<PAGE>   1
                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                              WASHINGTON, DC 20549

                                    FORM 10-Q

(Mark One)

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

        For the quarterly period ended March 31, 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 Number 0-20815

                                     AVIRON
             (Exact name of registrant as specified in its charter)

              DELAWARE                                      77-0309686
   (State or other jurisdiction                          (I.R.S. Employer
of incorporation or organization)                       Identification No.)

           297 North Bernardo Avenue, Mountain View, California 94043
           (Address of principal executive offices including zip code)

                                 (650) 919-6500
              (Registrant's telephone number, including area code)


--------------------------------------------------------------------------------
   (Former name, former address and former fiscal year, if changed since last
                                     report)

        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

        Indicate the number of shares outstanding of each of the issuer's
classes of common stock, as of the latest practicable date.

<TABLE>
<CAPTION>
           Common Stock $.001 par value                  15,635,293 shares
           ----------------------------            -----------------------------
<S>                                                <C>  
                   (Class)                         (Outstanding at May 11, 1998)
</TABLE>



<PAGE>   2



                                     AVIRON

                                TABLE OF CONTENTS

<TABLE>
<CAPTION>
                                                                                  PAGE NUMBER
                                                                                  -----------
<S>                                                                               <C>
    PART I.      FINANCIAL INFORMATION

       ITEM 1.   FINANCIAL STATEMENTS AND NOTES (UNAUDITED).

                 Condensed Balance Sheets as of March 31, 1998
                 and December 31, 1997                                                 1

                 Condensed Statements of Operations for the three-
                 month periods ended March 31, 1998 and 1997                           2

                 Condensed Statements of Cash Flows for the three-
                 month periods ended March 31, 1998 and 1997                           3

                 Notes to Condensed Financial Statements                               4

       ITEM 2.   MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL
                 CONDITION AND RESULTS OF OPERATIONS.                                  6

    PART II.     OTHER INFORMATION

       ITEM 1.   LEGAL PROCEEDINGS.                                                    11

       ITEM 2.   CHANGES IN SECURITIES.                                                11

       ITEM 3.   DEFAULTS UPON SENIOR SECURITIES.                                      13

       ITEM 4.   SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS.                  13

       ITEM 5.   OTHER INFORMATION.                                                    13

       ITEM 6.   EXHIBITS AND REPORTS ON FORM 8-K.                                     14

    SIGNATURES                                                                         15

    EXHIBIT INDEX                                                                      16
</TABLE>



                                      (i)
<PAGE>   3


PART I - FINANCIAL INFORMATION

ITEM 1.          FINANCIAL STATEMENTS

                                     AVIRON
                            CONDENSED BALANCE SHEETS
                        (IN THOUSANDS, EXCEPT SHARE DATA)

<TABLE>
<CAPTION>
                                                                                   MARCH 31,        DECEMBER 31,
                                                                                     1998              1997
                                                                                   ---------        ------------
                                                                                  (Unaudited)         (Note 1)
<S>                                                                                <C>              <C>      
                                     ASSETS
CURRENT ASSETS:
  Cash and cash equivalents ...............................................        $  90,224         $  15,239
  Short-term investments ..................................................           40,254            47,285
  Accounts receivable .....................................................               29                29
  Prepaid expenses and other current assets ...............................            1,216             1,001
                                                                                   ---------         ---------
    Total current assets ..................................................          131,723            63,554
Long-term investments .....................................................            8,506            12,587
Property and equipment, net ...............................................           12,863             7,582
Deposits and other assets .................................................            5,457             1,602
                                                                                   ---------         ---------
TOTAL ASSETS ..............................................................        $ 158,549         $  85,325
                                                                                   =========         =========

                      LIABILITIES AND STOCKHOLDERS' EQUITY

CURRENT LIABILITIES:
  Accounts payable ........................................................        $   3,241         $   3,636
  Accrued compensation ....................................................              266               756
  Accrued clinical trial costs ............................................              880             3,592
  Accrued expenses and other liabilities ..................................            1,062               513
  Current portion of capital lease obligations ............................              434               477
                                                                                   ---------         ---------
    Total current liabilities .............................................            5,883             8,974
                                                                                   ---------         ---------
  Deferred rent ...........................................................              220                88
  Capital lease obligations, noncurrent ...................................              424               521
  Long-term debt ..........................................................          100,000                --
                                                                                   ---------         ---------
  Total long-term liabilities .............................................          100,644               609
                                                                                   ---------         ---------

