<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 JUNE 30, 1998

                         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)

                                 (650) 853-1500

              (Registrant's telephone number, including area code)

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

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

<TABLE>
<S>                                                <C>
             Title of each class                   Name of each exchange on which registered
        COMMON STOCK, $ .01 PAR VALUE                    NASDAQ NATIONAL MARKET SYSTEM
</TABLE>

          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 JULY 30, 1998 WAS
23,307,502 SHARES.

This report on Form 10-Q contains 16 pages.

================================================================================



                                       2
<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 - June 30, 1998 and December 31, 1997.............       3

        b.   Condensed Consolidated Statements of Operations - Three and six Months Ended June
             30, 1998 and 1997.......................................................................       4

        c.   Condensed Consolidated Statements of Cash Flows - Six Months Ended June 30, 1998 and
             1997....................................................................................       5

        d.   Notes to Condensed Consolidated Financial Statements....................................      6-8


  2.    Management's Discussion and Analysis of Financial Condition and Results of
             Operations..............................................................................      9-11


                                         PART II. OTHER INFORMATION

  1.    Legal Proceedings............................................................................       12

  2.    Changes in Securities........................................................................       12

  3.    Defaults Upon Senior Securities..............................................................       12

  4.    Submission of Matters to a Vote of Security Holders..........................................       12

  5.    Other Information............................................................................       12

  6.    Exhibits and Reports on Form 8-K.............................................................       12

        Signatures...................................................................................       13
</TABLE>



                                       3
<PAGE>   3

                         PART I - FINANCIAL INFORMATION

ITEM 1.       FINANCIAL STATEMENTS

                               NEUREX CORPORATION

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

                                     ASSETS

<TABLE>
<CAPTION>
                                                                                     JUNE 30,            DECEMBER 31,
                                                                                       1998                 1997
                                                                                    ------------         ------------
<S>                                                                                 <C>                  <C>         
Current assets:
   Cash and cash equivalents ...............................................        $     18,241         $     11,297
   Short-term investments ..................................................              22,022               46,121
   Trade receivables, net ..................................................                 869                   --
   Other current assets ....................................................               1,823                  277
                                                                                    ------------         ------------
     Total current assets ..................................................              42,955               57,695
Property and equipment, net ................................................               3,517                2,806
Notes receivable from officers .............................................                 180                   94
Other assets, net ..........................................................                  66                   69
                                                                                    ------------         ------------
                                                                                    $     46,718         $     60,664
                                                                                    ============         ============
                      LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
   Accounts payable ........................................................        $      2,485         $      1,912
   Accrued wages and benefits ..............................................                 830                  691
   Accrued clinical and preclinical testing ................................               5,494                5,374
   Other accrued liabilities ...............................................               1,246                  749
   Prepaid milestone repayable to Medtronic, Inc., a stockholder ...........               1,971                1,870
   Deferred revenue ........................................................               1,000                1,000
   Current portion of capital lease obligations ............................                 157                  178
                                                                                    ------------         ------------
     Total current liabilities .............................................              13,183               11,774
Long-term capital lease obligations ........................................                  30                  114
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: 23,286,414 shares at June 30, 1998 and 22,239,267
      shares at December 31, 1997 ..........................................                 233                  222
   Additional paid-in capital ..............................................             161,507              156,299
   Deferred compensation ...................................................                  --                   (5)
   Shareholder receivable ..................................................                  --                  (48)
   Unrealized loss on investments ..........................................                 (13)                  (1)
   Accumulated deficit .....................................................            (128,222)            (107,691)
                                                                                    ------------         ------------
     Total stockholders' equity ............................................              33,505               48,776
                                                                                    ------------         ------------
                                                                                    $     46,718         $     60,664
                                                                                    ============         ============
</TABLE>



                             See accompanying notes.



