Exhibit 4.2

THESE SECURITIES HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “ACT”).  THEY MAY NOT BE SOLD, OFFERED FOR SALE, PLEDGED, OR HYPOTHECATED IN THE ABSENCE OF AN EFFECTIVE REGISTRATION STATEMENT AS TO THE SECURITIES UNDER THE ACT OR AN OPINION OF COUNSEL, REASONABLY SATISFACTORY TO THE COMPANY, THAT SUCH REGISTRATION IS NOT REQUIRED.

THESE SECURITIES ARE SUBJECT TO CERTAIN RESTRICTIONS ON TRANSFER AND RIGHTS OF FIRST REFUSAL AS SET FORTH IN AN AGREEMENT BETWEEN THE COMPANY AND THE WARRANTHOLDER, A COPY OF WHICH IS ON FILE WITH THE SECRETARY OF THE COMPANY.

SECOND CLOSING WARRANT

To Purchase Shares of the Series B Preferred Stock of

ACORDA THERAPEUTICS, INC.

1.             GRANT OF THE RIGHT TO PURCHASE SERIES B PREFERRED STOCK.

For value received, Acorda Therapeutics, Inc., a Delaware corporation (the “Company”) hereby grants to Elan International Services, Ltd., a Bermuda corporation (the “Warrantholder”), and the Warrantholder is entitled, upon the terms and subject to the conditions hereinafter set forth, to subscribe for and purchase from the Company up to 100,000 fully paid and nonassessable shares of the Company’s Series B Preferred Stock (the “Series B Preferred”). The exercise price will be equal to U.S. $2.00 per share of Series B Preferred (the “Exercise Price”).  The number and Exercise Price of such shares are subject to adjustment as provided in Section 8 hereof.

For purposes of this Warrant, “Series B Preferred” shall be deemed to include the Common Stock of the Company upon the automatic conversion of all of the outstanding Preferred Stock of the Company in accordance with the provisions of the Company’s Certificate of Incorporation.

2.             TERM OF THE WARRANT.

Except as otherwise provided herein, the term of this Warrant and the right to purchase the Series B Preferred as granted herein will commence on the Second Closing Date, as such term is defined in that certain Preferred Stock, Convertible Note and Warrant Purchase Agreement dated as of January 22, 1997 between the Company and the Warrantholder (the “Purchase Agreement”), and will expire at 11:59 p.m. on the fifth anniversary of the Second Closing Date.

3.             EXERCISE OF PURCHASE RIGHTS.

The purchase rights set forth in this Warrant are exercisable by the Warrantholder, in whole or in part, at any time, or from time to time, prior to the expiration of the term set forth in Section 2 above, by tendering to the Company at its principal office a notice of exercise (the “Notice of Exercise”), duly completed and executed.  Upon receipt of the Notice of Exercise and the payment of the purchase price in accordance with the terms set forth below, the Company will issue to the Warrantholder a certificate for the number of shares of the Series B Preferred purchased and will execute the Notice of Exercise indicating the number of shares that remain subject to future purchases, if any.

The Warrantholder may exercise all or any portion of the outstanding warrants by paying to the Company, by cash or check, an amount equal to the aggregate Exercise Price of the shares being purchased.

4.             RESERVATION OF SHARES.

During the term of this Warrant, the Company will at all times have authorized and reserved a sufficient number of shares of its Series B Preferred to provide for the exercise of the rights to purchase Series B Preferred as provided for herein and will have authorized and reserved a sufficient number of shares of the Company’s Common Stock for issuance upon conversion of the Series B Preferred issuable upon exercise of this Warrant.

5.             NO FRACTIONAL SHARES OR SCRIP.

No fractional share or scrip representing fractional shares will be issued upon the exercise of the Warrantholder’s right to purchase the Series B Preferred, but in lieu of such fractional shares, the Company will make a cash payment therefor upon the basis of the Exercise Price then in effect.

6.             NO RIGHTS AS STOCKHOLDER.

This Warrant does not entitle the Warrantholder to any voting right, dividend right or other rights as a stockholder of the Company prior to the exercise of the Warrantholder’s rights to purchase Series B Preferred as provided for herein.