STOCKHOLDERS' EQUITY:
  Preferred stock, $0.001 par value; 5,000,000 shares
    authorized, issuable in series; none outstanding  
    at March 31, 1998 and December 31, 1997 ...............................               --                --
  Common stock, $0.001 par value; 30,000,000
    shares authorized; 15,628,925 and 16,082,476
    shares issued and outstanding at March 31, 1998 and 
        December 31, 1997, respectively ...................................               16                16
  Additional paid-in capital ..............................................          129,667           142,840
  Notes receivable from stockholders ......................................             (115)             (115)
  Deferred compensation ...................................................             (469)             (588)
  Accumulated deficit .....................................................          (77,077)          (66,411)
                                                                                   ---------         ---------
Total Stockholders' Equity ................................................           52,022            75,742
                                                                                   ---------         ---------
TOTAL LIABILITIES AND STOCKHOLDERS' EQUITY ................................        $ 158,549         $  85,325
                                                                                   =========         =========
</TABLE>



                             See accompanying notes.


<PAGE>   4


                                     AVIRON
                       CONDENSED STATEMENTS OF OPERATIONS
                                   (UNAUDITED)
                (IN THOUSANDS, EXCEPT SHARE AND PER SHARE DATA)

<TABLE>
<CAPTION>
                                                    THREE MONTHS ENDED
                                                          MARCH 31,
                                             ----------------------------------
                                                 1998                  1997
                                             ------------          ------------
<S>                                          <C>                   <C>         
TOTAL REVENUES .....................         $        253          $        305

OPERATING EXPENSES:

  Research and development .........                9,783                 4,291

  General and administrative .......                2,061                 1,160
                                             ------------          ------------

TOTAL OPERATING EXPENSES ...........               11,844                 5,451
                                             ------------          ------------

LOSS FROM OPERATIONS ...............              (11,591)               (5,146)

OTHER INCOME/(EXPENSE):

  Interest income ..................                  953                   222

  Interest expense .................                  (43)                  (53)
                                             ------------          ------------

TOTAL OTHER INCOME, NET ............                  910                   169
                                             ------------          ------------

NET LOSS ...........................         $    (10,681)         $     (4,977)
                                             ============          ============

Basic net loss per share ...........         $      (0.67)         $      (0.44)
                                             ============          ============

Shares used in computing basic
net loss per share .................           16,003,786            11,389,024
</TABLE>



                             See accompanying notes.



                                       2
<PAGE>   5

                                     AVIRON
                       CONDENSED STATEMENTS OF CASH FLOWS
                                   (UNAUDITED)
                                 (IN THOUSANDS)
<TABLE>
<CAPTION>
                                                                        THREE MONTHS ENDED
                                                                             MARCH 31
                                                                    ---------------------------
                                                                      1998              1997
                                                                    ---------         ---------
<S>                                                                 <C>               <C>       
CASH FLOWS FROM OPERATING ACTIVITIES

Net loss ...................................................        $ (10,681)        $  (4,977)

Adjustment to reconcile net loss to net cash used
 in operating activities:

       Depreciation and amortization .......................              354               154

       Amortization of deferred compensation ...............              119               166

Changes in assets and liabilities:

       Accounts receivable .................................               --               195

       Prepaid expenses and other current assets ...........             (215)              124

       Accounts payable ....................................             (395)             (172)

       Accrued expenses and other liabilities ..............           (2,653)             (375)

       Deferred rent .......................................              132                --
                                                                    ---------         ---------

Net Cash Used in Operating Activities ......................          (13,339)           (4,885)
                                                                    ---------         ---------

Cash Flows From Investing Activities:

       Purchases of investments ............................           (1,764)           (1,472)

       Maturities of investments ...........................           13,036             3,301

       Expenditures for property and equipment .............           (5,635)              (33)
                                                                    ---------         ---------

Net Cash Provided by Investing Activities ..................            5,637             1,796
                                                                    ---------         ---------
                                                                                      