                                       4
<PAGE>   4

                               NEUREX CORPORATION

                 CONDENSED CONSOLIDATED STATEMENTS OF OPERATIONS

                                   (UNAUDITED)
                    (IN THOUSANDS, EXCEPT PER SHARE AMOUNTS)



<TABLE>
<CAPTION>
                                                THREE MONTHS ENDED                 SIX MONTHS ENDED
                                                      JUNE 30,                          JUNE 30,
                                              -------------------------         -------------------------
                                                1998             1997             1998             1997
                                              --------         --------         --------         --------
<S>                                           <C>              <C>              <C>              <C>     
Revenues:
  Product sales, net .................        $  1,177         $     --         $  3,277         $     --
  Revenues from collaborative
     agreements and grants:
     Related parties .................             430              379              722              806
     Other ...........................              --               10               --               20
                                              --------         --------         --------         --------
          Total revenues .............           1,607              389            3,999              826

Costs and expenses:
     Cost of sales ...................              97               --              331               --
     Research and development ........           7,458            5,865           16,284           13,441
     Selling, general and
        administrative ...............           4,438            1,616            9,075            3,156
                                              --------         --------         --------         --------
          Total costs and expenses ...          11,993            7,481           25,690           16,597
                                              --------         --------         --------         --------
Loss from operations .................         (10,386)          (7,092)         (21,691)         (15,771)
Interest income, net .................             412            1,033            1,160            2,071
                                              --------         --------         --------         --------
Net loss .............................        $ (9,974)        $ (6,059)        $(20,531)        $(13,700)
                                              ========         ========         ========         ========
Basic and diluted net loss per
  share ..............................        $  (0.44)        $  (0.27)        $  (0.91)        $  (0.62)
                                              ========         ========         ========         ========
Shares used in computing basic and
  diluted net loss per share .........          22,619           22,122           22,491           22,101
</TABLE>



                             See accompanying notes.



                                       5
<PAGE>   5

                               NEUREX CORPORATION

                 CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS

                INCREASE (DECREASE) IN CASH AND CASH EQUIVALENTS

                                   (UNAUDITED)
                                 (IN THOUSANDS)



<TABLE>
<CAPTION>
                                                                                  SIX MONTHS ENDED
                                                                                      JUNE 30,
                                                                             ---------------------------
                                                                               1998               1997
                                                                             ---------         ---------
<S>                                                                          <C>               <C>       
Cash flows used for operating activities:
   Net loss .........................................................        $ (20,531)        $ (13,700)
     Adjustments to reconcile net loss to net cash used for operating
     activities:
        Depreciation and amortization ...............................              509               308
        Noncash expenses from stock, debt and warrant issuances .....               18                52
     Changes in assets and liabilities:
        Current assets ..............................................           (2,500)               12
        Current liabilities .........................................            1,298              (647)
        Accrued clinical and preclinical testing ....................              120             2,167
                                                                             ---------         ---------
         Net cash used for operating activities .....................          (21,086)          (11,808)
Cash flows from investing activities:
   Purchase of property and equipment ...............................           (1,218)             (686)
   Purchases of short-term investments ..............................          (50,062)         (143,389)
   Sales and maturities of short-term investments ...................           74,148           135,832
                                                                             ---------         ---------
         Net cash provided by (used for) investing activities .......           22,868            (8,243)
Cash flows from financing activities:
   Sales of common stock ............................................            5,267               345
   Payments of capital lease obligations ............................             (105)             (107)
                                                                             ---------         ---------
         Net cash provided by financing activities ..................            5,162               238
                                                                             ---------         ---------
Net increase (decrease) in cash and cash equivalents ................            6,944           (19,813)
Cash and cash equivalents at beginning of period ....................           11,297            40,552
                                                                             ---------         ---------
Cash and cash equivalents at end of period ..........................           18,241            20,739
Short-term investments at end of period .............................           22,022            54,252
                                                                             ---------         ---------
Cash, cash equivalents and short-term investments at 
 end of period ......................................................        $  40,263         $  74,991
                                                                             =========         =========
</TABLE>



                             See accompanying notes.