7.             WARRANTHOLDER REGISTRY.

The Company will maintain a registry showing the name and address of the registered holder of this Warrant.  This Warrant may be surrendered for exchange, transfer or exercise, in accordance with its terms, at the principal offices of the Company, and the Company shall be entitled to rely in all respects, prior to written notice to the contrary, upon such registry.

8.             ADJUSTMENT RIGHTS.

The Exercise Price and the number of shares of Series B Preferred purchasable hereunder shall be subject to adjustment from time to time in accordance with the following provisions:

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(a)           In case the Company shall at any time subdivide the outstanding shares of its Series B Preferred, the Exercise Price in effect immediately prior to such subdivision shall be proportionately decreased, and in case the Company shall at any time combine the outstanding shares of its Series B Preferred, the Exercise Price in effect immediately prior to such combination shall be proportionately increased, effective at the close of business on the date of such subdivision or combination, as the case may be.  Upon each adjustment pursuant to this Section 8(a), the Warrantholder shall thereafter (until another such adjustment) be entitled to purchase shares of the Series B Preferred at the adjusted Exercise Price.

(b)           If at any time after the date of grant of this Warrant the Company shall take any action that results in an adjustment to the conversion ratio of the Series B Preferred under the Company’s Amended and Restated Certificate of Incorporation, upon exercise of this Warrant the shares of Series B Preferred issued hereunder shall be entitled to the full benefit of such conversion ratio adjustment as if such shares had been issued and outstanding as of the date of such adjustment.

(c)           If at any time while this Warrant is outstanding there shall be any reorganization or reclassification of the capital stock of the Company (other than a subdivision or combination of shares provided for in Section 8(a) above), or any consolidation or merger of the Company with another corporation, the Warrantholder shall thereafter be entitled to receive, during the term hereof and upon payment of the Exercise Price, the number of shares of stock or other securities or property of the Company or of the successor corporation resulting from such consolidation or merger, as the case may be, to which a holder of the Series B Preferred, deliverable upon the exercise of this Warrant, would have been entitled upon such reorganization, reclassification, consolidation or merger if this Warrant had been exercised, immediately prior to such reorganization, reclassification, consolidation or merger; and in any such case, appropriate adjustment (as reasonably determined in good faith by the Board of Directors of the Company) shall be made in the application of the provisions herein set forth with respect to the rights and interest thereafter of the Warrantholder to the end that the provisions set forth herein (including the adjustment of the Exercise Price and the number of shares issuable upon the exercise of this Warrant) shall thereafter be applicable as near as reasonably may be, in relation to any shares or other property thereafter deliverable upon the exercise hereof.

9.             NOTICE OF ADJUSTMENTS.

Upon any adjustment of the Exercise Price and any increase or decrease in the number of shares of Series B Preferred purchasable upon the exercise of this Warrant, then, and in each such case, the Company, within fifteen (15) days thereafter, shall give written notice thereof to the Warrantholder at the address of the Warrantholder as shown on the books of the Company which notice shall state the Exercise Price as adjusted and the increased or decreased number of shares purchasable upon the exercise of this Warrant, setting forth in reasonable detail the method of calculation of each.

10.           TRANSFERS.

This Warrant may not be transferred or assigned by the Warrantholder without the prior written consent of the Company; provided, however, that no consent of the Company shall

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be required for any transfer or assignment of this Warrant to an affiliate (within the meaning of the Securities Act of 1933, as amended) of the Holder.  Any transfer of this Warrant must comply with the requirements of this Section 10, and any assignee or transferee of this Warrant (“permitted assignee”) shall be required to accept this Warrant subject to all rights and obligations of the Warrantholder as set forth herein.  Any securities to be issued upon exercise of this Warrant may not be sold, assigned, transferred, or otherwise disposed of unless the securities are registered under the Act or unless the person seeking to effect such disposition shall have requested and the Company shall have received an opinion of the Company’s counsel that the proposed disposition may be effected without registration of such securities under the Act or any applicable state securities laws;  provided, however, that any transfers to affiliates of the Warrantholder shall not require such an opinion of the Company’s counsel.  Unless a registration statement with respect to such shares of Series B Preferred is effective at the time, any shares of Series B Preferred issued upon the exercise of this Warrant shall bear the following legend:

“THESE SECURITIES HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “ACT”).  THEY MAY NOT BE SOLD, OFFERED FOR SALE, PLEDGED OR HYPOTHECATED IN THE ABSENCE OF AN EFFECTIVE REGISTRATION STATEMENT IN EFFECT WITH RESPECT TO THE SECURITIES UNDER THE ACT OR AN OPINION OF COUNSEL, REASONABLY SATISFACTORY TO THE COMPANY, THAT SUCH REGISTRATION IS NOT REQUIRED.”

11.           MARKET STANDOFF AGREEMENT.

The Warrantholder agrees in connection with a public offering of the Company’s securities, upon request of the Company or the underwriters managing any underwritten offering of the Company’s securities, not to sell, make any short sale of, loan, grant any option for the purchase of, or otherwise dispose of this Warrant, of the shares of Series B Preferred issuable upon exercise hereof, or the shares of Common Stock issuable upon conversion thereof, other than to affiliates of the Warrantholder who shall agree to be similarly bound, without the prior written consent of the Company or such underwriters, as the case may be, for such period of time (not to exceed, in the case of the Company’s initial public offering, one hundred eighty (180) days) from the effective date of such registration as may be requested by the underwriters; provided, however, that the officers and directors of the Company who own stock of the Company and a majority-in-interest of the Company’s Series A Preferred Stock shall also agree to such restrictions.

12.           MISCELLANEOUS.

(a)           Effective Date.  The provisions of this Warrant will be construed and will be given effect in all respects as if it had been executed and delivered by the Company on the date hereof.  This Warrant will be binding upon any successors or assigns of the Company.

(b)           Loss, Theft, Destruction or Mutilation of Warrant.  Upon receipt by the Company of evidence reasonably satisfactory to it of the loss, theft, destruction or mutilation of this Warrant, and in case of loss, theft or destruction, of indemnity or security reasonably satisfactory to it, and upon reimbursement to the Company of all reasonable expenses incidental

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thereto, and upon surrender and cancellation of this Warrant, if mutilated, the Company will make and deliver a new Warrant of like tenor and dated as of such cancellation, in lieu of this Warrant.

(c)           Saturdays, Sundays, Holidays etc.  If the last or appointed day for the taking of any action or the expiration of any right required or granted herein shall be a Saturday or a Sunday or shall be a legal holiday, then such action may be taken or such right may be exercised on the next succeeding day not a Saturday or a Sunday or a legal holiday.

(d)           Attorneys’ Fees.  In any litigation, arbitration, or court proceeding between the Company and the Warrantholder relating hereto, the prevailing party will be entitled to attorneys’ fees and expenses and all costs of proceedings incurred in enforcing this Warrant.

(e)           Governing Law.  This Warrant will be governed by and construed for all purposes under and in accordance with the laws of the State of Delaware as applied to agreements between Delaware residents entered and to be performed entirely within Delaware.

(f)            Counterparts.  This Warrant may be executed in two or more counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument.

(g)           Titles and Subtitles.  The titles of the paragraphs and subparagraphs of this Warrant are for convenience and are not to be considered in construing this Warrant.

(h)           Notices.  Any notice required or permitted hereunder shall be given in writing and shall be deemed effectively given upon personal delivery or upon deposit in the United States mail, by registered or certified mail, addressed (i) to the Warrantholder at the address set forth on the signature page hereof, (ii) to the Company at its principal executive offices, addressed to the attention of the President, or (iii) at such other address as any such party may subsequently designate by written notice to the other party.

(i)            Surviva1.  The representations, warranties, covenants and conditions of the respective parties contained herein or made pursuant to this Warrant shall survive the execution and delivery of this Warrant.

(j)            Amendments.  Any provision of this Warrant may be amended and the observance of any term of this Warrant may be waived only by a written instrument signed by the Company and by the Warrantholder.

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IN WITNESS WHEREOF, the parties hereto have caused this Warrant to be executed by its officers thereunto duly authorized.