CASH FLOWS FROM FINANCING ACTIVITIES:

       Principal payments on capital lease
       obligation ..........................................             (140)             (178)

       Proceeds from convertible debt offering .............           96,000                --

       Repurchase of Common Stock ..........................          (13,337)               --

       Proceeds from issuance of Common stock, net: ........              164            14,955
                                                                    ---------         ---------
Net Cash Provided by Financing Activities ..................           82,687            14,777
                                                                    ---------         ---------
Net Increase/(Decrease) in Cash and Cash Equivalents .......           74,985            11,688

Cash and Cash Equivalents at Beginning of Period ...........           15,239            12,166
                                                                    ---------         ---------
CASH AND CASH EQUIVALENTS AT END OF PERIOD .................        $  90,224         $  23,854
                                                                    =========         =========
SUPPLEMENTAL  SCHEDULE  OF  NON-CASH  FINANCING  AND
INVESTING ACTIVITIES:
       Equipment acquired under lease line of credit .......               --               107
       Warrant issued in lieu of payment of legal fees .....               --               100
       Common  stock  issued in  exchange  for notes
       receivable, less cancellations ......................               --               100
</TABLE>


                             See accompanying notes.


                                       3
<PAGE>   6

                                     AVIRON
                     NOTES TO CONDENSED FINANCIAL STATEMENTS
                           MARCH 31, 1998 (UNAUDITED)

1.      Summary of Significant Accounting Policies

Basis of Presentation

       The accompanying unaudited condensed financial statements have been
prepared in accordance with generally accepted accounting principles for interim
financial information and with the instructions to Form 10-Q and Article 10 of
Regulation S-X.

       The financial information as of March 31, 1998 and for the three months
ended March 31, 1998 and 1997 is unaudited, but includes all adjustments
(consisting only of normal recurring adjustments) which Aviron (the "Company")
considers necessary for a fair presentation of the financial position at such
date and the operating results and cash flows for those periods. The balance
sheet data at December 31, 1997 is derived from audited financial statements at
that date. The accompanying condensed financial statements should be read in
conjunction with the financial statements and notes thereto included in the
Company's Annual Report on Form 10-K for the year ended December 31, 1997. The
results of the Company's operations for any interim period are not necessarily
indicative of the results of the Company's operations for a full fiscal year.

2.      Net Loss Per Share

       Effective December 31, 1997, the Company adopted Statement of Financial
Accounting Standards No. 128 "Earnings Per Share" ("SFAS 128"). SFAS 128
requires the presentation of basic earnings (loss) per share and diluted
earnings per share, if more dilutive, for all periods presented. Basic net loss
per share is computed using the weighted average number of common shares
outstanding during the period. Diluted net loss per share has not been presented
separately as, given the Company's net loss position, the result would be
anti-dilutive.

3.      Changes in Securities

       In March 1998, the Company issued $100.0 million of 5-3/4% Convertible
Subordinated Notes due 2005 (the "Notes").


                                       4

<PAGE>   7
The net proceeds to Aviron from the Note Offering were approximately $96.0
million. Of the net proceeds, approximately $13.3 million was used to repurchase
530,831 shares of Aviron Common Stock formerly held by Sang-A Pharm. Co., Ltd.,
the Company's Korean partner ("Sang-A"). The Notes are convertible into shares
of common stock at the option of the holder at a price per share of $30.904.

4.      New Accounting Pronouncements

       As of January 1, 1998, the Company adopted Statement of Financial
Accounting Standards No. 130, Reporting Comprehensive Income ("Statement 130").
Statement 130 establishes rules for the reporting of comprehensive income
(loss) and its components, accordingly the adoption of this Statement had no
impact on the Company's net loss or stockholders' equity. Comprehensive income
(loss) has not been presented separately herein as it approximates the
Company's net loss.

       The Company is currently evaluating the requirements of Statement of
Financial Standards No. 131, Disclosures about Segments of an Enterprise and
Related Information ("Statement 131") which must be adopted in the Company's
financial statements for the year ended December 31, 1998, if applicable. The
adoption of Statement 131 will not impact results of operations or financial
position.




