Exhibit 5.1

Confidential

To:
Addex Therapeutics Ltd
c/o Addex Pharma SA
Chemin des Aulx 12
1228 Plan-les-Ouates
Switzerland

Homburger AG

Prime Tower

Hardstrasse 201

CH-8005 Zürich

homburger.ch
T +41 43 222 10 00

April 7, 2021

Addex Therapeutics Ltd | Registration Statement on Form F-3 — Exhibit 5.1

Ladies and Gentlemen

We have acted as special Swiss counsel to Addex Therapeutics Ltd, a stock corporation incorporated under the laws of Switzerland (the Company), in connection with the filing of a registration statement on Form F-3 (the Registration Statement) with the United States Securities and Exchange Commission (the SEC) on the date hereof, for the purpose of registering under the United States Securities Act of 1933, as amended (the Securities Act), (i) the offer and sale by the Company of registered shares with a nominal value of CHF 1.00 each, of the Company, to be issued out of the authorized share capital of the Company (the Capital Increase Shares) for a proposed maximum aggregate offering price of USD 150 million and (ii) the offer and sale by a selling shareholder of up to 7,704,600 registered shares with a nominal value of CHF 1.00 each, conisting of 5,648,690 registered shares with a nominal value of CHF 1.00 each (the Secondary Shares) and 2,055,910 registered shares with a nominal value of CHF 1.00 each, issuable upon exercise of outstanding warrants directly held by the selling shareholder (the Warrant Shares).

Capitalized terms used but not defined herein shall have the meaning ascribed to them in the Documents.

A. Basis of Opinion

This opinion is confined to and given on the basis of the laws of Switzerland in force at the date hereof. Such laws and the interpretation thereof are subject to change. In the absence of explicit statutory law, we base our opinion solely on our independent professional judgment. This opinion is also confined to the matters stated herein and the Documents (as defined below), and is not to

be read as extending, by implication or otherwise, to any agreement or document referred to in any of the Documents (including, in the case of the Registration Statement (as defined below), any document incorporated by reference therein or exhibited thereto) or any other matter.

For purposes of this opinion, we have only reviewed originals or copies of the following documents (collectively the Documents):

(i) an electronic copy of the Registration Statement;

(ii) an electronic copy of the amended and restated warrant agreement dated March 22, 2018 (the Warrant Agreement);

(iii) an electronic copy of the resolutions of the extraordinary shareholders’ meeting of the Company dated March 16, 2018 (the 2018 Capital Increase Shareholders Resolutions), regarding, inter alia, an ordinary increase of the capital by CHF 13,037,577 through the issuance of 13,037,577 registered shares with a nominal value of CHF 1.00 each (the 2018 Capital Increase);

(iv) an electronic copy of the resolutions of the board of directors of the Company dated March 28, 2018 (the 2018 Capital Increase Board Resolutions), regarding, inter alia, (a) the completion of the capital increase of the Company’s share capital by CHF 13,037,577 through the issuance of 13,037,577 registered shares with a nominal value of CHF 1.00 each (décision de constatation), and (c) the entry into force of the 2018 Articles (as defined below) (décision de modification des statuts);

(v) an electronic copy of the report of the board of directors of the Company regarding the Capital Increase (rapport d’augmentation), dated March 28, 2018 (the 2018 Board Report);

(vi) electronic copies of the subscription forms (bulletins de souscription) executed by Addex Pharma SA on March 28, 2018, by New Leaf Biopharma Opportunities I, L.P. on March 20, 2021 and by Growth Equity Opportunities Fund IV, LLC on March 21, 2018 regarding the subscription of 13,037,577 registered shares with a nominal value of CHF 1.00 each, in the 2018 Capital Increase (the 2018 Subscription Forms);

(vii) an electronic copy of the audit confirmation by PricewaterhouseCoopers SA (attestation de vérification) on the Board Report, dated March 28, 2018 (the 2018 Audit Confirmation);

(viii) an electronic copy of the declarations of the Company vis-à-vis the Commercial Register of the Canton of Vaud (déclarations Stampa et Lex Friedrich), dated March 28, 2018 (the 2018 Declarations);

(ix) an electronic copy of the articles of association (statuts) of the Company dated March 28, 2018, notarized by a licensed notary of the Canton of Geneva on March 28, 2018 (the 2018 Articles);

(x) an electronic copy of an excerpt from the daily registry of the Commercial Register of the Canton of Geneva with the same-day approval of the Swiss Federal Office of the Commercial Register dated March 28, 2018, relating to the Company and regarding the

registration of the 2018 Capital Increase and the 2018 Articles in the commercial register (the 2018 Daily Register Excerpt);

