Celyad Oncology (CLYYF) 6-K Current report (foreign)

Exhibit 5.1

    Celyad SA Rue Edouard Belin 2 1435 Mont-Saint-Guibert Belgium CMS DeBacker
Avocats-Advocaten   Chaussée de La Hulpe 178 1170 Brussels Belgium   T+32 2 743 69 00 F+32 2 743 69 01   www.cms.law   Vincent Dirckx T direct+32 2 743 69 48 Evincent.dirckx@cms-db.com   12 September 2019

Ladies and Gentlemen,

Re : Celyad SA – Legal Opinion

We are acting as Belgian legal advisors to CELYAD SA, a publicly traded limited liability company (naamloze vennootschap /société anonyme) organised under the laws of Belgium with registered office at rue Edouard Belin 2, 1435 Mont-Saint-Guibert, Belgium, registered with the Register of Legal Entities (RPM Nivelles) under the enterprise number 0891.118.115 (theCompany) on certain matters of Belgian law in connection with the Company’s registration statement on FormF-3 as filed with the U.S. Securities and Exchange Commission (theCommission), as thereafter amended or supplemented (theRegistration Statement), relating to the registration under the U.S. Securities Act of 1933, as amended (theSecurities Act), of the offer and sale of 2,000,000 new ordinary shares of the Company, no par value per share, to be offered (i) in Europe and countries outside of the United States and Canada by way of a private placement to qualified investors, whereby ordinary shares will be offered (theOrdinary Shares) and (ii) in the United States, Canada and certain countries outside of Europe, whereby the shares will be offered in the form of American Depositary Shares (theADSs,together withthe Ordinary Shares, theSecurities), each ADS representing one new share, covered by the Registration Statement to which this opinion is an exhibit (theTransaction). The Ordinary Shares and the ordinary shares underlying the ADSs will be created through one or more capital increases under Belgian Law (theNew Ordinary Shares).

CMS DeBacker SCRL-RPM Bruxelles—TVA: BE0430.408.301- IBAN: BE98 63002257 5393—BIC: BBRUBEBB

CMS DeBacker is a member of CMS, the organisation of European law firms. In certain circumstances, CMS is used as a brand or business name of some or all of the member firms. Further information can be found at www.cms.law.

CMS offices and associated offices:Aberdeen, Algiers, Amsterdam, Antwerp, Barcelona, Beijing, Belgrade, Berlin, Bogotá, Bratislava, Bristol, Brussels, Bucharest, Budapest, Casablanca, Cologne, Dubai, Düsseldorf, Edinburgh, Frankfurt, Geneva, Glasgow, Hamburg, Hong Kong, Istanbul, Kyiv, Leipzig, Lima, Lisbon, Ljubljana, London, Luxembourg, Lyon, Madrid, Medellin, Mexico City, Milan, Moscow, Munich, Muscat, Paris, Podgorica, Prague, Rio de Janeiro, Rome, Santiago de Chile, Sarajevo, Seville, Shanghai, Sofia, Strasbourg, Stuttgart, Tehran, Tirana, Utrecht, Vienna, Warsaw, Zagreb and Zurich.

Nature of the opinion and limitations

This opinion is subject to the following limitations:

(a) this opinion is confined to the laws of Belgium, all as they stand as at the date hereof and as such laws are interpreted by the courts of Belgium (Belgian law); accordingly, we express no opinion with regard to any other system of law (including the law of jurisdictions other than Belgium in which our firm has an office), even in cases where, under Belgian law, any foreign law should be applied, and we therefore assume that any applicable law (other than Belgian law) would not affect or qualify the opinions as set out below; furthermore we do not express any opinion on public international law or on the rules of or promulgated under any treaty or by any treaty organisation (except insofar as they are directly applicable in Belgium);

(b) in rendering this opinion, we have examined the Registration Statement, the prospectus of the Company included in the Registration Statement (theProspectus), as supplemented by the prospectus supplement specifically relating to the offer and sale of the Securities (theSupplement), the coordinated articles of association of the Company dated 23 May 2019 (theArticles), and such corporate documents and records of the Company and such other instruments, certificates and documents as we have deemed necessary and appropriate as a basis of the opinion hereinafter expressed (theDocuments) and we have conducted such investigations of Belgian law as we have deemed necessary or advisable for the purpose of giving this opinion letter; as to matters of fact, we have relied on any other document we have deemed relevant and on statements of public officials and directors and officers of the Company;

(c) we express no opinion that the future or continued performance of a party’s obligations or the consummation of the Transaction will not contravene Belgian law, its application or interpretation to the extent that Belgian law is altered in the future;

(d) this opinion cannot be construed as giving certainty that Belgian courts will in the future take the same decisions as in the existing case law and doctrine on which this opinion is based; moreover, not all legal issues discussed in this opinion have been the subject matter of case law and any opinion expressed on such issues herein cannot be construed as giving certainty that a Belgian court will decide in the manner as opined therein;

(e) we express no opinion as to the correctness of any representation given by any of the parties (express or implied), including the Company, under or by virtue of any of the Documents, save if and insofar as the matters represented are the subject matter of a specific opinion herein;

(f) to the extent that the laws of other jurisdictions may be relevant, we have made no independent investigation of such laws, and our opinion is subject to the effect of such laws including the matters contained in the opinion of local counsel in these jurisdictions; we express no views in this opinion on the validity of the matters set out in such opinion(s);

(g) we express no opinion on any taxation laws of any jurisdiction (including Belgium) otherwise than as stated herein;

