<PAGE>
 
                                                                     EXHIBIT 4.1

                                                                          Page 1

                               STATE OF DELAWARE

                       OFFICE OF THE SECRETARY OF STATE


     I, EDWARD J. FREEL, SECRETARY OF STATE OF THE STATE OF DELAWARE, DO HEREBY 

CERTIFY THE ATTACHED IS A TRUE AND CORRECT COPY OF THE CERTIFICATE OF 

INCORPORATION OF "ASCEND MEDICAL CORP.", FILED IN THIS OFFICE ON THE THIRTIETH 

DAY OF OCTOBER, A.D. 1992, AT 4:01 O'CLOCK P.M.







                                       /s/ EDWARD J. FREEL
                                       -----------------------------------
                                       Edware J. Freel, Secretary of State
       
                                       AUTHENTICATION:  8504081
                                                 DATE:  06-10-97
<PAGE>
 
SECRETARY OF STATE
DIVISION OF CORPORATIONS
FILED 04:01 PM 10/30/1992
722304186 - 2314505

                         CERTIFICATE OF INCORPORATION 
                                      OF
                             ASCEND MEDICAL CORP.


     THE UNDERSIGNED, for the purpose of forming a corporation pursuant to the 
provisions of the General Corporation Law of Delaware, does hereby certify as 
follows:

     FIRST:   The name of the Corporation is Ascend Medical Corp.

     SECOND:  The address of the Corporation's registered office in the State of
Delaware is 1209 Orange Street, Wilmington, New Castle County.  The name of the 
Corporation's registered agent at such address is The Corporation Trust Company.

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

     FOURTH:  The total number of shares of stock which the Corporation shall 
have authority to issue is two million (2,000,000) shares, divided into two 
classes consisting of one million (1,000,000) Preferred Shares; and the other 
class consisting of one million (1,000,000) Common Shares, each of which shall 
have the par value of $.01 per share.

     The Board of Directors of the Corporation shall have the power by 
resolution to (a) provide for the issuance of shares of preferred stock in 
series, (b) determine the number of shares of such stock in any such series, and
(c) fix the designations,
<PAGE>
 
preferences, qualifications, limitations, restrictions and special or relative 
rights of shares of preferred stock or any series thereof.

     FIFTH:   The name and mailing address of the incorporator is as follows:

                     Name                       Mailing Address
                     ----                       ---------------

              Kyle M. Fink, M.D.                c/o HOA
                                                2005 Franklin Street
                                                Suite 150
                                                Denver, Colorado 80205

     SIXTH:   In furtherance and not in limitation of the general powers 
conferred by the laws of the State of Delaware, the Board of Directors is 
expressly authorized to make, alter or repeal the Bylaws of the Corporation, 
except as specifically otherwise provided therein.

     SEVENTH: A director of the Corporation shall have no personal liability to 
the Corporation or its stockholders for monetary damages for breach of fiduciary
duty as a director except to the extent that Section 102(b)(7) (or any successor
provision) of the Delaware General Corporation Law, as amended from time to 
time, expressly provides that the liability of a director may not be eliminated 
or limited.

     EIGHTH:  Whenever a compromise or arrangement is proposed between this 
Corporation and its creditors or any class of them and/or between this 
Corporation and its stockholders or any class of them, any court of equitable 
jurisdiction within the State of Delaware may, on the application in a summary 
way of this Corporation or of any creditor or stockholder thereof or on


                                      -2-
<PAGE>
 
the application of any receiver or receivers appointed for this Corporation 
under the provisions of Section 291 of Title 8 of the Delaware Code or on the 
application of trustees in dissolution or of any receiver or receivers appointed
for this Corporation under the provisions of Section 279 of Title 8 of the 
Delaware Code, order a meeting of the creditors or class of creditors, and/or of
the stockholders or class of stockholders of this Corporation, as the case may 
be, to be summoned in such manner as the said court directs.  If a majority in 
number representing three-fourths in value of the creditors or class of 
creditors, and/or of the stockholders or class of stockholders of this 
Corporation, as the case may be, agree to any compromise or arrangement and to 
any reorganization of this Corporation as consequence of such compromise or 
arrangement, the said compromise or arrangement and the said reorganization 
shall, if sanctioned by the court to which the said application has been made, 
be binding on all the creditors or class of creditors, and/or on all the 
stockholders or class of stockholders of this Corporation, as the case may be, 
and also on this Corporation.