                                       6
<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.

         Proposed Merger

         On April 30, 1998, the Company announced that it had signed a
definitive merger agreement with Elan Corporation, plc ("Elan") pursuant to
which a wholly-owned subsidiary of Elan will merge with and into the Company.
The Company shall survive the merger and become a wholly-owned subsidiary of
Elan. Under the terms of the agreement, each share of the Company's common stock
will be exchanged for 0.51 of an Elan American Depository Share (the "Exchange
Ratio"). Certain outstanding options and rights to purchase the Company's common
stock will be assumed by Elan and will become an option or right to purchase
Elan American Depository Shares, with appropriate adjustments to the number of
shares issuable thereunder and the exercise price thereof based on the Exchange
Ratio. The merger has been approved by the boards of directors of the Company
and Elan, but is still subject to approval by the stockholders of the Company at
a special meeting of the stockholders to be held August 11, 1998, at the
Company's headquarters in Menlo Park, California. In addition, on June 25, 1998,
the Company announced that various customary conditions to closing of the
merger, including, but not limited to, expiration of the required waiting period
under the Hart-Scott-Rodino Antitrust Improvements Act of 1976 and the required
clearance of the Merger by the Minister for Enterprise, Trade and Employment of
Ireland under the Mergers, Takeovers and Monopolies (Control) Act of 1978, as
amended, had been satisfactorily met.

         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, 1997 has been derived from audited
financial statements at that date. The information at June 30, 1998, and for the
three and six month periods ended June 30, 1998 and 1997, 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, 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 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 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 



                                       7
<PAGE>   7

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. 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 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.

         Revenue Recognition

         The Company recognizes product sales revenue at the time product is
shipped. Provisions are made for estimated product returns, cash discounts and
government discounts and rebates. Revenues recognized under the Company's
collaborative agreements, license and supply agreements and government grants
are recorded as earned based upon performance requirements of the contracts.
Payments received in advance under these agreements are recorded as deferred
revenues until earned.

         Net loss per share

         In 1997, the Financial Accounting Standards Board issued Statement No.
128, "Earnings per Share." Statement 128 replaced the calculation of primary and
fully diluted earnings per share with basic and diluted earnings per share.
Unlike primary earnings per share, basic earnings per share excludes any
dilutive effects of options, warrants and convertible securities. Diluted
earnings per share is very similar to the previously reported fully diluted
earnings per share. Common equivalent shares from stock options and warrants are
excluded from the diluted computation as their effect is antidilutive. All
earnings per share amounts for all periods have been presented, and where
appropriate restated, to conform to the Statement 128 requirements.

         New Accounting Standards

         In June 1997, the Financial Accounting Standards Board issued Statement
of Financial Accounting Standard No. 131, "Disclosures about Segments of an
Enterprise and Related Information" ("SFAS 131"). The Statement is effective for
fiscal years beginning after December 15, 1997. SFAS 131 establishes standards
for reporting financial and descriptive information about an enterprise's
operating segments in its annual financial statements and selected segment
information in interim financial reports. Reclassification or restatement of
comparative financial statements or financial information for earlier periods is
required upon adoption of SFAS 131. Application of the Statements' disclosure
requirements will have no impact on the Company's consolidated financial
position, results of operations or earnings per share data as currently
reported.

         As of January 1, 1998, the Company adopted Statement 130, "Reporting
Comprehensive Income." Statement 130 establishes new rules for the reporting and
display of comprehensive income or loss and its components. The adoption of this
Statement had no impact on the Company's net loss or stockholders' equity.
Statement 130 requires unrealized gains and losses on the Company's
available-for-sale securities, deferred compensation and foreign currency
translation adjustments, if any, which prior to adoption were reported
separately in stockholders' equity, to be included in other comprehensive
income. During the six month period ended June 30, 1998 and 1997, the total
comprehensive loss amounted to $20,544,000 and $13,706,000, respectively.



