POWER OF ATTORNEY

     Know all by these presents, that the undersigned hereby constitutes and
appoints each of Hazel M. Aker and Richard G. Vincent, signing singly, the
undersigned's true and lawful attorney-in-fact to:

     1.   execute for and on behalf of the undersigned, in the undersigned's
          capacity as an officer and/or director of Oncternal Therapeutics, Inc.
          (the "Company"), Forms 3, 4 and 5 in accordance with Section 16(a) of
          the Securities Exchange Act of 1934 and the rules thereunder;

     2.   do and perform any and all acts for and on behalf of the undersigned
          which may be necessary or desirable to complete and execute any such
          Form 3, 4 and 5, and any amendments thereto, and timely file such form
          or report with the Securities and Exchange Commission and any stock
          exchange or similar authority; and

     3.   take any other action of any type whatsoever in connection with the
          foregoing which, in the opinion of such attorney-in-fact, may be of
          benefit to, in the best interest of, or legally required by, the
          undersigned, it being understood that the documents executed by such
          attorney-in-fact on behalf of the undersigned pursuant to this Power
          of Attorney shall be in such form and shall contain such terms and
          conditions as such attorney-in-fact may approve in such attorney-in-
          fact's discretion.

     The undersigned hereby grants to each such attorney-in-fact full power and
authority to do and perform any and every act and thing whatsoever requisite,
necessary, or proper to be done in the exercise of any rights and powers herein
granted, as fully to all intents and purposes as the undersigned might or could
do if personally present, with full power of substitution or revocation, hereby
ratifying and confirming all that such attorney-in-fact, or such attorney-in-
fact's substitute or substitutes, shall lawfully do or cause to be done by
virtue of this power of attorney and the rights and powers herein granted. The
undersigned acknowledges that the foregoing attorneys-in-fact, in serving in
such capacity at the request of the undersigned, are not assuming, nor is the
company assuming, any of the undersigned's responsibilities to comply with
Section 16 of the Securities Exchange Act of 1934.

     This Power of Attorney supersedes any Power of Attorney previously granted
by the undersigned with respect to the foregoing matters and shall remain in
full force and effect until the undersigned is no longer required to file Forms
3, 4 and 5 with respect to the undersigned's holdings of and transactions in
securities issued by the Company, unless earlier revoked by the undersigned in a
signed writing delivered to the foregoing attorneys-in-fact.

     IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to be
executed as of this 4th day of June, 2019.

                                /s/ James B. Breitmeyer
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                                James B. Breitmeyer