                                       5
<PAGE>   8

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

       The following Management's Discussion and Analysis of Financial Condition
and Results of Operations contains, in addition to historical information,
forward-looking statements which involve risks and uncertainties. The Company's
actual results could differ materially from those anticipated in these
forward-looking statements as a result of certain factors, including those set
forth in the Company's Annual Report on Form 10-K in the section entitled
"Business Risks."

OVERVIEW

       Since its inception in April 1992, Aviron has devoted the majority of its
resources to its research and development programs. To date, Aviron has not
generated any revenues from the sale of products and does not expect to generate
any such revenues until at least late in 1999, if at all. Aviron has incurred
cumulative net losses of approximately $77.1 million as of March 31, 1998, and
it expects to incur increasing operating losses over at least the next few
years.

       Aviron has financed its operations through proceeds from private
placements of Preferred Stock, two public offerings and a private placement of
Common Stock, a private placement of convertible subordinated notes ("Notes"),
revenue from its collaborative agreements, equipment lease financings and
investment income earned on cash, cash equivalent balances and marketable
securities.

       The Company expects its research and development expenditures to increase
substantially over the next several years as the Company expands its research
and development efforts and preclinical testing and clinical trials with respect
to certain of its programs. In addition, general and administrative expenses are
expected to continue to increase as the Company expands its operations.

       In March 1998, $100.0 million of Notes were issued by the Company and
sold to "qualified institutional buyers" (as defined in Rule 144A of the
Securities Act) and a limited number of other institutional "accredited
investors" (as defined in Rule 501(a)(1), (2), (3) or (7) under the Securities
Act) in transactions exempt from registration under the Securities Act. The net
proceeds to Aviron from the Note Offering were approximately $96.0 million. Of
the net proceeds, approximately $13.3 million was used to repurchase 530,831
shares of Aviron Common Stock formerly held by Sang-A. The balance is expected
to be used for clinical trials, regulatory submissions, manufacturing and
marketing expenses in support of the product launch of FluMist(TM), the
Company's intranasal influenza vaccine (contingent on FDA approval); research
and development, clinical testing, clinical trials and regulatory submissions
for its other vaccine programs; and working capital.

       In October 1995, the Company signed an agreement with SmithKline Beecham
defining a collaboration on the Company's Epstein-Barr virus (EBV) vaccine
technology (the "SB Agreement"). Under the terms of the SB Agreement, the
Company granted SmithKline Beecham an exclusive license to produce, use and sell
EBV vaccines incorporating the Company's technology for prophylactic and
therapeutic uses on a worldwide basis, except in South and North Korea
(together, Korea). The Company has retained the right to co-market a 



                                       6

<PAGE>   9

monovalent formulation of the vaccine in certain markets in the United States
and to have SmithKline Beecham supply such vaccine. SmithKline Beecham has
agreed to fund research and development at the Company related to the EBV
vaccine, in specified minimum amounts, during the first two years of the SB
Agreement. SmithKline Beecham made an initial upfront payment to the Company and
agreed to make additional payments upon the achievement of certain product
development milestones, the first of which was paid to the Company in 1997. The
Company is entitled to royalties from SmithKline Beecham based on net sales of
the vaccine. No assurance can be given, however, that the Company will receive
any additional payments from SmithKline Beecham or that SmithKline Beecham will
not terminate its agreement with the Company.

       In May 1995, the Company entered into a Development and License Agreement
with Sang-A. The Company granted to Sang-A exclusive clinical development,
manufacturing and marketing rights in Korea for specified products developed by
Aviron, including vaccines for influenza (cold adapted and recombinant), EBV
(marketing rights only), cytomegalovirus, herpes simplex virus type 2 and
respiratory syncytial virus. However, the Company is under no obligation to
develop any product. Sang-A also agreed to make payments to the Company upon
meeting certain regulatory milestones for each product in Korea and to pay a
royalty to the Company on net sales of such products in Korea. No assurance can
be given, however, that the Company will receive any payments from Sang-A or
that Sang-A will not terminate its agreement with the Company.

       In January 1997, the Hanbo Group, the conglomerate that owns Sang-A,
declared bankruptcy. The Company is unable to predict what, if any, long-term
effect the bankruptcy of the Hanbo Group will have on Hanbo Group subsidiaries,
including Sang-A, or on the Company's agreement with Sang-A.

