Exhibit 5.1

ATTORNEYS • CIVIL LAW NOTARIES • TAX ADVISERS
P.O. Box 7113 1007 JC Amsterdam Beethovenstraat 400 1082 PR Amsterdam T +31 20 71 71 000 F +31 20 71 71 111	Amsterdam, 19 August 2020. To the Company

Ladies and Gentlemen:

We have acted as legal counsel as to Dutch law to the Company in connection with the Registration Statement and the filing thereof with the SEC. This opinion letter is rendered to you in order to be filed with the SEC as an exhibit to the Registration Statement.

Capitalised terms used in this opinion letter have the meanings set forth in Exhibit A to this opinion letter. The section headings used in this opinion letter are for convenience of reference only and are not to affect its construction or to be taken into consideration in its interpretation.

This opinion letter is addressed solely to you. This opinion letter is strictly limited to the matters stated in it and may not be read as extending by implication to any matters not specifically referred to in it. Nothing in this opinion letter should be taken as expressing an opinion in respect of any representations or warranties, or other information, contained in any document.

In rendering the opinions expressed in this opinion letter, we have exclusively reviewed and relied upon a draft of the Registration Statement and pdf copies of the Corporate Documents and the Plan and we have assumed that any grant of Awards and any issuance of Plan Shares shall be effected for bona fide commercial reasons. We have not investigated or verified any factual matter disclosed to us in the course of our review.

This opinion letter sets out our opinion on certain matters of the laws with general applicability of the Netherlands, and, insofar as they are directly applicable in the Netherlands, of the European Union, as at today’s date and as presently interpreted under published authoritative case law of the Dutch courts, the General Court and the Court of Justice of the European Union. We do not express any opinion on Dutch or European competition law, tax law, data protection law or regulatory law. No undertaking is assumed on our part to revise, update or amend this opinion letter in connection with or to notify or inform you of, any developments and/or changes of Dutch law subsequent to today’s date. We do not

Amsterdam   Brussels   London   Luxemburg   New York   Rotterdam This communication is confidential and may be subject to professional privilege. All legal relationships are subject to NautaDutilh N.V.’s general terms and conditions (see https://www.nautadutilh.com/terms), which apply mutatis mutandis to our relationship with third parties relying on statements of NautaDutilh N.V., include a limitation of liability clause, have been filed with the Rotterdam District Court and will be provided free of charge upon request. NautaDutilh N.V.; corporate seat Rotterdam; trade register no. 24338323.

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purport to opine on the consequences of amendments to the Registration Statement, the Plan or the Corporate Documents subsequent to the date of this opinion letter.

The opinions expressed in this opinion letter are to be construed and interpreted in accordance with Dutch law. The competent courts at Amsterdam, the Netherlands, have exclusive jurisdiction to settle any issues of interpretation or liability arising out of or in connection with this opinion letter. Any legal relationship arising out of or in connection with this opinion letter (whether contractual or non-contractual), including the above submission to jurisdiction, is governed by Dutch law and shall be subject to the general terms and conditions of NautaDutilh. No person other than NautaDutilh may be held liable in connection with this opinion letter.

In this opinion letter, legal concepts are expressed in English terms. The Dutch legal concepts concerned may not be identical in meaning to the concepts described by the English terms as they exist under the law of other jurisdictions. In the event of a conflict or inconsistency, the relevant expression shall be deemed to refer only to the Dutch legal concepts described by the English terms.

For the purposes of this opinion letter, we have assumed that:

a. drafts of documents reviewed by us will be signed in the form of those drafts, each copy of a document conforms to the original, each original is authentic, and each signature is the genuine signature of the individual purported to have placed that signature;

b. the Registration Statement has or will have been declared effective upon filing by the SEC in the form reviewed by us;

c. the Deed of Incorporation and the Deed of Conversion are valid notarial deeds and the Deed of Incorporation has been executed on the basis of a valid declaration of no objection (verklaring van geen bezwaar);

d. at each Relevant Moment, the Current Articles are the Articles of Association in force and effect;

e. at each Relevant Moment, the Plan is in force and effect;

f. at each Relevant Moment, the Company will not (i) have been dissolved (ontbonden), (ii) have ceased to exist pursuant to a merger (fusie) or a division (splitsing), (iii) have been converted (omgezet) into another legal form, either national or foreign, (iv) have had its assets placed under administration (onder bewind gesteld), (v) have been declared bankrupt

