ 60,759        $ 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    SIX MONTHS ENDED      FOR THE PERIOD
                                               JUNE 30,             JUNE 30,          FROM INCEPTION
                                          ------------------   ------------------   (FEBRUARY 16, 1995)
                                            1998      1997       1998      1997      TO JUNE 30, 1998
                                          --------   -------   --------   -------   -------------------
<S>                                       <C>        <C>       <C>        <C>       <C>
Operating expenses:
  Research and development..............  $  6,217   $ 3,547   $ 15,234   $ 6,583        $ 52,499
  Selling, general and administrative...     2,918     1,972      5,078     3,180          15,678
                                          --------   -------   --------   -------        --------
          Total operating expenses......     9,135     5,519     20,312     9,763          68,177
Interest income and other, net..........       787       525      1,699       963           4,905
                                          --------   -------   --------   -------        --------
Net loss................................  $ (8,348)  $(4,994)  $(18,613)  $(8,800)       $(63,272)
                                          ========   =======   ========   =======        ========
Basic and diluted net loss per share....  $  (0.62)  $ (0.50)  $  (1.39)  $ (1.05)
                                          ========   =======   ========   =======
Shares used in computing basic and
  diluted net loss per share............    13,444     9,999     13,411     8,404
                                          ========   =======   ========   =======
</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>
                                                              SIX MONTHS          FOR THE PERIOD
                                                            ENDED JUNE 30,        FROM INCEPTION
                                                         --------------------   (FEBRUARY 16, 1995)
                                                           1998        1997      TO JUNE 30, 1998
                                                         --------    --------   -------------------
<S>                                                      <C>         <C>        <C>
Cash flows from operating activities:
  Net loss.............................................  $(18,613)   $ (8,800)       $ (63,272)
  Adjustments to reconcile net loss to net cash
     provided by (used in) operating activities:
     Depreciation and amortization.....................       226          58              537
     Amortization of deferred compensation.............       214         594            1,629
  Changes in operating assets and liabilities:
     Prepaid expenses and other current assets.........      (155)        (18)            (424)
     Employee loans receivable.........................         5          37             (318)
     Other assets......................................       (34)          1             (405)
     Accounts payable..................................       622       1,011            2,460
     Accrued liabilities...............................      (441)     (3,128)           7,605
                                                         --------    --------        ---------
          Net cash used in operating activities........   (18,176)    (10,245)         (52,188)
                                                         --------    --------        ---------
Cash flows from investing activities:
  Purchases of short-term investments..................   (39,673)    (31,035)        (112,077)
  Maturities of short-term investments.................    45,737       9,006           60,867
  Sales of short-term investments......................     5,074          --            7,344
  Purchases of property and equipment..................    (1,866)       (649)          (4,436)
                                                         --------    --------        ---------
          Net cash provided by (used in) investing
            activities.................................     9,272     (22,678)         (48,302)
                                                         --------    --------        ---------
Cash flows from financing activities:
  Payments of equipment financing obligations and debt
     facility..........................................      (354)       (214)            (929)
  Borrowings under equipment financing obligations and
     debt facility.....................................        33       1,159            3,533
  Proceeds from issuance of convertible preferred
     stock, net........................................        --          --           28,355
  Proceeds from issuance of common stock, net..........       656      34,520           81,413
                                                         --------    --------        ---------
          Net cash provided by financing activities....       335      35,465          112,372
                                                         --------    --------        ---------
Net increase (decrease) in cash and cash equivalents...    (8,569)      2,542           11,882
Cash and cash equivalents at beginning of period.......    20,451       8,826               --
                                                         --------    --------        ---------
Cash and cash equivalents at end of period.............  $ 11,882    $ 11,368        $  11,882
                                                         ========    ========        =========
</TABLE>
 
                            See accompanying notes.
                                        5
<PAGE>   6
 
                          COULTER PHARMACEUTICAL, INC.
                         (A DEVELOPMENT STAGE COMPANY)
 
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                                 JUNE 30, 1998
                                  (UNAUDITED)
 
 1. SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES
 
  Basis of Presentation
 
     The information at June 30, 1998 for the three and six month periods ended
June 30, 1998 and 1997 and for the period from inception (February 16, 1995) to
June 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 June 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, "Earnings Per Share" ("SFAS 128"), 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
outstanding subject to continued vesting. 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 six
months periods ended June 30, 1997 has been restated to conform to the
requirements of SFAS 128.
 
  New Accounting Standards
 
     As of January 1, 1998, the Company adopted Statement 130, "Reporting
Comprehensive Income." Statement 130 establishes new rules for the reporting and
display of comprehensive income and its components; however, the adoption of
this Statement had no impact on the Company's net income or shareholders'
equity. Statement 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 Statement 130. For the quarters ended June 30, 1998 and 1997, total
comprehensive loss amounted to $8.4 million and $5.0 million, respectively. For
the six month periods ended June 30, 1998 and 1997, total comprehensive loss was
$18.6 million and $8.8 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 interim financial reports, SFAS 131 also establishes
standards for related disclosures about products and services, geographic areas
and major customers. The adoption of SFAS 131 had no impact on the Company's
results of operations, financial position or disclosure of segment information
at June 30, 1998.
 