     NINTH:  The term of existence of the Corporation shall be perpetual.

     TENTH:  Any director or the entire Board of Directors may be removed, with 
or without cause, by the holders of a


                                      -3-
<PAGE>
 
majority of the shares entitled to vote at an election of directors.

     IN WITNESS WHEREOF, the undersigned, being the incorporator hereinabove 
named, does hereby execute this Certificate of Incorporation this 30th day of 
October, 1992.

                                            /s/ KYLE M. FINK, M.D.
                                            --------------------------------
                                            Kyle M. Fink, M.D., Incorporator


                                      -4-
<PAGE>
 
                                                                          PAGE 1
                               STATE OF DELAWARE

                       OFFICE OF THE SECRETARY OF STATE



     I, EDWARD J. FREEL, SECRETARY OF STATE OF THE STATE OF DELAWARE, DO HEREBY 

CERTIFY THE ATTACHED IS A TRUE AND CORRECT COPY OF THE CERTIFICATE OF 

AMENDMENT OF "ASCEND MEDICAL CORP.", CHANGING ITS NAME FROM "ASCEND MEDICAL 

CORP." TO "AMERICAN ONCOLOGY RESOURCES, INC.", FILED IN THIS OFFICE ON THE 

TWELFTH DAY OF NOVEMBER, A.D. 1992, AT 10 O'CLOCK A.M.





                                             /s/ EDWARD J. FREEL
                                             -----------------------------------
                                             Edward J. Freel, Secretary of State

                                             AUTHENTICATION:  8504080
                                                       DATE:  06-10-97
<PAGE>
 
STATE OF DELAWARE
SECRETARY OF STATE
DIVISION OF CORPORATIONS
FILED 10:00 AM 11/12/1992
722317047 - 2314505


                           CERTIFICATE OF AMENDMENT
                                      OF
                         CERTIFICATE OF INCORPORATION
                                      OF
                             ASCEND MEDICAL CORP.


     Ascend Medical Corp., a corporation organized and existing under and by 
virtue of the General Corporation Law of the State of Delaware, does hereby 
certify:

     FIRST:  That the Sole Director of the corporation, by written consent, 
filed with the minutes of the Board, adopted a resolution proposing and 
declaring advisable the following amendment to the Certificate of Incorporation 
of the corporation:

             RESOLVED, that the amendment of Article FIRST of the Corporation's
     Certificate of Incorporation to read in its entirety as follows (the
     "Amendment") is hereby proposed and declared to be advisable and in the
     best interests of the Corporation:

             "FIRST, the name of the corporation is AMERICAN ONCOLOGY 
     RESOURCES, INC."

     SECOND:  That the sole stockholder has given a written consent to said 
amendment in accordance with the provisions of Section 228 of the General 
Corporation Law of the State of Delaware.

     THIRD:  That the amendment has been duly adopted in accordance with the 
provisions of Section 242 and 228 of the General Corporation Law of the State of
Delaware.

      IN WITNESS WHEREOF, the corporation has caused its corporate seal to be 
hereunto affixed and this certificate to be signed by its President and attested
by its Secretary, this 10th day of November, 1992.

                                            ASCEND MEDICAL CORP.


                                                  /s/ KYLE M. FINK, M.D.       
                                            BY: ------------------------------ 
                                                Kyle M. Fink, M.D., President   
                                               


                                                 /s/ KYLE M. FINK, M.D.
                                        ATTEST: ------------------------------ 
                                                Kyle M. Fink, M.D., Secretary




<PAGE>
 
                                                                          PAGE 1
                               STATE OF DELAWARE

                       OFFICE OF THE SECRETARY OF STATE



     I, EDWARD J. FREEL, SECRETARY OF STATE OF THE STATE OF DELAWARE, DO HEREBY 

CERTIFY THE ATTACHED IS A TRUE AND CORRECT COPY OF THE CERTIFICATE OF AMENDMENT 

OF "AMERICAN ONCOLOGY RESOURCES, INC.", FILED IN THIS OFFICE ON THE TENTH DAY OF

MARCH, A.D. 1994, AT 9 O'CLOCK A.M.