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(failliet verklaard), (vi) have been granted a suspension of payments (surseance van betaling verleend), or (vii) have been made subject to similar proceedings in any jurisdiction or otherwise been limited in its power to dispose of its assets;

g. at each Relevant Moment, (i) the relevant Award(s) shall have been validly granted by the corporate body authorized to do so and shall have been validly exercised in accordance with the terms and conditions applicable to such Awards and (ii) any pre-emption rights in respect of such Award(s) shall have been validly excluded by the corporate body authorized to do so;

h. at each Relevant Moment, each holder of the relevant Award(s) shall be an individual who has not (i) deceased, (ii) had his/her assets placed under administration (onder bewind gesteld), (iii) been declared bankrupt (failliet verklaard), (iv) been granted a suspension of payments (surseance van betaling verleend), or (v) been made subject to similar proceedings in any jurisdiction or otherwise been limited in the power to dispose of his/her assets;

i. at each Relevant Moment, the authorised share capital (maatschappelijk kapitaal) of the Company shall allow for the grant of Awards and the issuance of Plan Shares pursuant to the exercise thereof;

j. the offering of the Plan Shares, to the extent made in the Netherlands, has been, is and will be made in conformity with the Prospectus Regulation and the rules promulgated thereunder; and

k. at each relevant moment, the Company is not in possession of inside information (voorwetenschap) or acts in breach of the prohibition of insider dealing and of unlawful disclosure of inside information contained in Article 14 of the MAR or the prohibition on market manipulation contained in Article 15 of the MAR.

Based upon and subject to the foregoing and subject to the qualifications set forth in this opinion letter and to any matters, documents or events not disclosed to us, we express the following opinions:

Corporate Status

1. The Company has been duly incorporated as a besloten vennootschap met beperkte aansprakelijkheid and is validly existing as a naamloze vennootschap.

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Plan Shares

2. Subject to receipt by the Company of payment of at least the nominal value of the Plan Shares in accordance with the Plan, and when issued and accepted in accordance with the Plan, the Plan Shares will be validly issued, fully paid and non-assessable.

The opinions expressed above are subject to the following qualifications:

A. Opinion 1 must not be read to imply that the Company cannot be dissolved (ontbonden). A company such as the Company may be dissolved, inter alia by the competent court at the request of the company’s board of directors, any interested party (belanghebbende) or the public prosecution office in certain circumstances, such as when there are certain defects in the incorporation of the company. Any such dissolution will not have retro-active effect.

B. Pursuant to Section 2:7 NCC, any transaction entered into by a legal entity may be nullified by the legal entity itself or its liquidator in bankruptcy proceedings (curator) if the objects of that entity were transgressed by the transaction and the other party to the transaction knew or should have known this without independent investigation (wist of zonder eigen onderzoek moest weten). The Dutch Supreme Court (Hoge Raad der Nederlanden) has ruled that in determining whether the objects of a legal entity are transgressed, not only the description of the objects in that legal entity’s articles of association (statuten) is decisive, but all (relevant) circumstances must be taken into account, in particular whether the interests of the legal entity were served by the transaction. Based on the objects clauses contained in the Current Articles, we have no reason to believe that, by issuing Plan Shares, the Company will transgress the description of the objects contained in the Current Articles. However, we cannot assess whether there are other relevant circumstances that must be taken into account, in particular whether the interests of the Company are served by issuing Plan Shares since this is a matter of fact.

C. Pursuant to Section 2:98c NCC, a naamloze vennootschap may grant loans (leningen verstrekken) only in accordance with the restrictions set out in Section 2:98c NCC, and may not provide security (zekerheid stellen), give a price guarantee (koersgarantie geven) or otherwise bind itself, whether jointly and severally or otherwise with or for third parties (zich op andere wijze sterk maken of zich hoofdelijk of anderszins naast of voor anderen verbinden) with a view to (met het oog op) the

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subscription or acquisition by third parties of shares in its share capital or depository receipts. This prohibition also applies to its subsidiaries (dochtervennootschappen). It is generally assumed that a transaction entered into in violation of Section 2:98c NCC is null and void (nietig). Based on the Plan, we have no reason to believe that the Company or its subsidiaries will violate Section 2:98c NCC in connection with the issue of Plan Shares. However, we cannot confirm this definitively, since the determination of whether a company (or a subsidiary) has provided security, has given a price guarantee or has otherwise bound itself, with a view to the subscription or acquisition by third parties of shares in its share capital or depository receipts, as described above, is a matter of fact.