                                       8

<PAGE>   8

2.       AVAILABLE-FOR-SALE SECURITIES

         The Company's debt securities including $22,022,000 classified as
short-term investments are available-for-sale and consist primarily of U.S.
Treasury Notes and other U.S. government securities of $8,556,000 and corporate
debt securities of $27,977,000 on June 30, 1998. The gross realized gains and
losses on sales of available-for-sale securities were insignificant in the six
months ended June 30, 1998.


3.       RELATED PARTY TRANSACTIONS

         During April 1998, the Company loaned $100,000 to an officer of the
Company to aid in the relocation of his residence. The first note totaling
$75,000 and bearing an interest rate of 5.50% per annum, will be forgiven as
compensation expense to the officer at a rate of 33% per year pending the
officer's continued employment by the Company. The additional note of $25,000
bears interest at 6.55% per annum and is due in full on April 15, 2001, or
immediately if the officer's employment with the Company is terminated by him or
by the Company with cause. Both notes receivable are secured by the officer's
primary residence.

4.       PREPAID MILESTONE REPAYABLE TO MEDTRONIC, INC.

         The Company's note payable and accrued interest to Medtronic, resulting
from a prepaid milestone, was originally due and payable on April 30, 1998.
Under an amendment to the agreement, the terms of this milestone were revised
such that the revised milestone payment if not earned, will be repayable on
March 31, 1999.



                                       9
<PAGE>   9

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
the majority 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 June 30, 1998, the
Company's cumulative net loss was $128,222,000. The Company's principal sources
of working capital have been public and private equity financings, convertible
notes payable, milestone and other payments from collaborative research and
development agreements, license fees, interest income, lease financings,
research grants and product sales of CORLOPAM(R).

         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.

         On April 30, 1998, the Company announced that it had signed a
definitive merger agreement with Elan Corporation, plc ("Elan") pursuant to
which a wholly-owned subsidiary of Elan will merge with and into the Company.
The Company shall survive the merger and become a wholly-owned subsidiary of
Elan. Under the terms of the agreement, each share of the Company's common stock
will be exchanged for 0.51 of an Elan American Depository Share (the "Exchange
Ratio"). Certain outstanding options and rights to purchase the Company's common
stock will be assumed by Elan and will become an option or right to purchase
Elan American Depository Shares, with appropriate adjustments to the number of
shares issuable thereunder and the exercise price thereof based on the Exchange
Ratio. The merger has been approved by the boards of directors of the Company
and Elan, but is still subject to approval by the stockholders of the Company at
a special meeting of the stockholders to be held August 11, 1998, at the
Company's headquarters in Menlo Park, California. In addition, on June 25, 1998,
the Company announced that various customary conditions to closing of the
merger, including, but not limited to, expiration of the required waiting period
under the Hart-Scott-Rodino Antitrust Improvements Act of 1976 and the required
clearance of the Merger by the Minister for Enterprise, Trade and Employment of
Ireland under the Mergers, Takeovers and Monopolies (Control) Act of 1978, as
amended, had been satisfactorily met.

         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 the
year ended December 31, 1997.



                                       10

<PAGE>   10
RESULTS OF OPERATIONS

Three Months Ended June 30, 1998 and 1997

         Revenues were $1,607,000 and $389,000 for the three months ended June
30, 1998 and 1997, respectively. Revenues in 1998 consisted primarily of
CORLOPAM(R) product sales totaling $1,177,000 in the United States. The product
sales for the 1998 period reflect the second quarter of CORLOPAM product sales
since the Food & Drug Administration's ("FDA") approval of this drug on
September 23, 1997. Revenues in 1997 consisted primarily of expense
reimbursements from a related party and included no product sales of CORLOPAM.

         Research and Development expenses increased by $1,593,000 or 27%, to
$7,458,000 for the three months ended June 30, 1998, compared to $5,865,000 in
the earlier period. The increase was due primarily to increased activities for
the Company's preparation of the New Drug Application ("NDA") for ziconotide for
the treatment of chronic pain. The Company expects research and development
expenses to increase significantly over the next several years.

