<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D. C. 20549

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

                                    FORM 10-Q

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

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

                  FOR THE QUARTERLY PERIOD ENDED MARCH 31, 1997

                         COMMISSION FILE NUMBER 0-19874

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

                               NEUREX CORPORATION
             (Exact name of registrant as specified in its charter)


                 DELAWARE                               77-0128552
     (State or other jurisdiction of                 (I.R.S. Employer
      incorporation or organization)               Identification No.)

              3760 HAVEN AVENUE, MENLO PARK, CALIFORNIA 94025-1012
                    (Address of principal executive offices)

                                 (415) 853-1500
              (Registrant's telephone number, including area code)

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

           SECURITIES REGISTERED PURSUANT TO SECTION 12(b) OF THE ACT:

     Title of each class               Name of each exchange on which registered
COMMON STOCK, $ .01 PAR VALUE                NASDAQ NATIONAL MARKET SYSTEM


           SECURITIES REGISTERED PURSUANT TO SECTION 12(g) OF THE ACT:

                                      NONE

         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
FILING REQUIREMENTS FOR THE PAST 90 DAYS. YES  X   NO
                                             -----    -----

               THE NUMBER OF SHARES OF COMMON STOCK OUTSTANDING AT
                       MAY 8, 1997 WAS 22,124,435 SHARES.

This report on Form 10-Q contains 12 pages.




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<PAGE>   2
                               NEUREX CORPORATION

                                      INDEX


<TABLE>
<CAPTION>
                                                                                                           PAGE
 ITEM                                     PART I. FINANCIAL INFORMATION                                   NUMBER
                                                                                                          ------
<S>      <C>                                                                                                <C>
  1.    Financial Statements (unaudited):

        a.   Condensed Consolidated Balance Sheets - March 31, 1997 and December 31, 1996............       3

        b.   Consolidated Statements of Operations - Three Months Ended March 31, 1997 and 1996......       4

        c.   Condensed Consolidated Statements of Cash Flows - Three Months Ended March 31, 1997 and
             1996....................................................................................       5

        d.   Notes to Condensed Consolidated Financial Statements....................................      6-7


  2.    Management's Discussion and Analysis of Financial Condition and Results of
             Operations..............................................................................      8-10


                                         PART II. OTHER INFORMATION

  1.    Legal Proceedings............................................................................       10

  2.    Changes in Securities........................................................................       10

  3.    Defaults Upon Senior Securities..............................................................       10

  4.    Submission of Matters to a Vote of Security Holders..........................................       10

  5.    Other Information............................................................................       10

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

        Signatures...................................................................................       11
</TABLE>






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<PAGE>   3
                         PART I - FINANCIAL INFORMATION

ITEM 1.       FINANCIAL STATEMENTS

                               NEUREX CORPORATION

                      CONDENSED CONSOLIDATED BALANCE SHEETS
                                   (UNAUDITED)



<TABLE>
<CAPTION>
                                                                                      MARCH 31,          DECEMBER 31,
                                                                                        1997                1996
                                                                                    -------------       -------------
<S>                                                                                 <C>                 <C>          
                                     ASSETS
Current assets:
   Cash and cash equivalents ...................................................    $  25,663,571       $  40,551,609
   Short-term investments ......................................................       55,489,226          46,691,312
   Other current assets ........................................................          251,545             380,799
                                                                                    -------------       -------------
     Total current assets ......................................................       81,404,342          87,623,720
Property and equipment, net ....................................................        2,030,733           1,747,613
Notes receivable from officers .................................................          236,405             123,215
Other assets, net ..............................................................           75,235              76,724
                                                                                    -------------       -------------
                                                                                    $  83,746,714       $  89,571,272
                                                                                    =============       =============
                      LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
   Accounts payable ............................................................    $   1,620,778       $   1,960,832
   Accrued wages and benefits ..................................................          520,067             458,024
   Accrued payables to related parties .........................................           70,000              50,000
   Accrued clinical and preclinical testing ....................................        4,625,405           2,508,788
   Other accrued liabilities ...................................................          523,820             621,159
   Deferred revenue ............................................................        1,052,271           1,043,420
   Deferred revenue - Warner Lambert, a stockholder ............................          756,000             803,000
   Current portion of capital lease obligations ................................          196,861             204,398
                                                                                    -------------       -------------
     Total current liabilities .................................................        9,365,202           7,649,621
Long-term capital lease obligations ............................................          249,043             294,559
Prepaid milestone repayable to Medtronic, Inc., a stockholder ..................        1,719,623           1,669,344
Commitments
Stockholders' equity:
   Convertible preferred stock, $ .01 par value; authorized:
      15,000,000 shares; none outstanding ......................................             --                  --
   Common stock, $ .01 par value; authorized:  45,000,000 shares;
      issued and outstanding: 22,091,644 shares at March 31, 1997
      and 22,036,080 shares at December 31, 1996 ...............................          220,916             220,361
   Additional paid-in capital ..................................................      155,728,871         155,598,852
   Deferred compensation .......................................................           (9,751)            (41,307)
   Unrealized loss on investments ..............................................          (74,263)             (9,541)
   Accumulated deficit .........................................................      (83,452,927)        (75,810,617)
                                                                                    -------------       -------------
     Total stockholders' equity ................................................       72,412,846          79,957,748
                                                                                    -------------       -------------
                                                                                     $ 83,746,714        $ 89,571,272
                                                                                     =============       =============
</TABLE>

