[LETTERHEAD]

October 13, 2000

Axonyx Inc.
825 Third Avenue, 40th Floor
New York, NY 10022

Re: Registration Statement on Form S-8

Ladies and Gentlemen:

    We have acted as special Nevada counsel to Axonyx Inc., a Nevada corporation (the "Company"), for the purpose of issuing this letter in connection with the proposed issuance and sale by the Company of up to 2,395,900 shares (subject to adjustment as provided in the Registration Statement (as defined below)) of the Company's Common Stock, $0.001 par value per share (the "Shares"). The Shares are to be offered and sold under the Company's 1998 Stock Option Plan (the "1998 Plan") and 2000 Stock Option Plan (the "2000 Plan" and, together with the 1998 Plan, the "Plans"), pursuant to the Company's Registration Statement on Form S-8 (the "Registration Statement"), to be filed with the Securities and Exchange Commission (the "Commission") under the Securities Act of 1933, as amended (the "Act").

    This letter is being furnished in accordance with the requirements of Item 8 of Form S-8 and Item 601(b)(5)(i) of Regulation S-K, as promulgated by the Commission.

    For the purpose of rendering our opinion set forth herein, we have examined and relied on (i) a Secretary's Certificate, dated as of September 29, 2000, executed by the Secretary of the Company (the "Secretary's Certificate"); (ii) a Certificate of Existence with Status in Good Standing, dated September 20, 2000, issued by the Secretary of State of the State of Nevada (the "Secretary of State") with respect to the Company; (iii) Certificate of Amendment to the Articles of Incorporation of the Company, dated December 30, 1998, filed with the Secretary of State on December 30, 1998, corrected by three Certificates of Correction filed with the Secretary of State as of February 9, 1999, and certified by the Secretary of State as of October 6, 2000; (iv) Articles of Merger, dated December 28, 1998, executed by Axonyx, a Delaware corporation, and the Company under its prior corporate name "Ionosphere, Inc.," filed with the Secretary of State on December 30, 1998, and certified by the Secretary of State as of October 6, 2000; (v) Restated Articles of Incorporation of the Company, dated June 23, 2000, filed with the Secretary of State on June 28, 2000, and certified by the Secretary of State as of October 6, 2000; and (vi) such records and other documents of the Company as we considered appropriate including, without limitation, the Company's articles of incorporation, bylaws and minutes of the proceedings of the Company's board of directors in connection with the authorization of the Shares and the Plans, all certified by the Secretary of the Company in the Secretary's Certificate; and (vii) the Registration Statement and the Plans, which are included as Exhibits to the Registration Statement, as furnished to us by the Company.

    We have assumed (A) the authenticity of any and all documents submitted to us as originals; (B) the genuineness of all signatures on documents submitted to us; (C) the legal capacity of natural persons executing all relevant documents; (D) the accuracy and completeness of all corporate records provided to us by the Company; (E) the veracity as of the date of this letter of the certificates, records, documents and other instruments furnished to us by the Company, even though they may have been signed or issued on an earlier date (although, with your permission, we have not independently verified the statements made therein nor have we investigated the basis for the representations contained therein); (F) the conformity to the originals of all documents submitted to us as copies; (G) approval of the 2000 Plan by the shareholders of the Company at the 2000 annual meeting of shareholders; and (H) no changes in applicable law between the date of this letter and the date of the events which are the subject of this letter.

    Based on our review and subject to the assumptions, qualifications and limitations set forth herein, we are of the opinion that the Shares have been duly authorized and if, as and when the Shares are issued in accordance with the Registration Statement and the 1998 Plan or the 2000 Plan (as the case may be) upon due exercise of the options thereunder, the Shares will be legally issued, fully paid and non-assessable.

    We are licensed to practice law in the State of Nevada and the opinion set forth herein is expressly limited to the laws of the State of Nevada. No opinion is given or implied regarding federal law or the laws of any jurisdiction other than the State of Nevada as currently in effect.

    This letter is being delivered to the Company in connection with the filing of the Registration Statement with the Commission and may not be used or relied upon for any other purpose.

    We consent to the filing of this letter as Exhibit 5.1 to the Registration Statement and to the reference to this firm under the caption "Legal Matters" in the prospectus which is part of the Registration Statement. In giving this consent, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Act, the rules and regulations of the Commission promulgated thereunder, or Item 509 of Regulation S-K.

    Our opinion herein is rendered as of the date of this letter and we disclaim any obligation to advise you of facts, circumstances, events or developments which hereafter may come to our attention and which may alter, affect or modify such opinion. Our opinion is expressly limited to the matters set forth above and we render no opinion, whether by implication or otherwise, as to any other matters relating to the Company or the Shares.

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