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Exhibit 5.1



November 20, 2025
 
BioCryst Pharmaceuticals, Inc.
4505 Emperor Blvd., Suite 200
Durham, North Carolina 27703
 
Ladies and Gentlemen:
 
We have acted as counsel to BioCryst Pharmaceuticals, Inc., a Delaware corporation (the “Company”), and are rendering this opinion in connection with the registration by the Company under the Securities Act of 1933 (the “Securities Act”) of the offer and sale of an aggregate of 45,000,000 shares of the Company’s common stock, par value $0.01 per share (the “Shares”), pursuant to the Registration Statement on Form S-4 filed with the United States Securities and Exchange Commission on the date hereof (as it may be amended from time to time, the “Registration Statement”).  The Shares are to be issued pursuant to an Agreement and Plan of Merger, dated as of October 14, 2025 (the “Merger Agreement”), by and among the Company, Axel Merger Sub, Inc., a Delaware corporation (“Merger Sub”), and Astria Therapeutics, Inc., a Delaware corporation (“Astria”), pursuant to which, among other things, Merger Sub will merge with and into Astria, with Astria surviving and becoming a wholly owned subsidiary of the Company.
 
We have reviewed the Registration Statement, the Merger Agreement, the Third Restated Certificate of Incorporation of the Company, as amended, the Amended and Restated By-Laws of the Company, and such other corporate records, certificates and other documents, and such questions of law, as we have deemed 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 such documents submitted to us conform to the originals. We have assumed that the Shares will be duly registered on the books of the transfer agent and registrar of the common stock and that the Company will comply with applicable notice requirements regarding uncertificated shares provided under the Delaware General Corporation Law (the “DGCL”). We have assumed further that, except as to legal conclusions expressly set forth in this opinion, the information and representations and warranties contained in the agreements, instruments, records, certificates and other documents we reviewed were true, accurate and complete as of their stated date and are true, accurate and complete as of the date of this letter.
 
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.
 
We have assumed that, prior to the issuance of any of the Shares, (a) the Registration Statement will have become effective under the Securities Act, (b) to the extent required under the DGCL, the stockholders of Astria will have approved the adoption of the Merger Agreement, and (c) the transactions contemplated by the Merger Agreement will have been consummated in accordance with the Merger Agreement following the satisfaction or waiver of the conditions set forth therein and in conformity with applicable requirements under the DGCL.
 
Based upon the foregoing, we are of the opinion that the Shares have been duly authorized and, when the Registration Statement has become effective under the Securities Act, the Shares, when duly issued as contemplated in the Merger Agreement, will be validly issued, fully paid and non-assessable.
 
We are members of the bar of the State of New York.  We do not express any opinion herein on any laws other than the DGCL.

BioCryst Pharmaceuticals, Inc.
November 20, 2025
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 proxy statement/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