                             See accompanying notes.






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<PAGE>   4
                               NEUREX CORPORATION

                      CONSOLIDATED STATEMENTS OF OPERATIONS

                                   (UNAUDITED)



<TABLE>
<CAPTION>

                                                    THREE MONTHS ENDED
                                                          MARCH 31,
                                              ---------------------------------
                                                  1997                 1996
                                              ------------         ------------
<S>                                           <C>                  <C>         
Revenues from collaborative
agreements and grants:

Related parties ......................        $    426,465         $    360,420
Other                                               10,202                5,000
                                              ------------         ------------
                                                   436,667              365,420

Costs and expenses:

   Research and development ..........           7,607,593            3,140,157

   Selling, general and
     administrative ..................           1,508,737              726,831
                                              ------------         ------------

     Total costs and expenses ........           9,116,330            3,866,988
                                              ------------         ------------

Loss from operations .................          (8,679,663)          (3,501,568)

Interest income ......................           1,104,330              313,214

Interest expense .....................             (66,977)             (67,441)
                                              ------------         ------------

Net loss .............................        $ (7,642,310)        $ (3,255,795)
                                              ============         ============

Net loss per share ...................        $      (0.35)        $      (0.18)
                                              ============         ============

Shares used in net loss per share
   computation .......................          22,077,878           18,216,862
</TABLE>


                             See accompanying notes.




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<PAGE>   5
                               NEUREX CORPORATION

                 CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS

                INCREASE (DECREASE) IN CASH AND CASH EQUIVALENTS

                                   (UNAUDITED)



<TABLE>
<CAPTION>
                                                                            THREE MONTHS ENDED
                                                                                  MARCH 31,
                                                                      -------------------------------
                                                                          1997               1996
                                                                      ------------       ------------
<S>                                                                   <C>                <C>          
Cash flows used for operating activities:
   Net loss ....................................................      $ (7,642,310)      $ (3,255,795)
     Adjustments to reconcile net loss to net cash used
     for operating activities:
         Depreciation and amortization .........................           146,081            131,769
         Noncash expenses from stock, debt and warrant issuances            37,772             53,235
     Changes in assets and liabilities:
         Current assets ........................................            16,064             (8,410)
         Current liabilities ...................................          (349,436)          (257,011)
         Accrued clinical and preclinical testing ..............         2,116,617                764
                                                                      ------------       ------------
         Net cash used for operating activities ................        (5,675,212)        (3,335,448)
Cash flows from investing activities:
   Purchase of property and equipment ..........................          (427,712)          (152,845)
   Purchases of short-term investments .........................       (66,343,515)        (4,490,826)
   Maturities of short-term investments ........................        57,480,880          5,251,038
                                                                      ------------       ------------
         Net cash provided by (used for) investing activities ..        (9,290,347)           607,367
Cash flows from financing activities:
   Sales of common stock .......................................           130,574          1,517,473
   Payments of capital lease obligations .......................           (53,053)           (48,017)
                                                                      ------------       ------------
         Net cash provided by financing activities .............            77,521          1,469,456
                                                                      ------------       ------------
Net decrease in cash and cash equivalents ......................       (14,888,038)        (1,258,625)
Cash and cash equivalents at beginning of period ...............        40,551,609          2,655,116
                                                                      ------------       ------------
Cash and cash equivalents at end of period .....................      $ 25,663,571       $  1,396,491
                                                                      ============       ============
</TABLE>



                             See accompanying notes.




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<PAGE>   6
                               NEUREX CORPORATION

                         NOTES TO CONDENSED CONSOLIDATED
                              FINANCIAL STATEMENTS


1.       SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES

         Organization

         Neurex was incorporated in Delaware on October 15, 1986 to develop
products for the treatment of diseases based upon advances in neuroscience
technology and other therapeutic areas with unmet medical needs.

