<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 SEPTEMBER 30, 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 Identification No.)
incorporation or organization)

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

                                 (650) 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 OCTOBER 10, 1997
WAS 22,163,918 SHARES.

This report on Form 10-Q contains 12 pages.



<PAGE>   2
                               NEUREX CORPORATION

                                      INDEX


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

          a.    Condensed Consolidated Balance Sheets - September 30, 1997 and December 31, 1996.......................        3

          b.    Consolidated Statements of Operations - Three and Nine Months Ended September 30, 1997 and 1996........
                                                                                                                               4

          c.    Condensed Consolidated Statements of Cash Flows - Nine Months Ended September 30, 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............................................................................................        11

   2.     Changes in Securities........................................................................................        11

   3.     Defaults Upon Senior Securities..............................................................................        11

   4.     Submission of Matters to a Vote of Security Holders..........................................................        11

   5.     Other Information............................................................................................        11

   6.     Exhibits and Reports on Form 8-K.............................................................................        11

          Signatures...................................................................................................        12
</TABLE>


                                       2


<PAGE>   3
                         PART I - FINANCIAL INFORMATION
ITEM 1.         FINANCIAL STATEMENTS

                               NEUREX CORPORATION

                      CONDENSED CONSOLIDATED BALANCE SHEETS
                (IN THOUSANDS EXCEPT SHARE AND PER SHARE AMOUNTS)
                                   (UNAUDITED)

                                     ASSETS


<TABLE>
<CAPTION>
                                                                                SEPTEMBER 30,  DECEMBER 31,
                                                                                     1997         1996
                                                                                   ---------    ---------
<S>                                                                                <C>          <C>      
Current assets:
   Cash and cash equivalents ...................................................   $  18,060    $  40,552
   Short-term investments ......................................................      49,729       46,691
   Other current assets ........................................................         367          381
                                                                                   ---------    ---------
      Total current assets .....................................................      68,156       87,624
Property and equipment, net ....................................................       2,306        1,748
Notes receivable from officer ..................................................         100          123
Other assets, net ..............................................................          73           77
                                                                                   ---------    ---------
                                                                                   $  70,635    $  89,572
                                                                                   =========    =========
                      LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
   Accounts payable ............................................................   $   2,085    $   1,963
   Accrued wages and benefits ..................................................         676          458
   Accrued payables to related party ...........................................          40           50
   Accrued clinical and preclinical testing ....................................       4,940        2,509
   Other accrued liabilities ...................................................         996          621
Prepaid milestone repayable to Medtronic, Inc., a stockholder ..................       1,820         --
   Deferred revenue ............................................................       1,000        1,043
   Deferred revenue - Warner Lambert, a stockholder ............................         756          803
   Current portion of capital lease obligations ................................         162          204
                                                                                   ---------    ---------
      Total current liabilities ................................................      12,475        7,651
Long-term capital lease obligations ............................................         158          295
Prepaid milestone repayable to Medtronic, Inc., a stockholder ..................        --          1,669
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: 22,163,918 shares at September 30, 1997 and 22,036,080
      shares at December 31, 1996 ..............................................         222          220
   Additional paid-in capital ..................................................     156,042      155,599
   Deferred compensation .......................................................          (6)         (41)
   Unrealized gain (loss) on investments .......................................          16          (10)
   Accumulated deficit .........................................................     (98,272)     (75,811)
                                                                                   ---------    ---------
      Total stockholders' equity ...............................................      58,002       79,957
                                                                                   =========    =========
                                                                                   $  70,635    $  89,572
                                                                                   =========    =========
</TABLE>

                             See accompanying notes.


                                       3


<PAGE>   4
                               NEUREX CORPORATION

                      CONSOLIDATED STATEMENTS OF OPERATIONS
                     (IN THOUSANDS EXCEPT PER SHARE AMOUNTS)
                                   (UNAUDITED)




<TABLE>
<CAPTION>
                                          THREE MONTHS ENDED      NINE MONTHS ENDED
                                             SEPTEMBER 30,          SEPTEMBER 30,
                                         --------------------    --------------------
                                           1997        1996        1997        1996
                                         --------    --------    --------    --------
<S>                                      <C>         <C>         <C>         <C>     
Revenues from collaborative agreements
and grants:

   Related parties ...................   $    350    $     39    $  1,156    $  1,132
   Other .............................         19       1,640          39       1,646
                                         --------    --------    --------    --------
                                              369       1,679       1,195       2,778

Costs and expenses:

   Research and development ..........      7,533       4,949      20,974      12,892

   Selling, general and administrative      2,559       1,164       5,715       2,588
                                         --------    --------    --------    --------