                                        6
<PAGE>   7
                          COULTER PHARMACEUTICAL, INC.
                         (A DEVELOPMENT STAGE COMPANY)
 
             NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (CONTINUED)
 
     In March 1998, the Financial Accounting Standards Board issued Statement of
Financial Accounting Standards No. 132, "Employers' Disclosures about Pensions
and Other Postretirement Benefits" ("SFAS 132"). SFAS 132 does not change the
recognition or measurement of pension or postretirement benefit plans, but
revises and standardizes disclosure requirements for pensions and other
postretirement benefits. The adoption of SFAS 132 has no impact on the Company's
results of operations of financial condition.
 
     In June 1998, the Financial Accounting Standards Board issued Statement of
Financial Accounting Standards No. 133, "Accounting for Derivative Financial
Instruments and for Hedging Activities" ("SFAS 133") which provides a
comprehensive and consistent standard for the recognition and measurement of
derivatives and hedging activities. SFAS 133 is effective for years beginning
after June 15, 1999 and is not anticipated to have an impact on the Company's
results of operations or financialcondition when adopted.
 
 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 June 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...................................  $  2,307       $--          $ --       $  2,307
Commercial paper.....................................    17,974        --           (28)        17,946
Corporate bond.......................................    10,241        --            (8)        10,233
Certificate of Deposits..............................    25,063         1            --         25,064
                                                       --------       ---          ----       --------
          Total......................................    55,585         1           (36)        55,550
Less amounts classified as cash equivalents..........   (11,729)       --             6        (11,723)
                                                       --------       ---          ----       --------
          Total short-term investments...............  $ 43,856       $ 1          $(30)      $ 43,827
                                                       ========       ===          ====       ========
</TABLE>
 
     There were no realized gains or losses on the sale of available-for-sale
securities for the quarter ended June 30, 1998 and June 30, 1997.
 
     At June 30, 1998 the contractual maturities of short term investments were
as follows (in thousands):
 
<TABLE>
<CAPTION>
                                                         AMORTIZED    ESTIMATED
                                                           COST       FAIR VALUE
                                                         ---------    ----------
<S>                                                      <C>          <C>
Due in one year or less................................   $20,819      $20,796
Due after one year through two years...................    23,037       23,031
                                                          -------      -------
                                                          $43,856      $43,827
                                                          =======      =======
</TABLE>
 
 3. SUBSEQUENT EVENT
 
     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.
 
     If the underwriters exercise their full over-allotment option to purchase
360,000 shares, additional net proceeds will be approximately $8.5 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-drug
technology.
 
     The Company's most advanced product candidate, Bexxar (formerly known as
the "B-1 Therapy"), consists of a monoclonal antibody conjugated with a
radioisotope. The Company intends to seek initial FDA 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 upon
which occurrence Coulter Corporation became known as Beckman Coulter ("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 June 30, 1998, the Company's accumulated deficit during the
development stage was approximately $63.3 million.
 
RESULTS OF OPERATIONS
 
  Operating Costs and Expenses
 
     Research and development expenses were $6.2 million for the three months
ended June 30, 1998 compared to $3.5 million for the same period in 1997. For
the six months ended June 30, 1998, research and development expenses were $15.2
million compared to $6.6 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 costs of clinical trials and manufacturing
expenses. 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.
 
                                        8
<PAGE>   9
 
     Selling, general and administrative expenses were $2.9 million for the
three months ended June 30, 1998, compared to $2.0 million for the same period
in 1997, and were $5.1 million for the six months ended June 30, 1998 and $3.2
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 was $787,000 for the three months ended June 30, 1998,
compared to $525,000 for the same period in 1997, and was $1.7 million for the
six months ended June 30, 1998 and $963,000 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 follow-on
offering in October 1997. The Company expects its interest income will increase
during the remainder of fiscal 1998 due to higher cash balances as a result of
the completion of its public offering of common stock in July 1998.
 
     Interest expense is not material for any period presented.
 
LIQUIDITY AND CAPITAL RESOURCES
 
     Since its inception through June 30, 1998, the Company has financed its
operations primarily through private placements and public offerings of equity
securities totaling $109.8 million. In addition, the Company entered into a $3.8
million equipment lease financing and debt facility in December 1996, $0.3
million of which is available at June 30, 1998. Cash, cash equivalents and
short-term investments totaled $55.7 million at June 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 $18.2 million for the six month period
ended June 30, 1998, compared to $10.2 million for the same period in 1997. This
$8.0 million increase is primarily the result of the increased net loss for the
six month period ended June 30, 1998. Net cash provided by investing activities
was $9.3 million in the six months ended June 30, 1998 compared to $22.7 million
used in the same period of 1997. The 1998 positive cash flow represents
maturities and sales of short-term investments in excess of purchases of such
investments. Financing activities provided $335,000, net, in the six months
ended June 30, 1998, primarily from issuances of common stock. In the same
period of 1997, the Company completed its initial public offering of common
stock, resulting in net cash provided by financing activities of $35.5 million.
 