         Principles of consolidation

         The consolidated financial statements include the accounts of Neurex
and its wholly-owned subsidiary. All significant intercompany accounts and
transactions have been eliminated.

         Interim financial statements

         The balance sheet at December 31, 1996 has been derived from audited
financial statements at that date. The information at March 31, 1997, and for
the three month periods ended March 31, 1997 and 1996, is unaudited, but in the
Company's opinion, the accompanying condensed interim financial statements
include all adjustments, consisting only of normal recurring adjustments, which
the Company considers necessary to fairly state the Company's financial position
and the results of operations and cash flows. Certain information and footnote
disclosures normally included in financial statements prepared in accordance
with generally accepted accounting principles have been condensed or omitted.
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, 1996. The results of the
Company's operations for any interim period are not necessarily indicative of
the results of the Company's operations for any other interim period or for a
full fiscal year.

         Cash and investments

         Cash and cash equivalents consist of cash held in U.S. banks, time
deposits and other highly liquid investments with a maturity of 90 days or less
from the date of purchase. Cash equivalents are readily convertible into cash
and have insignificant interest rate risk. Short-term and long-term investments
include corporate fixed income obligations and U.S. government notes with a
maturity of 90 days to three years from the date of purchase, short-term
investments mature within one year of the balance sheet date. The Company's
investment policy stipulates that a diversified portfolio be maintained and
invested in a manner appropriate for the Company's primary business operations.
The policy defines investment objectives to provide optimal investment return
within constraints that optimize safety and liquidity.

         Management determines the appropriate classification of debt securities
at the time of purchase and reevaluates such designation as of each balance
sheet date. All debt securities to date have been classified as
available-for-sale. The Company has designated all debt securities as
available-for-sale and are carried at estimated fair value in short-term
investments. Available-for-sale securities are carried at fair value, with the
unrealized gains and losses reported in a separate component of stockholders'
equity. The cost of debt securities in this category is adjusted for
amortization of premiums and accretion of discounts to maturity. Such
amortization and accretion is included in interest income and expense. Realized
gains and losses and declines in value judged to be other-than-temporary on
available-for-sale securities are included in interest income or 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.







                                       6
<PAGE>   7
         Net loss per share

         Net loss per share is computed using the weighted average number of
shares of common stock outstanding. Common equivalent shares from stock options
and warrants are excluded from the computation as their effect is antidilutive.

         In February 1997, the Financial Accounting Standards Board issued
Statement No. 128, Earnings per Share, which is required to be adopted on
December 31, 1997. At that time, the Company will be required to change the
method currently used to compute earnings per share and to restate all prior
periods. Under the new requirements for calculating primary earnings per share,
the dilutive effect of stock options will be excluded. The impact of adoption is
expected to result in no change in primary or fully diluted earnings per share
for the first quarter ended March 31, 1997 and 1996.


2.       AVAILABLE-FOR-SALE SECURITIES

         The Company's short and long-term investments are available-for-sale
and consist primarily of U.S. Treasury Notes and other U.S. government
securities of $21,582,205 and corporate debt securities of $58,575,397 at March
31, 1997. Short-term investments have original maturities ranging from one to 18
months. Long-term investments have original maturities ranging from one to three
years. The gross realized gains and losses on sales of available-for-sale
securities were insignificant in the three months ended March 31, 1997.












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<PAGE>   8
ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND 
        RESULTS OF OPERATIONS

OVERVIEW

         Since commencement of operations in October 1986, Neurex has devoted
substantially all of its resources to its research and development programs. The
Company has been unprofitable since inception and expects to incur significant
and increasing losses over at least the next few years in order to continue
clinical development and to commercialize its products. As of March 31, 1997,
the Company's cumulative net loss was $83,452,927. The Company's principal
sources of working capital have been public and private equity financings,
convertible notes payable including the convertible note payable to Medtronic,
Inc., a stockholder (the "Medtronic Note"), milestone and other payments from
collaborative research and development agreements, license fees, interest
income, lease financings and research grants. The Company has not generated any
product sales.

         The Company's business is subject to significant risks, including, but
not limited to the success of its research, development, commercialization,
product acceptance and capital raising efforts, uncertainties associated with
obtaining and enforcing patents important to the Company's business, the lengthy
and expensive regulatory process, and possible competition from other products.
Even if the Company's products appear promising at an early stage of
development, they may not reach the market for a number of reasons. Such reasons
include, but are not limited to, the possibilities that the potential products
will be found ineffective during clinical trials, fail to receive the necessary
regulatory approvals, be difficult to manufacture on a large scale, be
uneconomical to market or be precluded from commercialization by the proprietary
rights of third parties. Additional expenses, delays and losses of opportunities
that may arise out of these and other risks could have a material adverse impact
on the Company's financial condition, results of operations and cash flows.

