Algernon Pharmaceuticals Inc.: Exhibit 5.1

Our File No.	1008406-282191
Date	April 22, 2022

Algernon Pharmaceuticals Inc.
Suite 1500 - 1055 West Georgia Street
Vancouver, British Columbia
Canada V6E 4N7

Dear Sirs:

Re: Algernon Pharmaceuticals Inc. - Registration Statement on Form F-1

We have acted as legal counsel to Algernon Pharmaceuticals Inc., a British Columbia corporation (the "Company"), in connection with the Company's Registration Statement on Form F-1 (File No. 333-262878) filed on February 22, 2022 (as amended and supplemented from time to time, the "Registration Statement") with the Securities and Exchange Commission (the "Commission") including a related prospectus filed with the Registration Statement (the "Prospectus"), covering:

(a) the offering (the "Offering") for sale to Ladenburg Thalmann & Co. Inc. and other underwriters (together the "Underwriters") of (i) up to an aggregate of 1,684,201 units (each, a "Unit") at the offering price of US$4.75 per Unit (the "Unit Offering Price"), and (ii) up to an aggregate of 1,684,210 pre-funded units (the "Pre-Funded Units") at the offering price of US$4.7499 per Pre-Funded Unit (together with the "Unit Offering Price", the "Offering Price"); and

(b) the public offering of such securities by the Underwriters.

Each Unit consists of (a) one common share without par value in the capital of the Company (each a "Unit Share") and (b) one common share purchase warrant (each, a "Warrant"). The Units will not be issued or certificated, and, although the Unit Shares and Warrants comprising the Units will be purchased together in the Offering, the Unit Shares and Warrants will be issued separately. Each Warrant entitles the holder to purchase one common share without par value in the capital of the Company (each a "Warrant Share") at an exercise price of US$5.225 for a period of five years following its date of issue. The issuance, registration, transfer, exchange, exercise and replacement of the Warrants is governed by the warrant agent agreement to be entered into between the Company and American Stock Transfer & Trust Company, LLC.

Each Pre-Funded Unit consists of one pre-funded warrant (each, a "Pre-Funded Warrant") to purchase one common share without par value in the capital of the Company (each, a "Pre-Funded Warrant Share") and one Warrant. The Pre-Funded Units will not be issued or certificated, and, although the Pre-Funded Warrants and Warrants comprising the Pre-Funded Units will be purchased together in the Offering, the Pre-Funded Warrants and Warrants will be issued separately. Each Pre-Funded Warrant entitles the holder to purchase a Pre-Funded Warrant Share at an exercise price of US$0.0001.

April 22, 2022
Page 2

The Company has granted to the Underwriters a 45-day option to purchase up to an additional 252,631 common shares without par value in the capital of the Company (together with the Unit Shares, the "Shares") and/or up to an additional 252,631 Warrants at the applicable Offering Price per Share and per Warrant, respectively, less the underwriting discount and commissions, solely to cover over-allotments.

Pursuant to the underwriting agreement to be entered into among the Company and the Underwriters, the Company agrees to issue to the Underwriters, as partial compensation for their services, 84,210 common share purchase warrants (each, an "Underwriter Warrant") (being the amount equal to 5.0% of the Shares and/or Pre-Funded Warrants sold in the Offering). Each Underwriter Warrant will entitle the holder to purchase one common share in the capital of the Company (each, an "Underwriter Warrant Share") at a price of US$5.225 per Underwriter Warrant Share for a period of five years following the commencement of sales of the Offering.

In connection with this opinion, we have reviewed and relied upon the Registration Statement and Prospectus, the Company's Notice of Articles, the Company's Articles, records of the Company's corporate proceedings in connection with the Offering, and such other documents, records, certificates, memoranda and other instruments as we deem necessary as a basis for this opinion. With respect to the foregoing documents, we have assumed: (i) the authenticity of all records, documents, and instruments submitted to us as originals; (ii) the genuineness of all signatures on all agreements, instruments and other documents submitted to us; (iii) the legal capacity and authority of all persons or entities (other than the Company) executing all agreements, instruments or other documents submitted to us; (iv) the authenticity and the conformity to the originals of all records, documents, and instruments submitted to us as certified, photostatic or other copies; (v) that the documents, in the forms submitted to us for our review, have not been and will not e altered or amended in any respect; (vi) that the statements contained in the certificates and comparable documents of public officials, officers and representatives of the Company and other persons on which we have relied for purposes of this opinion are true and correct; and (vii) the due authorization, execution and delivery of all agreements, instruments and other documents by all parties thereto (other than the due authorization, execution and delivery of each such agreement, instrument and document by the Company). We have also obtained from officers of the Company certificates as to certain factual matters and, insofar as this opinion is based on matters of fact, we have relied on such certificates without independent investigation.

We have further assumed that Units, Pre-Funded Units, Warrants, Pre-Funded Warrants, Underwriter Warrants, Warrant Shares, Pre-Funded Warrant Shares and Underwriter Warrant Shares will be offered, issued and sold in compliance with applicable United States federal and state securities laws and in the manner stated in the Registration Statement and the Prospectus.

Our opinion is limited to law of the Province of British Columbia, including all applicable provisions of the British Columbia Business Corporations Act. We have not considered, and have not expressed any opinion with regard to, or as to the effect of, any other law, rule, or regulation, state or federal, applicable to the Company. In particular, we express no opinion as to United States federal securities laws.

April 22, 2022
Page 3

Various issues concerning the laws of the State of New York, including with respect to the validity and enforceability of the Warrants, the Pre-Funded Warrants and the Underwriter Warrants, are addressed in the opinion of Kelley Drye & Warren LLP, separately provided to you. We express no opinion with respect to those matters herein, and to the extent elements of those opinions are necessary to the conclusions expressed herein, we have, with your consent, assumed such matters.

Based upon the foregoing and in reliance thereon, and subject to the qualifications and limitations set forth herein, we are of the opinion that:

1. the Units and Pre-Funded Units have been duly authorized by all necessary corporate action by the Company;

2. the Shares have been duly authorized and, when the Shares are issued and sold in the manner contemplated by the Underwriting Agreement and the Registration Statement, will be validly issued, fully paid and non-assessable;

3. the Warrant Shares have been duly authorized and, when issued and paid for upon exercise of the Warrants in accordance with their terms, will be validly issued, fully paid and non-assessable;

4. the Pre-Funded Warrant Shares have been duly authorized and, when issued and paid for upon exercise of the Pre-Funded Warrants in accordance with their terms, will be validly issued, fully paid and non-assessable; and

5. The Underwriter Warrant Shares have been duly authorized and, when issued and paid for upon exercise of the Underwriter Warrants in accordance with their terms, will be validly issued, fully paid and non-assessable.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to the use of our firm's name in the section of the Registration Statement and the Prospectus included therein entitled "Legal Matters". In giving this consent, we do not admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act of 1933, as amended, or the rules and regulations of the Commission.

April 22, 2022
Page 4

This opinion is furnished in accordance with the requirements of Item 8.a. of Form F-1 and Item 601(b)(5)(i) of Regulation S-K in connection with the filing of the Registration Statement and the related Prospectus, and is not to be used, circulated, quoted or otherwise relied upon for any other purpose. This opinion is limited to the specific issues addressed herein, and no opinion may be inferred or implied beyond that expressly stated herein. We disclaim any obligation to advise you of facts, circumstances, events or developments that hereafter may be brought to our attention and that may alter, affect or modify the opinion expressed herein after the effective date of the Registration Statement.

Yours truly,

/s/ McMillan LLP