D. The opinions expressed in this opinion letter may be limited or affected by:

a. any applicable bankruptcy, insolvency, reorganisation, moratorium or other similar laws or procedures now or hereafter in effect, relating to or affecting the enforcement or protection of creditors’ rights generally;

b. the provisions of fraudulent preference and fraudulent conveyance (Actio Pauliana) and similar rights available in other jurisdictions to insolvency practitioners and insolvency office holders in bankruptcy proceedings or creditors;

c. claims based on tort (onrechtmatige daad);

d. sanctions and measures, including but not limited to those concerning export control, pursuant to European Union regulations, under the Sanctions Act 1977 (Sanctiewet 1977) or other legislation;

e. the Anti-Boycott Regulation and related legislation; and

f. the rules of force majeure (niet toerekenbare tekortkoming), reasonableness and fairness (redelijkheid en billijkheid), suspension (opschorting), dissolution (ontbinding), unforeseen circumstances (onvoorziene omstandigheden) and vitiated consent (i.e., duress (bedreiging), fraud (bedrog), abuse of circumstances (misbruik van omstandigheden) and error (dwaling)) or a difference of intention (wil) and declaration (verklaring).

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E. The term “non-assessable” has no equivalent in the Dutch language and for purposes of this opinion letter such term should be interpreted to mean that a holder of a Common Share shall not by reason of merely being such a holder be subject to assessment or calls by the Company or its creditors for further payment on such Common Share.

F. This opinion letter does not purport to express any opinion or view on the operational rules and procedures of any clearing or settlement system or agency.

We consent to the filing of this opinion letter as an exhibit to the Registration Statement. In giving this consent we do not admit of imply that we are a person whose consent is required under Section 7 of the United States Securities Act of 1933, as amended, or any rules and regulations promulgated thereunder.

Sincerely yours,

/s/ NautaDutilh N.V.

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EXHIBIT A

LIST OF DEFINITIONS

“Anti-Boycott Regulation”	The Council Regulation (EC) No 2271/96 of 22 November 1996 on protecting against the effects of the extra-territorial application of legislation adopted by a third country, and actions based thereon or resulting therefrom.
“Articles of Association”	The Company’s articles of association (statuten) as they read from time to time.
“Awards”	Right to subscribe for Common Shares pursuant to the terms and conditions of the Plan.
“Commercial Register”	The Dutch Commercial Register (handelsregister).
“Common Shares”	Common shares in the Company’s capital, with a nominal value of EUR 0.02 each.
“Company”	Core Laboratories N.V., a public company with limited liability (naamloze vennootschap), registered with the Commercial Register under number 33261158.
“Corporate Documents”	The Deed of Incorporation, the Deed of Conversion, the Deed of Amendment and the Current Articles.
“Current Articles”	The Articles of Association as they read immediately after the execution of the Deed of Amendment.
“DCC”	The Dutch Civil Code (Burgerlijk Wetboek).
“Deed of Amendment”	The deed of amendment to the Articles of Association, dated May 24, 2017.
“Deed of Conversion”	The deed of conversion and amendment to the Articles of Association, dated August 31, 1995.
“Deed of Incorporation”	The Company’s deed of incorporation (akte van oprichting), dated August 8, 1994.

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“MAR”	Regulation (EU) No 596/2014 of the European Parliament and of the Council of 16 April 2014 on market abuse (market abuse regulation) and repealing Directive 2003/6/EC of the European Parliament and of the Council and Commission Directives 2003/124/EC, 2003/125/EC and 2004/72/EC and the rules and regulations promulgated pursuant thereto.
“NautaDutilh”	NautaDutilh N.V.
“the Netherlands” or “Dutch”	The European territory of the Kingdom of the Netherlands.
“Plan”	The Company’s employee long-term incentive plan, the most recent version of which is the 2020 Long-Term Incentive Plan.
“Plan Shares”	The Common Shares available for issuance under the Plan pursuant to the exercise of Awards, according to the Registration Statement.
“Prospectus Regulation”	Regulation (EU) 2017/1129 of the European Parliament and of the Council of 14 June 2017 on the prospectus to be published when securities are offered to the public or admitted to trading on a regulated market, and repealing Directive 2003/71/EC.
“Registration Statement”	The Company’s registration statement on Form S-8 filed or to be filed with the SEC on or about the date of this opinion letter.
“Relevant Moment”	Each time when Awards are issued or Plan Shares are issued pursuant to the exercise of the relevant Award(s).
“SEC”	The United States Securities and Exchange Commission.