<PAGE>   1
                                                                     Exhibit 3.1



                          CERTIFICATE OF INCORPORATION

                                       OF

                              CELL PATHWAYS, INC.

                                       I.

         The name of the corporation is Cell Pathways Holdings, Inc. (the
"Corporation").

                                       II.

         The address of the registered office of the Corporation in the State of
Delaware is 1013 Centre Road, City of Wilmington, County of New Castle, and the
name of the registered agent of the Corporation in the State of Delaware at such
address is Corporation Service Company.

                                      III.

         The purpose of the Corporation is to engage in any lawful act or
activity for which a corporation may be organized under the General Corporation
Law of the State of Delaware.

                                       IV.

A.       The Corporation shall be authorized to issue two classes of stock to be
designated, respectively, "Common Stock" and "Preferred Stock". The total number
of shares that the Corporation shall be authorized to issue is seventy-five
million (75,000,000) shares. Seventy million (70,000,000) shares shall be Common
Stock, each having a par value of One Cent ($.01). Five million (5,000,000)
shares shall be Preferred Stock, each having a par value of One Cent ($.01).

B.       The Preferred Stock may be issued from time to time in one or more
series. The Board of Directors is hereby authorized, by filing a certificate (a
"Preferred Stock Designation") pursuant to the Delaware General Corporation Law,
to provide for such issuance, and to fix or alter from time to time the
designation, powers, preferences and rights of the shares of each such series
and the qualifications, limitations or restrictions of any wholly unissued
series of Preferred Stock, and to establish from time to time the number of
shares constituting any such series or any of them; and to increase or decrease
the number of shares of any series subsequent to the issuance of shares of that
series, but not below the number of shares of such series then outstanding. In
case the number of shares of any series shall be decreased in accordance with
the foregoing sentence, the shares constituting such decrease shall resume the
status that they had prior to the adoption of the resolution originally fixing
the number of shares of such series.
<PAGE>   2
C.       Subject to the rights of any Preferred Stock then outstanding, each
issued and outstanding share of Common Stock shall entitle the Holder thereof to
receive such dividends as may be declared from time to time by the Board of
Directors of the Corporation out of funds legally available therefor, and shall
entitle the Holder thereof to share ratably with other Holders of Common Stock
in all assets available for distribution in the event of any liquidation,
dissolution or winding up of the Corporation. Each issued and outstanding share
of Common Stock shall be identical to all other shares of that class, and shall
entitle the Holder thereof to cast one vote on each matter submitted to a vote
of the Corporation's stockholders. No Holder of Common Stock shall be entitled
to any cumulative voting rights or to any preemptive rights upon the issuance or
sale of any Securities.

                                       V.

         For the management of the business and for the conduct of the affairs
of the Corporation, and in further definition, limitation and regulation of the
powers of the Corporation, of its directors and of its stockholders or any class
thereof, as the case may be, it is further provided that:

A.       1. The business and affairs of the Corporation shall be managed by or
under the direction of the Board of Directors. The number of directors that
shall constitute the whole Board of Directors shall be fixed exclusively by one
or more resolutions adopted by the Board of Directors.

         2. Subject to the rights of the holders of any series of Preferred
Stock to elect additional directors under specified circumstances, the directors
shall be divided into three classes designated as Class I, Class II and Class
III, respectively. Directors shall be assigned to each class in accordance with
a resolution or resolutions adopted by the Board of Directors. At the first
annual meeting of stockholders following the filing of this Certificate of
Incorporation, the term of office of the Class I directors shall expire and
Class I directors shall be elected for a full term of three years. At the second
annual meeting of stockholders following the filing of this Certificate of
Incorporation, the term of office of the Class II directors shall expire and
Class II directors shall be elected for a full term of three years. At the third
annual meeting of stockholders following the filing of this Certificate of
Incorporation, the term of office of the Class III directors shall expire and
Class III directors shall be elected for a full term of three years. At each
succeeding annual meeting of stockholders, directors shall be elected for a full
term of three years to succeed the directors of the class whose terms expire at
such annual meeting. Each director shall serve beyond the term specified until
his successor is duly elected and qualified or until his death, resignation or
removal. No decrease in the number of directors constituting the Board of
Directors shall shorten the term of any incumbent director.

         3. Subject to the rights of the holders of any series of Preferred
Stock, a director may be removed only for cause and only by the affirmative vote
of the holders of a
<PAGE>   3
majority of the voting power of all the then-outstanding shares of voting stock
of the Corporation, entitled to vote at an election of directors (the "Voting
Stock").

         4. Subject to the rights of the holders of any series of Preferred
Stock, any vacancies on the Board of Directors resulting from death,
resignation, disqualification, removal or other causes and any newly created
directorships resulting from any increase in the number of directors, shall,
unless the Board of Directors determines by resolution that any such vacancies
or newly created directorships shall be filled by the stockholders, be filled
only by the affirmative vote of a majority of the directors then in office, even
though less than a quorum of the Board of Directors, and not by the
stockholders. Any director elected in accordance with the preceding sentence
shall hold office for the remainder of the full term of the director for which
the vacancy was created or occurred and until such director's successor shall
have been elected and qualified.