(xi) an electronic copy of the Company’s uncertificated securities book (registre des droits-valeurs) dated March 28, 2018, evidencing the creation of 13,037,577 uncertificated securities of the Company (the 2018 Securities Book);

(xii) an electronic copy of the articles of association (statuts) of the Company dated June 9, 2020, notarized by a licensed notary of the Canton of Geneva on June 10, 2020 (the 2020 Articles), providing for, inter alia, authorized share capital in the aggregate nominal amount of CHF 16,424,317, authorizing the board of directors of the Company to issue up to 16,424,317 fully paid up registered shares with a nominal value of CHF 1.00 each (the Authorization);

(xiii) an electronic copy of the resolutions of the board of directors of the Company dated January 8, 2011 (the 2021 Capital Increase Board Resolutions), regarding, inter alia, (a) the increase of the Company’s share capital by CHF 6,900,000 through the issuance of 6,900,000 registered shares with a nominal value of CHF 1.00 each (the 2021 Capital Increase) based on the Authorization and under exclusion of the pre-emptive subscription rights of the existing shareholders (décision d’augmentation), (b) the completion of the Capital Increase (décision de constatation), and (c) the entry into force of the Articles (as defined below) (décision de modification des statuts);

(xiv) an electronic copy of the report of the board of directors of the Company regarding the Capital Increase (rapport d’augmentation), dated January 8, 2021 (the 2021 Board Report);

(xv) electronic copies of the subscription forms (bulletins de souscription) executed by Addex Pharma SA and H.C. Wainwright & Co., LLC, both dated January 8, 2021, regarding the subscription of 6,900,000 registered shares in the 2021 Capital Increase (the 2021 Subscription Forms);

(xvi) an electronic copy of the audit confirmation by BDO SA (attestation de vérification) on the Board Report, dated January 8, 2021 (the Audit Confirmation);

(xvii) an electronic copy of the declarations of the Company vis-à-vis the Commercial Register of the Canton of Vaud (déclarations Stampa et Lex Friedrich), dated January 8, 2021 (the Declarations);

(xviii) an electronic copy of an excerpt from the daily registry of the Commercial Register of the Canton of Geneva with the same-day approval of the Swiss Federal Office of the Commercial Register dated January 8, 2021, relating to the Company and regarding the registration of the Capital Increase and the Revised Articles in the commercial register (the Daily Register Excerpt);

(xix) an electronic copy of the Company’s uncertificated securities book (registre des droits-valeurs) dated January 8, 2021, evidencing the creation of 6,900,000 uncertificated securities of the Company and the Underwriter as the first holder of 6,750,000 registered shares with a nominal value of CHF 1 (the Securities Book);

(xx) an electronic copy of articles of association (statuts) of the Company dated January 8, 2021, notarized by a licensed notary of the Canton of Geneva on January 8, 2021 (the Articles);

(xxi) an electronic copy of the internal regulations (règlement d’organisation) of the Company in their version approved by the board of directors of the Company on January 28, 2020 (the Organizational Regulations);

(xxii) an electronic copy of an internet excerpt (extrait internet) from the Commercial Register of the Canton of Geneva dated April 7, 2021, relating to the Company (the Internet Excerpt).

No documents, other than the Documents, have been reviewed by us in connection with this opinion. Accordingly, we shall limit our opinion to the Documents and their legal implications under Swiss law.

In this opinion, Swiss legal concepts are expressed in English terms and not in their original language. These concepts may not be identical to the concepts described by the same English terms as they exist under the laws of other jurisdictions.

B. Assumptions

In rendering the opinion below, we have assumed the following:

(a) all documents produced to us as originals are authentic and complete, and all documents produced to us as copies (including, without limitation, electronic copies) conform to the original;

(b) all documents produced to us as originals and the originals of all documents produced to us as copies were duly executed and certified, as applicable, by the individuals purported to have executed or certified, as the case may be, such documents, and any electronic or facsimile signatures thereon have been produced and used in accordance with applicable internal rules and/or procedures and the individual to whom any such electronic or facsimile signature belongs has consented to the use of his or her signature for each such document on which it appears;

(d) the Registration Statement is unchanged and correct, complete and up-to-date and in full force and effect as of the date hereof and no changes have been made which should have been or should be reflected in the Registration Statement as of the date hereof;

(e) all signatures appearing on all original documents or copies thereof which we have examined are genuine and authentic;

(f) to the extent relevant for purposes of this opinion, any and all information contained in the Documents is, and all material statements made to us in connection with the Documents are and will be, true, complete and accurate at all relevant times;

