EXHIBIT 5.1

June 29, 2020

Acorda Therapeutics, Inc.

420 Saw Mill River Road

Ardsley, New York 10502

Ladies and Gentlemen:

We have acted as counsel to Acorda Therapeutics, Inc., a Delaware corporation (the “Company”), in connection with the registration by the Company under the Securities Act of 1933 (the “Securities Act”), pursuant to a Registration Statement on Form S-3 filed with the Securities and Exchange Commission on or about the date hereof (such registration statement is herein referred to as the “Registration Statement”), of the resale of up to 8,698,049 shares (the “Resale Shares”) of the Company’s common stock, $0.001 par value per share (the “Common Stock”), issuable upon conversion of, or in payment of interest with respect to, the Company’s 6.00% Convertible Senior Secured Notes due 2024, issued pursuant to the Indenture, dated as of December 23, 2019, among the Company, the guarantors party thereto, and Wilmington Trust, National Association, as trustee and collateral agent (the “Indenture”).

We have reviewed such corporate records, certificates and other documents, and such questions of law, as we have considered necessary or appropriate for the purposes of this opinion. We have assumed that all signatures are genuine, that all documents submitted to us as originals are authentic and that all copies of documents submitted to us conform to the originals.

We have further assumed that the Resale Shares, if issued in certificated form, will conform to the specimen incorporated by reference as an exhibit to the Registration Statement and will be duly countersigned by the transfer agent of the Company’s Common Stock and duly registered by the registrar of the Company’s Common Stock.

We have relied as to certain matters on information obtained from public officials, officers of the Company, and other sources believed by us to be responsible.

Based upon the foregoing, we are of the opinion that the Resale Shares have been duly authorized and reserved for issuance and, when the Registration Statement and any required post-effective amendments thereto have all been declared effective under the Securities Act, the Resale Shares, when issued upon conversion or as payment of interest in accordance with the terms of the Indenture, will be validly issued, fully paid and nonassessable.

We are members of the bar of the State of New York and the District of Columbia. We do not express any opinion herein on any laws other than the Delaware General Corporation Law.

Acorda Therapeutics, Inc.

June 29, 2020

Page 2

We hereby consent to the filing of this opinion as Exhibit 5.1 to the Registration Statement. We also hereby consent to the reference to our firm under the heading “Legal Matters” in the prospectus constituting part of the Registration Statement. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act.

Very truly yours,

/s/ Covington & Burling LLP