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                                                                       EXHIBIT 1

            SECOND AMENDMENT TO THE PREFERRED SHARES RIGHTS AGREEMENT
             AND CERTIFICATION OF COMPLIANCE WITH SECTION 27 THEREOF


        Pursuant to Section 27 of the Preferred Shares Rights Agreement, as
amended, (the "Agreement") dated as of September 13, 1996, between Ligand
Pharmaceuticals Incorporated, a Delaware corporation (the "Company"), and
ChaseMellon Shareholder Services, L.L.C. (as successor to and acquiror of Wells
Fargo Bank, N.A.) (the "Rights Agent") and subsequently amended on November 10,
1998, the Company and the Rights Agent hereby amend the Agreement as of December
23, 1998, as provided below.

        1. Certain Definitions. Section 1 of the Agreement shall be amended as
follows:

                (a) The definition of Continuing Director shall be deleted.

                (b) The phrase "a majority of Continuing Directors then in
        office" which appears twice in subsection (h) shall be replaced with the
        phrase "the Company's Board of Directors."

                (c) The definition of Permitted Offer shall be deleted.

        2. Appointment of Rights Agent. Section 2 shall be amended by deleting
the phrase "and the holders of the Rights (who, in accordance with Section 3
hereof, shall prior to the Distribution Date also be the holders of the Common
Shares)."

        3. Adjustment of Purchase Price, Number of Shares or Number of Rights.
Section 11 shall be amended by deleting subsection (a)(iii).

        4. Consolidation, Merger or Sale or Transfer of Assets or Earning Power.
Section 13 shall be amended by deleting subsection (d).

        5. Redemption. Section 23 shall be amended as follows:

                (a) The phrase which reads "a majority of Continuing Directors
        then in office" in the first sentence of subsection (a) shall be
        replaced with the phrase "the Company's Board of Directors."

                (b) The proviso in subsection (a) which reads "provided,
        however, if the Board of Directors of the Company authorizes redemption
        of the Rights on or after the time a Person becomes an Acquiring Person,
        then there must be Continuing Directors then in office and such
        authorization shall require the concurrence of a majority of such
        Continuing Directors" shall be deleted.

        6. Exchange. Section 24 shall be amended by deleting the phrase "and a
majority vote of the Continuing Directors," in the first sentence of subsection
(a).



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        7. Supplements and Amendments. Section 27 shall be amended by deleting
the phrase "(which lengthening or shortening, following the first occurrence of
an event set forth in the proviso to Section 23(a) hereof, shall be effective
only if there are Continuing Directors and shall require the concurrence of a
majority of such Continuing Directors)."

        8. Determinations and Actions by the Board of Directors, etc. Section 29
shall be amended as follows:

                (a) The phrase "(and, where specifically provided for herein,
        the Continuing Directors)" in the second sentence shall be deleted;

                (b) The phrase "(or, where specifically provided for herein, the
        Continuing Directors)" in the second sentence shall be deleted;

                (c) The phrase "(or, where specifically provided for herein, by
        the Continuing Directors)" in the third sentence shall be deleted; and

                (d) The phrase "or the Continuing Directors" in the third
        sentence shall be deleted.

        9. Exhibit C. Exhibit C shall be amended as follows: (i) The phrase "a
majority of the Directors not affiliated with the acquiring person or group (the
"Continuing Directors")" in the second paragraph of Exhibit C shall be replaced
with the phrase "the Company's Board of Directors," (ii) the phrase "(other than
pursuant to a tender offer deemed adequate and in the best interests of the
Company and its stockholders by the Board of Directors (a "Permitted Offer"))"
shall be deleted in the fourth paragraph of Exhibit C, (iii) the phrase "(unless
the transaction satisfies certain conditions and is consummated with a person
who acquired shares pursuant to a Permitted Offer, in which case the Rights will
expire)" shall be deleted in the fifth paragraph of Exhibit C, and (iv) the
phrase "a majority of the Continuing Directors" in the seventh paragraph of
Exhibit C shall be replaced by the phrase "the Company's Board of Directors."


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        The undersigned officer of the Company, being an appropriate officer of
the Company and authorized to do so by resolution of the Board of Directors of
the Company dated as of December 10, 1998, hereby certifies to the Rights Agent
that these amendments are in compliance with the terms of Section 27 of the
Agreement.



                                       LIGAND PHARMACEUTICALS INCORPORATED


                                       By:    /s/ David E. Robinson
                                              -------------------------------- 
                                              David E. Robinson, President and 
                                              Chief Executive Officer




Acknowledged and Agreed:

CHASEMELLON SHAREHOLDER
SERVICES, L.L.C., as Rights Agent


By:     /s/ Rosa M. Bautista
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Name:      Rosa M. Bautista                         
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Title:     Relationship Manager                     
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              [SIGNATURE PAGE TO SECOND AMENDMENT TO THE PREFERRED
             SHARES RIGHTS AGREEMENT AND CERTIFICATION OF COMPLIANCE
                            WITH SECTION 27 THEREOF]