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                                                                     Exhibit 5.1
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R.A. Harrington                                        Conoco Inc.
Senior Vice President, Legal, and General Counsel      P.O. Box 4783
                                                       Houston, Texas 77210-4783



June 16, 1999


Board of Directors
Conoco Inc.
600 North Dairy Ashford
Houston, TX 77079

Dear Directors:

I am Senior Vice President, Legal, and General Counsel of Conoco Inc., a
Delaware corporation ("Conoco"). Pursuant to Item 601(b)(5) of Regulation S-K
under the Securities Act of 1933, as amended (the "Act"), I am rendering this
opinion in connection with the Registration Statement on Form S-4, as amended
(Registration No. 333-74823), filed by Conoco under the Act (the "Registration
Statement") relating to 436,543,573 shares of Conoco's Class B Common Stock,
par value $.01 per share (the "Shares") to be offered by E.I. du Pont de
Nemours and Company ("DuPont") in exchange for shares of its common stock.

In connection with this opinion, I have examined, directly or indirectly
through staff or otherwise, originals or copies, certified or otherwise
identified to my satisfaction, of each of the following documents.

     1.   The Registration Statement;

     2.   A specimen certificate representing the Class B Common Stock;

     3.   Conoco's Second Amended and Restated Certificate of Incorporation as
          currently in effect;

     4.   Conoco's Amended and Restated By-Laws as currently in effect; and

     5.   Certain resolutions of the Conoco Board of Directors relating to the
          issuance and sale of the Shares and related matters.


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I have also examined, directly or indirectly through staff or otherwise,
originals or copies, certified or otherwise identified to my satisfaction, of
such corporate records, certificates and other documents, such governmental
approvals and filings, and such questions of law, as I have considered
necessary or appropriate for the purposes of this opinion.

In giving the opinion below, I have assumed that the signatures on all
documents (other than those of Conoco, as to which I make no such assumption)
examined by me are genuine, an assumption which I have not independently
verified. I have also assumed (without investigation on my part), the
authenticity of all documents submitted for review as originals, the conformity
to original documents of all documents submitted for review as certified,
conformed or photostatic copies and the authenticity of the originals of such
latter documents.

Based upon the foregoing, it is my opinion that:

     1.   Conoco is a corporation duly organized and validly existing in good
standing under the laws of the State of Delaware.

     2.   The Shares have been duly authorized and are validly issued, fully
paid and non-assessable.


The foregoing opinion is limited to the laws of the United States and the laws
of the State of Delaware and I am expressing no opinion as to the effect of the
laws of any other jurisdiction.


I hereby consent to the filing of this opinion as Exhibit 5.1 to the
Registration Statement and the reference to my name under the caption "Legal
Matters" in the related Offering Circular-Prospectus. In giving such consent, I
do not admit that I am within the category of persons whose consent is required
under Section 7 of the Act or the rules and regulations of the Securities and
Exchange Commission thereunder.

Very truly yours,

/s/ RICK A. HARRINGTON

R.A. Harrington
Sr. Vice President, Legal, and General Counsel