      Total costs and expenses .......     10,092       6,113      26,689      15,480
                                         --------    --------    --------    --------

Loss from operations .................     (9,723)     (4,434)    (25,494)    (12,702)

Interest income, net .................        962       1,279       3,033       2,365
                                         --------    --------    --------    ========

Net loss .............................   $ (8,761)   $ (3,155)   $(22,461)   $(10,337)
                                         ========    ========    ========    ========

Net loss per share ...................   $  (0.40)   $  (0.14)   $  (1.02)   $  (0.51)
                                         ========    ========    ========    ========

Shares used in net loss per share
   computation .......................     22,164      22,013      22,120      20,230
</TABLE>


                             See accompanying notes.


                                       4


<PAGE>   5
                               NEUREX CORPORATION

                 CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS

                INCREASE (DECREASE) IN CASH AND CASH EQUIVALENTS

                                 (IN THOUSANDS)

                                   (UNAUDITED)


<TABLE>
<CAPTION>
                                                                       NINE MONTHS ENDED
                                                                         SEPTEMBER 30,
                                                                     ----------------------
                                                                       1997         1996
                                                                     ---------    ---------
<S>                                                                  <C>          <C>       
Cash flows used for operating activities:
   Net loss ......................................................   $ (22,461)   $ (10,337)
      Adjustments to reconcile net loss to net cash used
      for operating activities:
           Depreciation and amortization .........................         481          307
           Noncash expenses from stock, debt and warrant issuances          54          260
      Changes in assets and liabilities:
           Current assets ........................................          37          117
           Current liabilities ...................................         748          721
           Accrued clinical and preclinical testing ..............       2,431          341
                                                                     ---------    ---------
           Net cash used for operating activities ................     (18,710)      (8,591)
Cash flows from investing activities:
   Purchase of property and equipment ............................      (1,035)        (433)
   Purchases of short-term investments ...........................    (200,689)    (165,644)
   Maturities of short-term investments ..........................     197,676      130,184
   Payments of notes payable to stockholder ......................        --           (289)
                                                                     ---------    ---------
           Net cash used for investing activities ................      (4,048)     (36,182)
Cash flows from financing activities:
   Sales of common stock .........................................         445       75,724
   Payments of capital lease obligations .........................        (179)        (145)
                                                                     ---------    ---------
           Net cash provided by financing activities .............         266       75,579
                                                                     ---------    ---------
Net increase (decrease) in cash and cash equivalents .............     (22,492)      30,806
Cash and cash equivalents at beginning of period .................      40,552        2,655
                                                                     ---------    ---------
Cash and cash equivalents at end of period .......................      18,060       33,461
                                                                                     18,060
Short-term investments at end of period ..........................      49,729       54,504
                                                                     ---------    ---------
Cash, cash equivalents and short-term investments at end of period   $  67,789    $  87,965
                                                                     =========    =========
</TABLE>


                             See accompanying notes.


                                       5


<PAGE>   6
                               NEUREX CORPORATION

                         NOTES TO CONDENSED CONSOLIDATED
                              FINANCIAL STATEMENTS


1.         SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES

           Organization

           Neurex Corporation ("Neurex" or the "Company") 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 condensed 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 September 30, 1997, and
for the three and nine month periods ended September 30, 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 full fiscal year.

           Cash and investments

           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. 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.

           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 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. 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.


                                       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 three and nine month periods ended September 30, 1997 and 1996.


2.         AVAILABLE-FOR-SALE SECURITIES

           The Company's debt securities are available-for-sale and consist
primarily of corporate debt securities of $55,779,000, and U.S. Treasury Notes
and other U.S. government securities of $10,384,000 at September 30, 1997.
Short-term investments have original maturities ranging from 90 days to 3 years.
The gross realized gains and losses on sales of available-for-sale securities
were insignificant in the three and nine month periods ended September 30, 1997.


3.         RELATED PARTY TRANSACTION

           On August 8, 1997, a note receivable from an officer became due and
payable. The entire principal balance plus all accrued interest totaling
$129,895 was paid in full by the officer.


                                       7


<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 September 30,
1997, the Company's cumulative net loss was $98,272,000. 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, 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, which
include, but 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 within the meaning of
Section 27A of the Securities Act of 1933, as amended, and Section 21E of the
Securities & Exchange Act of 1934, as amended. These statements relate and
involve inherent risks and uncertainties. The Company's actual results may
differ materially from the results discussed in the forward-looking statements.
Factors that might cause actual results to differ materially include, but are
not limited to, the factors described in this Overview, and discussed in the
Company's Annual Report, on Form 10-K for the year ended December 31, 1996, and
in the Company's other filings with the Securities & Exchange Commission.