         This Report contains forward-looking statements relating to future
expense levels and financial results. These statements involve inherent risks
and uncertainties. The Company's actual results may differ significantly from
the results discussed in the forward-looking statements. Factors that might
cause such a difference include, but are not limited to, the risks described in
this Overview and discussed in the Company's Annual Report on Form 10-K for
twelve month period ended December 31, 1996.


RESULTS OF OPERATIONS

Three Months Ended March 31, 1997 and 1996

         Revenues were $437,000 and $366,000 for the three months ended March
31, 1997 and 1996, respectively. Revenues in both periods consisted primarily of
expense reimbursements from a related party.

         Research and Development expenses increased by $4,467,000 or 142%, to
$7,608,000 for the three months ended March 31, 1997, compared to $3,141,000 in
the earlier period. The increase was due primarily to increased Phase III
clinical studies expenses of SNX-111 for malignant and non-malignant pain,
clinical study expenses related to the Company's clinical studies for
CORLOPAM(R) and employment related expenses. The increase in expenses for the
period ended March 31, 1997, were partially offset by a reduction of expenses
associated with the research agreement with Vascular Laboratories, Inc. of the
New England Deaconess Hospital at Harvard University. The Company expects
research and development expenses to increase significantly over the next
several years.

         Selling, general and administrative expenses were $1,509,000 and
$727,000 for the three months ended March 31, 1997, and 1996, respectively,
representing an increase of 108%. This increase is attributable primarily to the
establishment of marketing development activities, as well as increased expenses
of new business development and employment related expenses. The Company expects
selling, general and administrative expenses to increase over the next several
years.






                                       8
<PAGE>   9
         Interest income increased to $1,105,000 for the three months ended
March 31, 1997, compared to $314,000 in the earlier period. The increase was due
to the increase in cash available for investments as the result of the
successful completion of a public offering in May 1996.


LIQUIDITY AND CAPITAL RESOURCES

         For the three months ended March 31, 1997, cash expenditures for
operating activities and additions to capital equipment were $6,102,924. The
Company anticipates that these expenditures will increase significantly in
future periods.

         The Company had available cash, cash equivalents and short and
long-term investments of $81,152,796 at March 31, 1997. Cash in excess of
immediate requirements is invested according to the Company's investment policy,
which provides guidelines with regard to liquidity and return and, wherever
possible, seeks to minimize the potential effects of concentration and degrees
of risk.

         The Company expects to continue to incur substantial additional
operating losses from costs related to continuation and expansion of research
and development, including clinical studies and increased administrative
activities over at least the next few years. The Company anticipates that its
existing capital resources and interest earned thereon will enable it to
maintain its current and planned operations through the foreseeable future.
However, the Company's requirements may change depending on numerous factors,
including, but not limited to, the progress of the Company's research and
development programs, the results of clinical studies, the number and nature of
the indications the Company pursues in clinical studies, the timing of domestic
and foreign regulatory approvals, technological advances, determinations as to
the commercial potential of the Company's products and the status of competitive
products. In addition, expenditures will be dependent on the establishment of
collaborative relationships with other companies, the availability of financing
and other factors. The Company plans to continue to fund its short and long-term
operations using a combination of public and private equity and debt offerings,
and payments from the licensing, sublicensing and/or sales of its intellectual
property rights. If such funds are not obtained, the Company may need to delay
or curtail its research and development activities to a significant extent.










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<PAGE>   10
                           PART II - OTHER INFORMATION

                               NEUREX CORPORATION


1.       LEGAL PROCEEDINGS

                  None.

2.       CHANGES IN SECURITIES

                  None.

3.       DEFAULTS UPON SENIOR SECURITIES

                  None.

4.       SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS

                  None.

5.       OTHER INFORMATION

                  None.

6.       EXHIBITS AND REPORTS ON FORM 8-K

                  (a) Exhibit 27 - Financial Data Schedule

                  (b) Reports on Form 8-K

                      During the quarter ended March 31, 1997, the Company filed
                      no Current Reports on Form 8-K.







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<PAGE>   11
                               NEUREX CORPORATION

                                   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.



Date:    May 8, 1997                  Neurex Corporation
         ----------------------




By:  /S/ PAUL GODDARD, PH.D.              By: /S/ BRADFORD M. WAIT
   ----------------------------              -----------------------------------
         Paul Goddard, Ph.D.                      Bradford M. Wait
         Chairman and Chief                       Vice President, Finance
         Executive Officer                        and Administration
                                                  and Chief Financial Officer








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