#

Management contract or compensation plan or arrangement.

+

Confidential portions of this exhibit have been omitted and filed separately with the Commission pursuant to confidential treatment granted under Rule 24b-2 promulgated under the Exchange Act

Exhibit 5.1

John T. McKenna

+1 650 843 5059

jmckenna@cooley.com

April 10, 2019

Vaxart, Inc.

290 Utah Ave

Suite 200

South San Francisco, CA 94080

Ladies and Gentlemen:

We have acted as counsel to Vaxart, Inc., a Delaware corporation, (the “Company”), in connection with the filing of a registration statement (No. 333-229536) on Form S-1 (the “Registration Statement”) with the Securities and Exchange Commission, including a related prospectus filed with the Registration Statement (the “Prospectus”), covering an underwritten public offering of:

(i)                               up to 2,289,091 shares (the “Shares”) of common stock of the Company, par value $0.10 per share (the “Common Stock”);

(ii)                            pre-funded warrants to purchase up to an aggregate of 8,165,455 shares of Common Stock (the “Pre-Funded Warrants”) and the shares of Common Stock issuable upon exercise thereunder; and

(iii)                         warrants to purchase up to 10,454,546 shares of Common Stock (the “Common Warrants”) and the shares of Common Stock issuable upon exercise thereunder;

including additional Shares and Common Warrants that may be sold pursuant to the exercise of an option to purchase additional Shares and/or Common Warrants. The Registration Statement also covers the issuance of warrants to purchase up to 731,818 shares of Common Stock being issued to the underwriters of the offering (the “Representative Warrants”) and the shares of Common Stock issuable upon exercise thereunder. The Pre-Funded Warrants, the Common Warrants, and the Representative Warrants are collectively referred to herein as the “Warrants” and the shares of Common Stock issuable upon exercise of the Warrants are referred to as the “Warrants Shares.”  The Shares, the Warrants and the Warrant Shares are to be issued by the Company as described in the Registration Statement and the Prospectus.

In connection with this opinion, we have examined and relied upon the Registration Statement and Prospectus, the form of Pre-Funded Warrant, the form of Common Warrant, the form of Representative Warrant, the Company’s Certificate of Incorporation, as amended, its Restated Bylaws and the originals or copies certified to our satisfaction of such records, documents, certificates, memoranda and other instruments as in our judgment are necessary or appropriate to enable us to render the opinion expressed below. We have assumed the genuineness and authenticity of all documents submitted to us as originals, and the conformity to originals of all documents submitted to us as copies thereof and the due execution and delivery of all documents by all persons other than the Company where due execution and delivery are a prerequisite to the effectiveness thereof.  In addition, we have assumed that the Board of Directors of the Company or a pricing committee thereof has taken action to set the sale price of the Shares and Warrants and the exercise price of the Warrants.

With regard to our opinion regarding the Warrants and the Warrant Shares, we express no opinion to the extent that, notwithstanding its current reservation of shares of Common Stock, future issuances of securities, including the Warrant Shares, of the Company and/or antidilution adjustments to outstanding

Cooley LLP   3175 Hanover Street   Palo Alto, CA   94304
t: (650) 843-5000  f: (650) 849-7400  cooley.com

Vaxart, Inc.

April 10, 2019

Page Two

securities, including the Warrants, of the Company cause the Warrants to be exercisable for more shares of Common Stock than the number that then remain authorized but unissued.

With regard to our opinion concerning the Warrants constituting valid and binding obligations of the Company:

(i)            Our opinion is subject to, and may be limited by, (a) applicable bankruptcy, reorganization, insolvency, moratorium, fraudulent conveyance, debtor and creditor, and similar laws which relate to or affect creditors’ rights generally, and (b) general principles of equity (including, without limitation, concepts of materiality, reasonableness, good faith and fair dealing) regardless of whether considered in a proceeding in equity or at law.

(ii)           Our opinion is subject to the qualification that the availability of specific performance, an injunction or other equitable remedies is subject to the discretion of the court before which the request is brought.

(iii)          We express no opinion as to any provision of the Warrants that: (a) provides for liquidated damages, buy-in damages, monetary penalties, prepayment or make-whole payments or other economic remedies to the extent such provisions may constitute unlawful penalties, (b) relates to advance waivers of claims, defenses, rights granted by law, or notice, opportunity for hearing, evidentiary requirements, statutes of limitations, trial by jury, or procedural rights, (c) restricts non-written modifications and waivers, (d) provides for the payment of legal and other professional fees where such payment is contrary to law or public policy, (e) relates to exclusivity, election or accumulation of rights or remedies, (f) authorizes or validates conclusive or discretionary determinations, or (g) provides that provisions of the Warrants are severable to the extent an essential part of the agreed exchange is determined to be invalid and unenforceable.

(iv)          We express no opinion as to whether a state court outside of the State of New York or a federal court of the United States would give effect to the choice of New York law or jurisdiction provided for in the Warrants.

Our opinion herein is expressed solely with respect to the General Corporation Law of the State of Delaware and, as to the Warrants constituting valid and legally binding obligations of the Company, the laws of the State of New York. Our opinion is based on these laws as in effect on the date hereof.  We express no opinion to the extent that any other laws are applicable to the subject matter hereof and express no opinion and provide no assurance as to compliance with any federal or state securities law, rule or regulation.

On the basis of the foregoing, and in reliance thereon, we are of the opinion that (i) the Shares, when sold in accordance with the Registration Statement and the Prospectus, will be validly issued, fully paid and nonassessable, (ii) provided that the Warrants have been duly executed and delivered by the Company to the purchasers thereof against payment therefor, the Warrants, when issued and sold as provided in the Registration Statement and the Prospectus will be valid and legally binding obligations of the Company, and (iii) the Warrant Shares, when issued and paid for in accordance with the terms of the Warrants, will be validly issued, fully paid and non-assessable.

Vaxart, Inc.

April 10, 2019

Page Three

We consent to the reference to our firm under the caption “Legal Matters” in the Prospectus included in the Registration Statement and to the filing of this opinion as an exhibit to the Registration Statement. This opinion is expressed as of the date hereof, and we disclaim any undertaking to advise you of any subsequent changes in the facts stated or assumed herein or of any subsequent changes in applicable law.

Sincerely,