         5. The Board of Directors shall designate and empower committees of the
Board of Directors, shall elect and empower the officers of the Corporation, may
appoint and empower other officers and agents of the Corporation, and shall
determine the time, place and notice of Board meetings, quorum and voting
requirements, and the manner of taking Board action. Subject to the other
provisions of this Article V, the Board of Directors shall determine the rights,
powers, duties, rules and procedures that shall affect the directors' power to
manage and direct the business and affairs of the Corporation. Notwithstanding
any other provision of this Certificate of Incorporation, the powers specified
in this Article V shall be exercised only by or under the direction of the Board
of Directors and may be exercised or expressed in the form of resolution, Bylaw
or other form of determination or exercise; and the form of the exercise of the
power shall not derogate the status of the power exercised or imply that such
exercise by the Board of Directors may be altered or superseded by any person,
group or entity other than the Board of Directors.

B.       1. Subject to paragraph (h) of Section 43 of the Bylaws, the Bylaws may
be altered or amended or new Bylaws adopted by the affirmative vote of at least
sixty-six and two-thirds percent (66-2/3%) of the voting power of all of the
then-outstanding shares of the Voting Stock. The Board of Directors shall also
have the power to adopt, amend, or repeal Bylaws.

         2. The directors of the Corporation need not be elected by written
ballot unless the Bylaws so provide.

         3. No action shall be taken by the stockholders of the Corporation
except at an annual or special meeting of stockholders called in accordance with
the Bylaws or by unanimous written consent of the stockholders.

         4. Special meetings of the stockholders of the Corporation may be
called, for any purpose or purposes, by (i) the Chairman of the Board of
Directors, (ii) the Chief Executive Officer, or (iii) the Board of Directors
pursuant to a resolution adopted by a
<PAGE>   4
majority of the total number of authorized directors (whether or not there exist
any vacancies in previously authorized directorships at the time any such
resolution is presented to the Board of Directors for adoption), and shall be
held at such place, on such date, and at such time as the Board of Directors
shall fix.

         5. Advance notice of stockholder nominations for the election of
directors and of business to be brought by stockholders before any meeting of
the stockholders of the Corporation shall be given in the manner provided in the
Bylaws of the Corporation.

                                       VI.

A.       A director of the Corporation shall not be personally liable to the
Corporation or its stockholders for monetary damages for any breach of fiduciary
duty as a director, except for liability (i) for any breach of the director's
duty of loyalty to the Corporation or its stockholders, (ii) for acts or
omissions not in good faith or that involve intentional misconduct or a knowing
violation of law (iii) under Section 174 of the Delaware General Corporation
Law, or (iv) for any transaction from which the director derived an improper
personal benefit. If the Delaware General Corporation Law is amended after
approval by the stockholders of this Article to authorize corporate action
further eliminating or limiting the personal liability of directors, then the
liability of a director shall be eliminated or limited to the fullest extent
permitted by the Delaware General Corporation Law, as so amended.

B.       Any repeal or modification of this Article VI shall be prospective and
shall not affect the rights under this Article VI in effect at the time of the
alleged occurrence of any act or omission to act giving rise to liability or
indemnification.

                                      VII.

A.       The Corporation reserves the right to amend, alter, change or repeal
any provision contained in this Certificate of Incorporation, in the manner now
or hereafter prescribed by statute, except as provided in Section B of this
Article VII, and all rights conferred upon the stockholders herein are granted
subject to this reservation.

B.       Notwithstanding any other provisions of this Certificate of
Incorporation or any provision of law that might otherwise permit a lesser vote
or no vote, but in addition to any affirmative vote of the holders of any
particular class or series of the Voting Stock required by law, this Certificate
of Incorporation or any Preferred Stock Designation, the affirmative vote of the
holders of at least sixty-six and two-thirds percent (66-2/3%) of the voting
power of all of the then-outstanding shares of the Voting Stock, voting together
as a single class, shall be required to alter, amend or repeal Articles V, VI
and VII.

         AS AMENDED by a Certificate of Amendment subscribed to the 15th day of
December, 1998.
<PAGE>   5
                            CERTIFICATE OF AMENDMENT
                     OF THE CERTIFICATE OF INCORPORATION OF
                          CELL PATHWAYS HOLDINGS, INC.

     Cell Pathways Holdings, Inc., a corporation organized and existing under
the General Corporation Law of the State of Delaware (the "Company"), hereby
certifies as follows:

     1.   The name of the Company is Cell Pathways Holdings, Inc.

     2.   Article I of the Certificate of Incorporation of the Company is
hereby amended in its entirety to read as follows:

                                      "I.

          The name of the corporation is Cell Pathways, Inc. (the
"Corporation")."

     3.   The foregoing amendment to the Certificate of Incorporation of the
Company has been duly adopted by the directors and stockholders of the Company
in accordance with the provisions of Sections 141, 228 and 242 of the General
Corporation Law of the State of Delaware. The amendment shall become effective
on November 3, 1998, at 4:30 p.m., Eastern Time.

     IN WITNESS WHEREOF, the Company has executed this Certificate of Amendment
on the 2nd day of November, 1998.

                                   CELL PATHWAYS HOLDINGS, INC.


                                   By: /s/ Robert J. Towarnicki
                                       ---------------------------
                                       Robert J. Towarnicki
                                       President and Chief Executive Officer