       In 1996, the Company initiated a two-year pivotal Phase III clinical
trial to evaluate FluMist(TM) in children. The Company enrolled 1,602 children
at 10 clinical sites, of which 1,314 were vaccinated with a second dose 46 to 74
days after initial vaccination. In July 1997, the Company and the National
Institute of Allergy and Infectious Diseases announced that, based on an initial
analysis of the first stage of the Phase III trial, Aviron's intranasal
influenza vaccine demonstrated a 93% protection rate against culture confirmed
influenza in those children receiving two doses, the primary endpoint of the
study. The clinical investigators presented the initial findings of this trial
at a scientific conference in fall 1997 and have submitted the findings for
publication in a peer-reviewed medical journal. The Company intends to submit a
Product License Application ("PLA") to the FDA based on the data from this trial
and prior studies, and will support its PLA with additional data from the second
stage of this Phase III clinical trial as well as other trials.

       The Company currently is evaluating the costs and benefits of developing
internal manufacturing capabilities or contracting for expanded or alternative
sources of supply from third-party manufacturers. In 1996, the Company completed
construction of a pilot manufacturing facility funded through its existing
capital lease line of credit. In April 1997, the Company entered into an
agreement with Evans Medical Limited, a subsidiary of Medeva plc ("Evans") for
the commercial manufacture of FluMist(TM) through December 2001. In October
1997, the Company entered into an agreement with Packaging Coordinators, Inc., a
subsidiary of Cardinal Health, Inc. ("PCI") for the blending, filling, packaging
and labeling of FluMist(TM) in the United States 



                                       7

<PAGE>   10
until October 2004. The agreements with Evans and PCI have required the Company
to fund the construction of facilities, improvements, and equipment and will
continue to require the Company to incur expenses for the duration of the
agreements for facility space, utilities and insurance.

       The Company's business is subject to significant risks, including but not
limited to the risks inherent in its research and development efforts, including
preclinical testing and clinical trials; uncertainties associated both with
obtaining and enforcing its patents and with the patent rights of others; the
lengthy, expensive and uncertain process of seeking regulatory approvals;
uncertainties regarding government reforms and product pricing and reimbursement
levels; technological change and competition; manufacturing uncertainties and
dependence on third parties. Even if the Company's product candidates appear
promising at an early stage of development, they may not reach the market for
numerous reasons. Such reasons include the possibilities that the products will
be found unsafe or ineffective during clinical trials, will fail to receive
necessary regulatory approvals, will be difficult to manufacture on a large
scale, will be uneconomical to market or will be precluded from
commercialization by proprietary rights of third parties.

RESULTS OF OPERATIONS

Three Months Ended March 31, 1998 and 1997

       Revenues

       The Company earned $253,000 in revenue for the three months ended March
31, 1998, compared to $305,000 for the three months ended March 31, 1997.  The
1998 revenue came from both a grant payment from the NIH for research on the
Company's CMV vaccine and from payments made for services rendered to other
biotechnology companies. The 1997 revenue resulted from research support
payments due to the Company under its license and development agreement with
SmithKline Beecham.

       Operating Expenses

       Research and development expenses increased to $9.8 million in the three
months ended March 31, 1998 from $4.3 million for the three months ended March
31, 1997. These increases were primarily due to increases in research and
development activities and staffing, expenses associated with clinical trials of
FluMist(TM) and the Company's PIV-3 vaccine, and preclinical testing associated
with other programs.

       General and administrative expenses increased to $2.1 million in the
three months ended March 31, 1998 from $1.2 million for the three months ended
March 31, 1997. These increases were primarily the result of market research
regarding FluMist(TM) and additions to staffing necessary to support the
Company's research and development, patent and legal, and corporate development
activities. These expenses are expected to increase in the future in continued
support of these activities.



                                       8

<PAGE>   11

       Net Interest Income

       Net Interest income increased to $910,000 in the three months ended March
31, 1998 from $169,000 for the three months ended March 31, 1997. The increase
in net interest income reflects the effect of the Company's increase in average
cash, cash equivalent and investment balances, due to the Company's private
placement of Common Stock in March 1997, and its public offering of Common Stock
in August 1997. The Company's net proceeds from these two transactions was
approximately $82.9 million.