                                            /s/ EDWARD J. FREEL
                                            ------------------------------------
                                            Edward  J. Freel, Secretary of State

                                            AUTHENTICATION:  8504078
                                                      DATE:  06-10-97
<PAGE>
 

                                                           STATE OF DELAWARE
                                                          SECRETARY OF STATE
                                                       DIVISION OF CORPORATIONS
                                                      FILED 09:00  AM 03/10/1994
                                                          944037641 - 2314505

                           CERTIFICATE OF AMENDMENT
                                      OF
                         CERTIFICATE OF INCORPORATION
                                      OF
                       AMERICAN ONCOLOGY RESOURCES, INC.


     It is hereby certified that:

     1.  The name of the corporation (hereinafter called the "Corporation") is
AMERICAN ONCOLOGY RESOURCES, INC.

     2.  The certificate of incorporation of the Corporation is hereby amended
by striking out the first paragraph of the fourth article thereof and by
substituting in lieu of said paragraph the following new paragraph:

          "The total number of shares of capital stock which the Corporation
          shall have authority to issue is twenty-six million (26,000,000)
          shares, consisting of one million (1,000,000) shares of preferred
          stock, par value $.01 per share, and twenty-five million (25,000,000)
          shares of common stock, par value $.01 per share."

     3.   The amendment of the certificate of incorporation herein certified has
been duly adopted in accordance with the provisions of Section 228 and 242 of
the General Corporation Law of the State of Delaware.  The holders of a majority
of outstanding stock entitled to vote thereon, by written consent in accordance
with the provisions of Section 228 of the General Corporation Law of the State
of Delaware, voted in favor of the amendment.  Prompt written notice of the
adoption of the amendment herein certified has been given to those stockholders
who have not consented in writing thereto, as provided in Section 228 of the
General Corporation Law of the State of Delaware.

     IN WITNESS WHEREOF, the Corporation has caused this certificate to be
signed by its Chairman of the Board and Chief Executive Officer and attested to
by its Secretary, this 9th day of March, 1994.

                              AMERICAN ONCOLOGY RESOURCES, INC.


                              By:/s/ R. Dale Ross
                                 -------------------------------------------
                                     R. Dale Ross, Chairman of the Board and
                                     Chief Executive Officer

ATTEST:


/s/ Leo E. Sands
-----------------------
Leo E. Sands, Secretary
<PAGE>
 
                                                                          PAGE 1
                               STATE OF DELAWARE

                       OFFICE OF THE SECRETARY OF STATE



     I, EDWARD J. FREEL, SECRETARY OF STATE OF THE STATE OF DELAWARE, DO HEREBY 

CERTIFY THE ATTACHED IS A TRUE AND CORRECT COPY OF THE CERTIFICATE OF AMENDMENT 

OF "AMERICAN ONCOLOGY RESOURCES, INC.", FILED IN THIS OFFICE ON THE SECOND DAY 

OF MAY, A.D. 1995, AT 3:30 O'CLOCK P.M.






                                            /s/ EDWARD J. FREEL
                                            ------------------------------------
                                            Edward  J. Freel, Secretary of State

                                            AUTHENTICATION:  8504077
                                                      DATE:  06-10-97

<PAGE>
 
    STATE OF DELAWARE
   SECRETARY OF STATE
 DIVISION OF CORPORATIONS
FILED 03:30 PM 05/02/1995
   950096983 - 2314505
                           CERTIFICATE OF AMENDMENT
                                      OF
                         CERTIFICATE OF INCORPORATION
                                      OF
                       AMERICAN ONCOLOGY RESOURCES, INC.