         Selling, general and administrative expenses were $4,438,000 and
$1,616,000 for the three months ended June 30, 1998, and 1997, respectively,
representing an increase of 175%. This increase is attributable primarily to
increased selling and marketing activities for CORLOPAM(R) in the United States,
as well as employment of a field sales force. The Company expects selling,
general and administrative expenses to continue to increase over the next
several years.

         Net interest income decreased to $412,000 for the three months ended
June 30, 1998, compared to $1,033,000 in the earlier period. The decrease in net
interest income was due to a decrease in cash available for investments as the
result of funding the Company's operating loss.


Six Months Ended June 30, 1998 and 1997

         Revenues were $3,999,000 and $826,000 for the six months ended June 30,
1998 and 1997, respectively. Revenues in 1998 consisted primarily of CORLOPAM(R)
product sales totaling $3,277,000 in the United States. The product sales for
the 1998 period reflect the first six month period of CORLOPAM(R) product sales
since the FDA's approval of this drug on September 23, 1997. Revenues in 1997
consisted primarily of expense reimbursements from a related party and included
no product sales of CORLOPAM(R).

         Research and Development expenses increased by $2,843,000 or 21%, to
$16,284,000 for the six months ended June 30, 1998, compared to $13,441,000 in
the earlier period. The increase was due primarily to increased Phase III
clinical study expenses of ziconotide for chronic pain, the Company's
preparation of the ziconotide NDA and employment related expenses. The Company
expects research and development expenses to increase significantly over the
next several years.

         Selling, general and administrative expenses were $9,075,000 and
$3,156,000 for the six months ended June 30, 1998, and 1997, respectively,
representing an increase of 188%. This increase is attributable primarily to
increased selling and marketing development activities for the January 1998
launch of CORLOPAM(R) in the United States, as well as employment of a field
sales force. The Company expects selling, general and administrative expenses to
continue to increase over the next several years.

         Net interest income decreased to $1,160,000 for the six months ended
June 30, 1998, compared to $2,071,000 in the earlier period. The decrease in net
interest income was due to a decrease in cash available for investments as the
result of funding the Company's operating loss.



                                       11
<PAGE>   11
LIQUIDITY AND CAPITAL RESOURCES

         For the six months ended June 30, 1998, cash expenditures for operating
activities and additions to capital equipment were $22,304,000. The Company
anticipates that these expenditures will increase significantly in future
periods.

         The Company had available cash, cash equivalents and short-term
investments of $40,263,000 at June 30, 1998. 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 CORLOPAM(R) commercial product launch
activities 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
supplemented by net product revenues 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 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 and 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. The
Company believes , however, that this concern will be eliminated if the Merger
with Elan is consummated.



                                       12
<PAGE>   12

                           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) Exhibits

                        Exhibit 27   Financial Data Schedule

                  (b)  Reports on Form 8-K

                       1.   On April 30, 1998, the Company filed with the
                            Commission a Current Report on Form 8-K to report
                            the merger transaction with Elan Corporation, plc. A
                            copy of the Merger Agreement was filed as an exhibit
                            to the Form 8-K.

                       2.   On July 22, 1998, the Company filed with the
                            Commission a Current Report on Form 8-K to report
                            that a purported class action lawsuit had been filed
                            against the Company, its Board of Directors and
                            certain of its officers alleging, among other things
                            that the consideration the Company's shareholders
                            will receive upon consummation of the merger
                            transaction between the Company and Elan
                            Corporation, plc is inadequate.



                                       13
<PAGE>   13

                               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:    August 7, 1998                      Neurex Corporation
         ----------------------------




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



                                       14

<PAGE>   14

                               INDEX TO EXHIBITS


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

     27.1                     Restated Financial Data Schedule - June 30, 1997

     27.2                     Restated Financial Data Schedule - June 30, 1996
</TABLE>