LIQUIDITY AND CAPITAL RESOURCES

       Aviron had cash, cash equivalents and marketable securities at March 31,
1998 of approximately $139.0 million. In order to preserve principal and
maintain liquidity, the Company's funds are invested in United States Treasury
obligations, highly rated corporate obligations and other liquid investments.

       The Company has financed its operations since inception primarily through
private placements of Preferred Stock from 1992 to 1995, an initial public
offering of Common Stock in November 1996, a private sale of Common Stock in
March 1997, a second public offering of Common Stock in August 1997, and the
Note Offering in March 1998. Through March 31, 1998, the Company had raised
approximately $236.3 million from such activities net of offering expenses. Cash
used in operations was $13.3 million and $4.9 million for the first three months
of 1998 and 1997, respectively. Net cash used in operating activities increased
primarily due to increased research and development expenditures. The Company
expects expenditures for research and development, clinical trials and general
and administrative expenses to continue to increase during the remainder of 1998
and in 1999 as the Company develops its products and expands its clinical
trials.

       The Company anticipates that its existing cash, cash equivalents and
short-term investments, and revenues from existing collaborations, will enable
it to maintain its current and planned operations through 1999. The Company's
future cash requirements will depend on numerous factors, including continued
scientific progress in the research and development of the Company's technology
and vaccine programs; the size and complexity of these programs; the ability of
the Company to establish and maintain collaborative arrangements; progress with
preclinical testing and clinical trials; the time and costs involved in
obtaining regulatory approvals; the cost involved in preparing, filing,
prosecuting, maintaining and enforcing patent claims; the cost of constructing
manufacturing facilities, should they be deemed necessary; and product
commercialization activities. In particular, if the Company were to construct
and equip such a manufacturing facility during this period, the Company
anticipates that it would likely begin to make substantial additional capital
expenditures in the second half of 1998 and beyond, which may require the
Company to seek additional funding. The Company is seeking additional
collaborative agreements with corporate partners. There can be no assurance,
however, that any such agreements will be entered into or that they will reduce
the Company's funding requirements or that additional funding will be available.
In addition, there can be no assurance that, should the Company require outside
funding through additional debt or equity financings, such funds will be
available on favorable 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 



                                       9

<PAGE>   12

or development programs or to obtain funds through collaborative agreements with
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 itself, which would materially adversely affect
the Company's business, financial condition and results of operations.

IMPACT OF "YEAR 2000"

       The Company is in the process of assessing its computer hardware and
software systems to evaluate difficulties that may be experienced in connection
with the so-called "Year 2000" problem. The Company has evaluated its financial
and accounting systems and concluded that they are not materially affected by
the Year 2000 issue. The extent, if any, of the impact of the Year 2000 issue on
other systems and equipment is currently unknown. There can be no assurance that
all third parties will address the Year 2000 issue in a timely fashion if at
all. Any significant Year 2000 compliance problems of the Company, its
suppliers, its clinical research organizations, or its collaborative partners
could have a material adverse effect on the Company's business, financial
condition and results of operations.



                                       10
<PAGE>   13

                                     AVIRON


PART II.         OTHER INFORMATION

       ITEM 1.   LEGAL PROCEEDINGS.

       ITEM 2.   CHANGES IN SECURITIES.

               On March 30, 1998, the Company sold $100,000,000 aggregate
        principal amount of 5 3/4% Convertible Subordinated Notes due 2005 (the
        "Notes"), of which $99,850,000 aggregate principal amount (the "Rule
        144A Notes") were sold to qualified institutional buyers in reliance
        upon Rule 144A under the Securities Act of 1933, as amended (the "Act"),
        and $150,000 aggregate principal amount were sold to institutional
        accredited investors (the "Accredited Institution Notes") in reliance
        upon Regulation D under the Act. The Notes were sold initially to Morgan
        Stanley & Co. Incorporated, Bear, Stearns & Co. Inc., Credit Suisse
        First Boston Corporation, and Hambrecht & Quist LLC (the "Initial
        Purchasers"). The Initial Purchasers received a discount of 3.5% of the
        principal amount of Regulation S Notes purchased, or $3,500,000. Net
        proceeds to the Company, after deducting legal and other expenses, were
        approximately $96,000,000.