     The Company expects that its existing capital resources, including the net
proceeds of its public offering of common stock completed on July 31, 1998 and
interest thereon, will be adequate to satisfy the requirements of its current
and planned operations into 2000. At June 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:
                                        9
<PAGE>   10
 
the scope and results of preclinical studies and clinical trials; the cost,
timing and outcome of regulatory approvals; the expenses of establishing a sales
and marketing capability; 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 acquisition
of technology licenses; the status of competitive products; and the availability
of other financing.
 
IMPACT OF THE YEAR 2000
 
     At this time, the Company believes that with upgrades of existing software
and conversions to new software, both of which are readily available in the
market, the Year 2000 issue will not pose significant operational problems for
its internal computer systems. Modifications and conversions to the Company's
internal computer systems are expected to be completed not later than September
30, 1999. Some risks associated with the Year 2000 issue are beyond the ability
of the Company to control, for example, the extent to which the Company's
suppliers and service providers, including providers of telephone services,
address the Year 2000 issue. A failure by a third party to adequately address
the Year 2000 issue would have a material adverse impact on such third party,
and could result in a material adverse impact on the Company. The Company,
however, has initiated formal communications with its significant suppliers and
service providers to determine the extent to which the Company may be vulnerable
to those third parties' failure to remediate their own Year 2000 issues. The
Company does not expect the estimated cost of implementing its Year 2000 plan to
be significant.
 
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(TM) or the Company's other product candidates and other risks, including
those detailed in the Company's other filings with the Securities and 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.
 
                                       10
<PAGE>   11
 
                           PART II. OTHER INFORMATION
 
ITEM 4. SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS
 
     At the Annual Meeting of Stockholders of the Company held on May 22, 1998,
the stockholders elected eight directors, approved the Company's 1996 Equity
Incentive Plan, as amended, to increase the aggregate number of shares of Common
Stock authorized for issuance under such plan by 1,400,000 shares (the "Plan
Amendment") and ratified the selection of Ernst & Young LLP as independent
auditors of the Company for its fiscal year ending December 31, 1998 (the
"Selection of Auditors").
 
     Of the 13,630,528 shares of Common Stock of the Company outstanding as of
April 9, 1998, the record date for the Annual Meeting (the "Outstanding
Shares"), the votes regarding the election of directors were as follows:
 
<TABLE>
<CAPTION>
                                        VOTES
                                       AGAINST
                                          OR
                          VOTES FOR    WITHHELD
                          ----------   --------
<S>                       <C>          <C>
Brian G. Atwood           11,580,459   259,300
Michael F. Bigham         11,581,459   258,300
Joseph R. Coulter, III    11,579,759   260,000
Donald L. Lucas           11,580,459   259,300
Robert R. Momsen          11,581,059   258,700
Arnold L. Oronsky, Ph.D.  11,581,459   258,300
George Sella, Jr.         11,580,459   259,300
Sue Van                   11,579,941   259,818
</TABLE>
 
     Of the Outstanding Shares, 7,566,605 shares were voted for the approval of
the Plan Amendment; 2,779,286 shares were voted against with respect to the
approval of the Plan Amendment; 31,733 shares abstained and 1,462,135 shares
were broker non-votes.
 
     Of the Outstanding Shares, 11,765,859 shares were voted for the
ratification of the Selection of Auditors; 3,100 shares were voted against with
respect to the ratification of the Selection of Auditors; 70,800 shares
abstained.
 
ITEM 5. OTHER INFORMATION
 
     Pursuant to the Company's bylaws, stockholders who wish to bring matters or
propose nominees for director at the Company's 1999 annual meeting of
stockholders must provide specified information to the Company not less than one
hundred twenty (120) calendar days in advance of the anniversary date of the
Company's 1998 proxy statement (unless such matters are included in the
Company's proxy statement pursuant to Rule 14a-8 under the Securities Exchange
Act of 1934, as amended).
 
ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K
 
(a) EXHIBITS
 
<TABLE>
<CAPTION>
    EXHIBIT
    NUMBER                     DESCRIPTION OF DOCUMENT
    -------                    -----------------------
    <S>      <C>
    10.18+   Commercial Supply Agreement, dated May 28, 1998 by and
             between Lonza Biologics PLC and the Company.
    27.0     Financial Data Schedule.
</TABLE>
 
+  Portions omitted pursuant to a request of confidentiality filed separately
   with the Commission.
 
(b) REPORTS ON FORM 8-K
 
     There were no reports on Form 8-K during the quarter ended June 30, 1998.
 
                                       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: August 13, 1998                                                     /s/  MICHAEL F. BIGHAM
                                                         --------------------------------------------------------
                                                                            Michael F. Bigham
                                                                  President and Chief Executive Officer
 
Date: August 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
    -------                      -----------------------
    <C>        <S>
    10.18+     Commercial Supply Agreement, dated May 28, 1998 by and
               between Lonza Biologics PLC and the Company.
    27.0       Financial Data Schedule.
</TABLE>
 
+  Portions omitted pursuant to a request of confidentiality filed separately
   with the Commission.