     It is hereby certified that:

     1.  The name of the corporation (hereinafter called the "Corporation") is
AMERICAN ONCOLOGY RESOURCES, INC.

     2.  The certificate of incorporation of the Corporation is hereby amended
by striking out the first paragraph of the fourth article thereof and by
substituting in lieu of said paragraph the following new paragraph:

          "The total number of shares of capital stock which the Corporation
          shall have authority to issue is forty-one million (41,000,000)
          shares, consisting of one million (1,000,000) shares of preferred
          stock, par value $.01 per share, and forty million (40,000,000) shares
          of common stock, par value $.01 per share."

     3.   The amendment of the certificate of incorporation herein certified has
been duly adopted in accordance with the provisions of Section 228 and 242 of
the General Corporation Law of the State of Delaware.  The holders of a majority
of outstanding stock entitled to vote thereon, by written consent in accordance
with the provisions of Section 228 of the General Corporation Law of the State
of Delaware, voted in favor of the amendment.  Prompt written notice of the
adoption of the amendment herein certified has been given to those stockholders
who have not consented in writing thereto, as provided in Section 228 of the
General Corporation Law of the State of Delaware.

     IN WITNESS WHEREOF, the Corporation has caused this certificate to be
signed by its Chairman of the Board and Chief Executive Officer and attested to
by its Secretary, this 2nd day of May, 1995.

                              AMERICAN ONCOLOGY RESOURCES, INC.


                              By:/s/ R. Dale Ross
                                 -------------------------------------------
                                     R. Dale Ross, Chairman of the Board and
                                     Chief Executive Officer

ATTEST:


/s/ Leo E. Sands
-----------------------
Leo E. Sands, Secretary
<PAGE>
 
                                                                          PAGE 1
                               STATE OF DELAWARE

                       OFFICE OF THE SECRETARY OF STATE



     I, EDWARD J. FREEL, SECRETARY OF STATE OF THE STATE OF DELAWARE, DO HEREBY 

CERTIFY THE ATTACHED IS A TRUE AND CORRECT COPY OF THE CERTIFICATE OF AMENDMENT 

OF "AMERICAN ONCOLOGY RESOURCES, INC.", FILED IN THIS OFFICE ON THE TENTH DAY OF

MAY, A.D. 1996, AT 9 O'CLOCK A.M.







                                            /s/ EDWARD J. FREEL
                                            ------------------------------------
                                            Edward  J. Freel, Secretary of State

                                            AUTHENTICATION:  8504076
                                                      DATE:  06-10-97


<PAGE>
 
                                                          STATE OF DELAWARE
                                                         SECRETARY OF STATE
                                                       DIVISION OF CORPORATIONS
                                                      FILED 09:00  AM 05/10/1996
                                                         960136590 - 2314505


                           CERTIFICATE OF AMENDMENT
                                      OF
                         CERTIFICATE OF INCORPORATION
                                      OF
                       AMERICAN ONCOLOGY RESOURCES, INC.


     It is hereby certified that:

     1.  The name of the corporation (hereinafter called the "Corporation") is
AMERICAN ONCOLOGY RESOURCES, INC.

     2.  The certificate of incorporation of the Corporation is hereby amended
by striking out the first paragraph of the fourth article thereof and by
substituting in lieu of said paragraph the following new paragraph:

          "The total number of shares of capital stock which the Corporation
          shall have authority to issue is sixty-one million (61,000,000)
          shares, consisting of one million (1,000,000) shares of preferred
          stock, par value $.01 per share, and sixty million (60,000,000) shares
          of common stock, par value $.01 per share."

     3.   The amendment of the certificate of incorporation herein certified has
been duly adopted in accordance with the provisions of Section 242 of the
General Corporation Law of the State of Delaware; the amendment was duly adopted
by resolution of the Board of Directors on February 8, 1996, and the necessary
shares as required by statute were voted in favor of the amendment of the Annual
Meeting of Stockholders held on May 9, 1996.

     IN WITNESS WHEREOF, the Corporation has caused this certificate to be
signed by its Chairman of the Board and Chief Executive Officer and attested to
by its Secretary, this 9th day of May, 1996.

                              AMERICAN ONCOLOGY RESOURCES, INC.