               The offering of the Rule 144A Notes was made in reliance on Rule
        144A promulgated under the Act, based on the fact that the securities
        were offered or sold in the United States only to "qualified
        institutional buyers" (as defined in Rule 144A) and the Notes were not,
        at the time of issuance, of the same class as securities listed on a
        national securities exchange, as "securities of the same class" is
        defined in Rule 144A. The offering of the Accredited Institution Notes
        was made in reliance on Regulation D under the Act, based on the fact
        that the securities were offered to a limited number of institutional
        "accredited investors" (as defined in Rule 501(a) (1), (2), (3) or (7)),
        in compliance with the general conditions of Rule 502.

               The initial conversion price of $30.904 per share (equivalent to
        a conversion rate of approximately 32.3583 shares per $1,000 principal
        amount of Notes), is subject to adjustment in certain events, including:

                (i) the issuance of Common Stock as a dividend or distribution
        on the Common Stock;

                (ii) certain subdivisions and combinations of the Common Stock;

                (iii) the issuance to all holders of Common Stock of certain
        rights or warrants to purchase Common Stock;

                (iv) the distribution to all holders of Common Stock of capital
        stock (other than Common Stock), evidences of indebtedness of the
        Company or of assets (including securities, but excluding those rights,
        warrants, dividends or distributions referred to above or paid in cash);



                                       11

<PAGE>   14

               (v) distributions consisting of cash, excluding any quarterly
        cash dividend on the Common Stock to the extent that the aggregate cash
        dividend per share of Common Stock in any fiscal quarter does not exceed
        the greater of (x) the amount per share of Common Stock of the next
        preceding quarterly cash dividend on the Common Stock to the extent that
        such preceding quarterly dividend did not require an adjustment of the
        conversion price pursuant to this clause (v) (as adjusted to reflect
        subdivisions or combinations of the Common Stock), and (y) 3.75% of the
        average of the last reported sales price of the Common Stock during the
        ten trading days immediately prior to the date of declaration of such
        dividend, and excluding any dividend or distribution in connection with
        the liquidation, dissolution or winding up of the Company. If an
        adjustment is required to be made as set forth in this clause (v) as a
        result of a distribution that is a quarterly dividend, such adjustment
        would be based upon the amount by which such distribution exceeds the
        amount of the quarterly cash dividend permitted to be excluded pursuant
        to this clause (v). If an adjustment is required to be made as set forth
        in this clause (v) as a result of a distribution that is not a quarterly
        dividend, such adjustment would be based upon the full amount of the
        distribution;

               (iv) payment in respect of a tender offer or exchange by the
        Company or any subsidiary of the Company for all or any portion of the
        Common Stock to the extent that the cash and value of any other
        consideration included in such payment per share of Common Stock exceeds
        the Current Market Price (as defined) per share of Common Stock on the
        trading day next succeeding the last date on which tenders or exchanges
        may be made pursuant to such tender or exchange offer; and

               (vii) payment in respect of a tender offer or exchange offer by a
        person other than the Company or any subsidiary of the Company in which,
        as of the closing date of the offer, the Board of Directors is not
        recommending rejection of the offer. The adjustment referred to in this
        clause (vii) will only be made if the tender offer or exchange offer is
        for an amount that increases the offeror's ownership of Common Stock to
        more than 25% of the total shares of Common Stock outstanding, and if
        the cash and value of any other consideration included in such payment
        per share of Common Stock exceeds the Current Market Price per share of
        Common Stock on the business day next succeeding the last date on which
        tenders or exchanges may be made pursuant to such tender or exchange
        offer. The adjustment referred to in this clause (vii) will generally
        not be made, however, if, as of the closing of the offer, the offering
        documents with respect to such offer disclose a plan or an intention to
        cause the Company to engage in a consolidation or merger of the Company
        or a sale of all or substantially all of the Company's assets.

        The "Current Market Price" for purposes of any conversion adjustment
shall generally mean the average of the daily closing prices per share of the
Common Stock on the Nasdaq National Market for the ten trading days prior to the
conversion date.