(h) Belgian legal concepts are expressed in English terms and not in their original Dutch or French terms; the concepts concerned may not be identical to the concepts described by the same English terms as they exist in the laws of other jurisdictions; accordingly, any issues of

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interpretation arising, the agreements and documents relating thereto and this present opinion will be determined by the Belgian courts in accordance with Belgian law, and we express no opinion on the interpretation that the Belgian court may make of any such expressions or descriptions; in particular, as far as the term“non-assessable” used in this opinion is concerned, please note that this word has no legal meaning under Belgian law and is used in this opinion only to mean that, with respect to the issuance of New Ordinary Shares, a holder of New Ordinary Shares will have no obligation to pay any additional amount in excess of the subscription price;

(i) any person who is entitled to, and does, rely on this opinion agrees, by so relying, that, to the fullest extent permitted by law and regulation (and except in the case of wilful misconduct or fraud) there is no assumption of a personal duty of care by, and such person will not bring any claim against, any individual who is a partner of, member of, associate of, employee of or consultant to CMS DeBacker or any other member of the group of CMS undertakings and that such person will instead confine any claim to CMS DeBacker (which includes the operations conducted in our Brussels office). This applies (save only where law and regulation requires otherwise) to any claim, whether in contract, tort (including negligence), for breach of statutory duty, or otherwise; and

(j) this opinion speaks as of the date hereof; no obligation is assumed to update this opinion or to inform any person of any changes of law or other matters coming to our knowledge and occurring after the date hereof, which may affect this opinion in any respect.

Assumptions

In considering the Documents and in rendering this opinion, we have assumed:

(a) the genuineness of all signatures on, and the authenticity and completeness of, all documents submitted to us whether as originals or copies;

(b) the conformity to originals of all documents supplied to us as photocopies,e-mail copies or facsimile copies;

(c) that the Registration Statement has been or shall be filed with the Commission and shall become effective, in the form referred to in this opinion;

(d) that the Documents have been decided upon or entered into forbona fide commercial reasons, within the corporate purpose and corporate interest of the parties thereto and on arms’ length terms by each of the parties, without any fraudulent intent (including as to the interests of creditors);

(e) that there has been no mistake of fact (erreur), fraud (dol), duress (violence) or undue influence (lésion) in relation to any Document;

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(f) that the directors (administrateurs) of the Company who have approved and/or executed Documents, have exercised their powers (i) in accordance with the best interest of the Company, (ii) in accordance with their duties under all applicable laws (including the rules regarding conflicts of interest), and (iii) in accordance with the articles of association of the Company and the powers conferred to them.

Opinion

Based upon and subject to the foregoing, and subject as set out below and to any matters not disclosed to us, we are of the opinion (so far as the laws of Belgium as in force on the date of this opinion are concerned) that the New Ordinary Shares will, to the extent that the Company will have received in full all amounts payable by the investors in respect of the New Ordinary Shares, be validly issued, fullypaid-up andnon-assessable.

Qualifications

Our opinion is subject to the following qualifications:

(a) this opinion is subject to bankruptcy, judicial reorganisation, insolvency, attachment, liquidation and other laws of general application relating to or affecting the rights of creditors generally;

(b) to the extent that any of the transactions effected under or pursuant to the Documents constitutes a breach or infringement by a party of an agreement or obligations by which it is bound, such breach or infringement may result in a court setting aside the transaction (including the creation of any security interest for the benefit of the third party or parties prejudiced by the breach or infringement if it is established that the parties to the relevant transaction were aware of the breach or infringement). Note however that court decisions do not have the value of binding precedent on other courts;

(c) we express no view on any provision stating that the document is the entire agreement or requiring written amendments or waivers insofar as such provision suggests that oral or other modifications, amendments or waivers could not be effectively agreed upon or granted by or between the parties or implied by the course of conduct of the parties;

(d) the introduction of legal proceedings in Belgium and enforcement of a judgment would give rise to certain nominal filing charges and notification fees; pursuant to article 851 of the Belgian Judicial Code a foreign plaintiff can be required, at the request of a Belgian defendant, to post a bond to secure payment of any expenses or damages for which the foreign plaintiff might be liable, unless waived in a applicable treaty;

(e) court decisions do not have the value of a binding precedent under Belgian law;

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(f) the enforcement of a foreign judgment rendered by a court which is not a court of states which are bound by the Council Regulation (or the Recast Council Regulation, as applicable), is subject to the procedures contained in the Belgian Code of Judicial Procedure and can include are-examination of the merits of the case by the Belgian courts;

(g) a suit filed before a Belgian court, including for the purpose of the recognition or enforcement in Belgium of a judgment of any court in the United States of America, is subject to any Belgian rules of civil procedure, including articles 22 to 31 of the International Private Code.

Governing law and jurisdiction

This opinion and anynon-contractual obligations arising out of or in relation to this opinion are governed by Belgian law. This opinion is given in accordance with the rules and standards of the Brussels Bar.

The Belgian courts shall havenon-exclusive jurisdiction in relation to all disputes (including claims forset-off and counterclaims) arising out of or in connection with this opinion, including, without limitation, disputes arising out of or in connection with (i) the creation, effect or interpretation of, or the legal relationships established by, this opinion, and (ii) anynon-contractual obligations arising out of or in connection with this opinion.

We hereby consent to the filing of this opinion as an exhibit to the Supplement, and to the reference to us under the heading “Legal Matters” in the Supplement, without admitting we are “experts” within the meaning of the Securities Act or the rules and regulations of the Commission promulgated thereunder with respect to any part of the Registration Statement.

Yours faithfully

/s/ CMS DeBacker

CMS DeBacker

Vincent Dirckx

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