(g) prior to the issuance of any Capital Increase Shares, the shareholders will have resolved to increase the authorized share capital (if the Capital Increase Shares will exceed the amount of the existing authorized share capital), the board of directors of the Company will have resolved in the presence of a notary on the execution of the corresponding capital increase, validly excluded the pre-emptive rights of the existing shareholders for purposes of offering and selling the Capital Increase Shares as contemplated in the Registration Statement, issued a capital increase report with respect to the Capital Increase and made the corresponding declarations required for implementing the First Capital Increase (constatations relatives à l’augmentation du capital) in the presence of a notary and the board resolutions and such further resolutions and ascertainments will not have been amended and will be in full force and effect until the issuance of all Capital Increase Shares, if the authorized capital will not be sufficient, the shareholders’ meeting will have resolved to increase the authorized capital of the Company ;

(h) the Company has not entered and will not enter into any transaction which could be construed as repayment of share capital (réstitution des versements) and has not undertaken and will not undertake an acquisition in kind (reprise des biens) or intended acquisition in kind (reprise des biens envisagée) without complying with the formal procedure set forth in article 628 of the Swiss Code of Obligations; and

(i) all authorizations, approvals, consents, licenses, exemptions, other than as required by mandatory Swiss law applicable to the Company or the Articles, and other requirements for the filing of the Registration Statement or for any other activities carried on in view of, or in connection with, the performance of the obligations expressed to be undertaken by the Company in the Registration Statement have been duly obtained or fulfilled in due time and are and will remain in full force and effect, and any related conditions to which the parties thereto are subject have been satisfied.

(j) the Articles, the Organizational Regulations and the Internet Excerpt are unchanged and correct, complete and up-to-date and in full force and effect as of the date hereof and no changes have been made which should have been or should be reflected in the Articles, the Organizational Regulations or the Internet Excerpt as of the date hereof;

(k) the Company is, at the date hereof, not insolvent or over-indebted (in the sense of article 725 of the Swiss Code of Obligations (the CO));

(l) the Company intends to produce and publish financial statements in accordance with articles 958 et seqq. at least annually; and

(m) no laws (other than those of Switzerland) affect any of the conclusions stated in this opinion.

C. Opinion

1. The Capital Increase Shares, if and when issued and paid for pursuant to the Articles and Swiss law, in particular upon registration of the corresponding share capital increase into the Commercial Register of the Canton of Geneva, and entered into the Company’s book of

uncertificated securities, will be validly issued, fully paid as to their nominal value and non-assessable.

2. The Secondary Shares have been duly issued, are fully paid as to their nominal value and non-assessable.

3. The Warrant Shares, if and when issued pursuant to the Articles, the Amended and Restated Warrant Agreement and Swiss law, and after the nominal amount for such Warrant Shares has been paid-in in cash, will be validly issued, fully paid as to their nominal value and non-assessable.

D. Qualifications

The above opinions are subject to the following qualifications:

(a) The lawyers of our firm are members of the Zurich bar and do not hold themselves out to be experts in any laws other than the laws of Switzerland. Accordingly, we are opining herein as to Swiss law only and we express no opinion with respect to the applicability or the effect of the laws of any other jurisdiction to or on the matters covered herein.

(b) The exercise of voting rights and rights related thereto with respect to any Shares is only permissible after registration in the Company’s share register as a shareholder with voting rights in accordance with the provisions of, and subject to the limitations provided in, the Articles.

(c) We express no opinion as to whether the Registration Statement is accurate, true, correct, complete or not misleading. In particular, and without limitation to the foregoing, we express no opinion on whether the Registration Statement provides sufficient information for investors to reach an informed assessment of the Company, any companies within the Company’s consolidation perimeter and the Shares.

(d) We express no opinion as regards the exclusion of shareholders’ pre-emptive subscription rights (droits de souscription préférentiel) in connection with the Offering.

(e) We express no opinion as to regulatory matters or as to any commercial, accounting, calculating, auditing, tax or other non-legal matter.

* * *

We have issued this opinion as of the date hereof and we assume no obligation to advise you of any changes that are made or brought to our attention hereafter.

This letter is addressed to you in connection with the Registration Statement. We consent to the filing of this letter as an exhibit to the Registration Statement. No other person may rely on this opinion for any purpose. Without our prior written consent, this opinion may not (in full or in part) be copied, furnished or quoted to any other person except your advisors and representatives in connection with the matters set forth herein.

This opinion shall be governed by and construed in accordance with the laws of Switzerland. We confirm our understanding that all disputes arising out of or in connection with this opinion shall be subject to the exclusive jurisdiction of the courts of the Canton of Zurich, Switzerland, venue being Zurich 1.

Sincerely yours
Homburger AG