        Under the provisions of the Company's Share Purchase Rights Plan, upon
conversion of the Notes into Common Stock to the extent that the Share Purchase
Rights Plan is still in effect upon such conversion, the holders will receive,
in addition to the Common Stock, the Rights described therein (whether or not
the rights have separated from the Common Stock at the time of conversion),
subject to certain limited exceptions.



                                       12

<PAGE>   15

        In the case of (i) any reclassification of the Common Stock or (ii) a
consolidation, merger of combination involving the Company or a sale of
conveyance to another person or all or substantially all the property and assets
of the Company, in each case, as a result of which holders of Common Stock shall
be entitled to receive stock, other securities, other property or assets
(including cash) with respect to or in exchange for such Common Stock, the
holders of the Notes then outstanding will generally be entitled thereafter to
convert such Notes into the kind and amount of shares of stock, other securities
or other property or assets (including cash) which they would have owned or been
entitled to receive upon such reclassification, consolidation, merger,
combination, sale or conveyance had such Notes been converted into Common Stock
immediately prior to such reclassification, consolidation, merger, combination,
sale or conveyance assuming that a holder of Notes would have exercised any
rights of election as to the stock, other securities or other property or assets
(including cash) receivable in connection therewith.

        In the event of a taxable distribution to holders of Common Stock or in
certain other circumstances requiring an adjustment to the conversion price, the
holders of Notes may, in certain circumstances, be deemed to have received a
distribution subject to United States income tax as a dividend; in certain other
circumstances, the absence of such an adjustment may result in a taxable
dividend to the holders of Common Stock.

        The Company, from time to time and to the extent permitted by law, may
reduce the conversion price by any amount for any period of at least 20 business
days, in which case the Company shall give at least 15 days notice of such
reduction, if the Board of Directors of the Company has made a determination
that such reduction would be in the best interests of the Company, which
determination shall be conclusive. The Company may, at its option, make such
reductions in the conversion price, in addition to those set forth above, as the
Board of Directors of the Company deems advisable to avoid or diminish any
income tax to holders of Common Stock resulting from any dividend or
distribution of stock (or rights to acquire stock) or from any event treated as
such for United States federal income tax purposes.

        On April 20, 1998, the Company filed a Registration Statement on Form
S-3, SEC File No. 333-50505 (the "Registration Statement"), for the resale of
the Notes and the shares of Common Stock into which the Notes may be converted.
The Registration Statement was declared effective by the Securities and Exchange
Commission on May 4, 1998.

       ITEM 3.   DEFAULTS UPON SENIOR SECURITIES.

                 None

       ITEM 4.   SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS.

                 None.

       ITEM 5.   OTHER INFORMATION.

                 None



                                       13

<PAGE>   16

       ITEM 6.   EXHIBITS AND REPORTS ON FORM 8-K.

                 (a)  EXHIBITS

<TABLE>
<CAPTION>
                 ITEM        DESCRIPTION
                 ----        -----------
<S>                          <C>
                 27.1        Financial Data Schedules.
</TABLE>

                 (b)  REPORTS ON FORM 8-K

                 The Company filed a Current Report on Form 8-K dated March 17,
                 1998 on April 1, 1998 (SEC File No. 0-20815) announcing the
                 completion of the Note Offering.



                                       14
<PAGE>   17


                                     AVIRON


                                   SIGNATURES

Pursuant to the requirements of the Securities and Exchange Act of 1934, the
registrant has duly caused this report to be signed in its behalf by the
undersigned thereunto duly authorized.



                                               AVIRON





Date:     May 14, 1998                         By:  /s/ J. Leighton Read, M.D.
     ------------------------                     ------------------------------
                                                    J. Leighton Read, M.D.
                                                    Chairman and
                                                    Chief Executive Officer



Date:      May 14, 1998                        By:  /s/ Fred Kurland
     ------------------------                     ------------------------------
                                                    Fred Kurland
                                                    Senior Vice President and
                                                    Chief Financial Officer



<PAGE>   18

                                  EXHIBIT INDEX


<TABLE>
<CAPTION>
        NO. OF EXHIBIT       DESCRIPTION
        --------------       -----------
<S>                          <C>
                27.1         Financial Data Schedule.
</TABLE>



                                       16