RESULTS OF OPERATIONS

Three Months Ended September 30,1997 and 1996

           Revenues were $369,000 and $1,679,000 for the three months ended
September 30, 1997 and 1996, respectively. Revenues in 1997 consisted primarily
of expense reimbursements from a related party. Other revenues in 1996 consisted
primarily of a payment from Grunenthal of $1,581,000 to sublicense the rights to
market Pro-urokinase in Europe.

           Research and development expenses increased by $2,584,000 or 52%, to
$7,533,000 for the three months ended September 30, 1997, compared to $4,949,000
in the earlier period. The increase was due primarily to increased Phase III
clinical studies of SNX-111 for malignant and non-malignant pain and personnel
costs. The increase in expenses for the period ended September 30, 1997, was
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 $2,559,000 and
$1,164,000 for the three months ended September 30, 1997, and 1996,
respectively, representing an increase of 120%. This increase is attributable


                                       8


<PAGE>   9
primarily to efforts to establish marketing capabilities, as well as other
personnel costs. The Company expects selling, general and administrative
expenses to increase significantly over the next several years.

           Net interest income decreased to $962,000 for the three months ended
September 30, 1997, compared to $1,279,000 in the earlier period. The decrease
in net interest income was due to a decrease in the cash available for
investments as a result of funding the operating losses.

Nine Months Ended September 30, 1997 and 1996

           Revenues were $1,195,000 and $2,778,000 for the nine months ended
September 30, 1997 and 1996, respectively. Revenues in 1997 consisted primarily
of expense reimbursements from a related party. Other revenues for the period
ended September 30, 1996 consisted primarily of a payment from Grunenthal of
$1,581,000 to sublicense the rights to market Pro-urokinase in Europe.

           Research and development expenses increased by $8,082,000 or 63%, to
$20,974,000 for the nine months ended September 30, 1997, compared to
$12,892,000 in the earlier period. The increase was due primarily to increased
Phase III clinical study expenses of SNX-111 for malignant and non-malignant
pain and clinical and scientific consultant expenses in preparation for the FDA
Advisory Committee Meeting held on June 26, 1997 regarding CORLOPAM(R) and
personnel costs. The increase in expenses for the period ended September 30,
1997, was 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 $5,715,000 and
$2,588,000 for the nine months ended September 30, 1997, and 1996, respectively,
representing an increase of 121%. This increase is attributable primarily to the
Company's efforts to establish marketing capabilities as well as personnel
costs. The Company expects selling, general and administrative expenses to
increase significantly over the next several years.

           Net interest income increased to $3,033,000 for the nine months ended
September 30, 1997, compared to $2,365,000 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 secondary offering of the Company's securities in May
1996.


                                       9


<PAGE>   10
LIQUIDITY AND CAPITAL RESOURCES

           For the nine months ended September 30, 1997, cash expenditures for
operating activities and additions to capital equipment were $19,745,000. The
Company anticipates that these expenditures will increase significantly in
future periods.

           The Company had available cash, cash equivalents and short-term
investments of $67,789,000 at September 30, 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 the commercial product launch activities
of CORLOPAM(R) and the 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
Company's timing and cost of commercial product launch activities of
CORLOPAM(R), 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, payments from the licensing,
sublicensing, sales of its intellectual property rights and sales of
CORLOPAM(R). If such funds are not obtained, the Company may need to delay or
curtail some of its research and development activities.


                                       10


<PAGE>   11
                           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

              On September 23, 1997, the Company received final marketing
              approval from the Food and Drug Administration ("FDA") for
              CORLOPAM(R) (fenoldopam mesylate), an intravenously administered
              product for the control of high blood pressure in the hospital
              setting.

6.         EXHIBITS AND REPORTS ON FORM 8-K

                     (a) Reports on Form 8-K

              During the quarter ended September 30, 1997, the Company did not
              file any Current Reports on Form 8-K.


                                       11


<PAGE>   12
                               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: November 11, 1997                               Neurex Corporation
      -------------------------------




By:         /S/ JOHN VARIAN
            --------------------------------------------------
            John Varian
            Vice President and Chief   Financial
            Officer (Principal Financial and
            Accounting Officer and Duly Authorized Officer)


                                       12


<PAGE>   13
                                INDEX TO EXHIBITS
                                -----------------

<TABLE>
<CAPTION>
Exhibit 
Number                            Description
-------                           -----------
<S>                  <C> 
   27                Financial Data Schedule
</TABLE>