Exhibit 5.1

Mayer Brown LLP

1221 Avenue of the Americas
New York, NY 10020-1001
United States of America

T: +1 212 506 2500

F: +1 212 262 1910

www.mayerbrown.com

November 19, 2018

Great Ajax Corp.

9400 SW Beaverton-Hillsdale Hwy, Suite 131

Beaverton, Oregon 97005

Ladies and Gentlemen:

We have acted as counsel to Great Ajax Corp., a Maryland corporation (the “Company”), in connection with the issuance and sale by the Company of $15,850,000 aggregate principal amount of its 7.25% convertible senior notes due 2024 (the “Notes”), under that certain indenture, dated April 19, 2017 (the “Base Indenture”), between the Company and Wilmington Savings Fund Society, FSB, as trustee (the “Trustee”), as supplemented by the first supplemental indenture, dated April 25, 2017 between the Company and the Trustee (the “Supplemental Indenture,” and, together with the Base Indenture, the “Indenture”), and pursuant to a Registration Statement on Form S-3 (Registration Statement No. 333-219923) (the “Registration Statement”), filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), the prospectus, dated August 22, 2017 (the “Base Prospectus”), and the prospectus supplement, dated November 15, 2018, filed with the Commission pursuant to Rule 424(b) of the Rules and Regulations promulgated under the Act (the “Prospectus Supplement”), and the Underwriting Agreement, dated as of November 15, 2018 (the “Underwriting Agreement”), among the Company, Great Ajax Operating Partnership L.P, Thetis Asset Management LLC and Raymond James & Associates, Inc. and JMP Securities LLC, as representatives of the underwriters named therein. The Base Prospectus and the Prospectus Supplement are collectively referred to as the “Prospectus.” The Notes are convertible, in accordance with their terms and the terms of the Indenture, into cash, shares of common stock, $0.01 par value per share, of the Company (“Common Stock”), or a combination of cash and shares of Common Stock, at the Company’s option.

In connection with this opinion, we have examined originals or copies, certified or otherwise identified to our satisfaction, of: (i) the charter of the Company; (ii) the Amended and Restated Bylaws of the Company, as amended through the date hereof; (iii) resolutions of the board of directors of the Company relating to the issuance and sale of the Notes and the authorization and reservation of the shares of Common Stock underlying the Notes; (iv) resolutions of the pricing committee of the board of directors of the Company relating to the authorization of issuance and sale of the Notes (v) the Registration Statement; and (vi) the Prospectus. In addition, we have examined originals or copies, certified or otherwise identified to our satisfaction, of certain other corporate records, documents, instruments and certificates of public officials and of the Company, and we have made such inquiries of officers of the Company and public officials and considered such questions of law as we have deemed necessary for purposes of rendering the opinions set forth herein.

Mayer Brown is a global services provider comprising an association of legal practices that are separate entities including
Mayer Brown LLP (Illinois, USA), Mayer Brown International LLP (England), Mayer Brown (a Hong Kong partnership)
and Tauil & Chequer Advogados (a Brazilian partnership).

Great Ajax Corp.

November 19, 2018

Page 2

In connection with this opinion, we have assumed the genuineness of all signatures and the authenticity of all items submitted to us as originals and the conformity with originals of all items submitted to us as copies. In making our examination of documents executed by parties other than the Company, we have assumed that each other party has the power and authority to execute and deliver, and to perform and observe the provisions of, such documents and has duly authorized, executed and delivered such documents, and that such documents constitute the legal, valid and binding obligations of each such party. We also have assumed the integrity and completeness of the minute books of the Company presented to us for examination. With respect to certain factual matters, we have relied upon certificates of officers of the Company.

Based upon, subject to and limited by the foregoing, we are of the opinion that, as of the date hereof:

(i)        The Notes have been duly authorized by all necessary corporate action of the Company and duly executed and delivered on behalf of the Company against payment therefor in accordance with the terms of the Indenture and the Underwriting Agreement and, upon due authentication by the Trustee in accordance with the terms of the Indenture, will constitute legally valid and binding obligations of the Company.

(ii)       The shares of Common Stock issuable upon conversion of the Notes have been duly and validly authorized by all necessary corporate action of the Company and reserved for issuance upon conversion of the Notes and, upon issuance upon conversion of the Notes in accordance with the terms of the Notes and the Indenture, will be validly issued, fully paid and nonassessable.

We do not express any opinion herein concerning any law other than the Maryland General Corporation Law, the New York Business Corporation Law and the federal laws of the United States of America, as in effect on the date hereof.

We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the Company’s Current Report on Form 8-K to be filed with the Commission on November 19, 2018, which will be incorporated by reference in the Registration Statement, and to the reference to us under the caption “Legal Matters” in the Prospectus, which is a part of the Registration Statement. In giving such consent, we do not hereby admit that we are acting within the category of persons whose consent is required under Section 7 of the Act or the rules or regulations of the Commission thereunder.