                              By:/s/ R. Dale Ross
                                 -------------------------------------------
                                     R. Dale Ross, Chairman of the Board and
                                     Chief Executive Officer

ATTEST:


/s/ Leo E. Sands
-----------------------
Leo E. Sands, Secretary
<PAGE>
 
                                                                          PAGE 1
                               STATE OF DELAWARE

                       OFFICE OF THE SECRETARY OF STATE



     I, EDWARD J. FREEL, SECRETARY OF STATE OF THE STATE OF DELAWARE, DO HEREBY 

CERTIFY THE ATTACHED IS A TRUE AND CORRECT COPY OF THE CERTIFICATE OF AMENDMENT 

OF "AMERICAN ONCOLOGY RESOURCES, INC.", FILED IN THIS OFFICE ON THE EIGHTH DAY 

OF MAY, A.D. 1997, AT 9 O'CLOCK A.M.







                                            /s/ EDWARD J. FREEL
                                            ------------------------------------
                                            Edward  J. Freel, Secretary of State

                                            AUTHENTICATION:  8504075
                                                      DATE:  06-10-97


<PAGE>
 
                           CERTIFICATE OF AMENDMENT
                                      OF
                         CERTIFICATE OF INCORPORATION
                                      OF
                       AMERICAN ONCOLOGY RESOURCES, INC.


     It is hereby certified that:

     1.  The name of the corporation (hereinafter called the "Corporation") is
AMERICAN ONCOLOGY RESOURCES, INC.

     2.  The certificate of incorporation of the Corporation is hereby amended
by striking out the first paragraph of the fourth article thereof and by
substituting in lieu of said paragraph the following new paragraph:

          "The total number of shares of capital stock which the Corporation
          shall have authority to issue is eighty-one million (81,000,000)
          shares, consisting of one million (1,000,000) shares of preferred
          stock, par value $.01 per share, and eighty million (80,000,000)
          shares of common stock, par value $.01 per share."

     3.   The amendment of the certificate of incorporation herein certified has
been duly adopted in accordance with the provisions of Section 242 of the
General Corporation Law of the State of Delaware; the amendment was duly adopted
by resolution of the Board of Directors on February 8, 1997, and the necessary
shares as required by statute were voted in favor of the amendment of the Annual
Meeting of Stockholders held on May 8, 1997.

     IN WITNESS WHEREOF, the Corporation has caused this certificate to be
signed by its Chairman of the Board and Chief Executive Officer and attested to
by its Secretary, this 8th day of May, 1997.

                              AMERICAN ONCOLOGY RESOURCES, INC.


                              By: /s/ R. Dale Ross
                                 --------------------------------------------
                                      R. Dale Ross, Chairman of the Board and
                                      Chief Executive Officer

ATTEST:

/s/ Leo E. Sands
----------------------- 
Leo E. Sands, Secretary


                                                          STATE OF DELAWARE
                                                         SECRETARY OF STATE
                                                       DIVISION OF CORPORATIONS
                                                      FILED 09:00  AM 05/08/1997
                                                         971151417 - 2314505

<PAGE>
 
                                                                          PAGE 1
                               STATE OF DELAWARE

                       OFFICE OF THE SECRETARY OF STATE



     I, EDWARD J. FREEL, SECRETARY OF STATE OF THE STATE OF DELAWARE, DO HEREBY 

CERTIFY THE ATTACHED IS A TRUE AND CORRECT COPY OF THE CERTIFICATE OF 

DESIGNATION OF "AMERICAN ONCOLOGY RESOURCES, INC.", FILED IN THIS OFFICE ON THE

SECOND DAY OF JUNE, A.D. 1997, AT 12:30 O'CLOCK P.M.







                                            /s/ EDWARD J. FREEL
                                            ------------------------------------
                                            Edward  J. Freel, Secretary of State

                                            AUTHENTICATION:  8504074
                                                      DATE:  06-10-97


<PAGE>
 
                                                           STATE OF DELAWARE
                                                          SECRETARY OF STATE
                                                       DIVISION OF CORPORATIONS
                                                      FILED 12:30 PM 06/02/1997
                                                         971178271 - 2314505


                          CERTIFICATE OF DESIGNATIONS,
               PREFERENCES AND RIGHTS OF SERIES A PREFERRED STOCK
                                       of
                       AMERICAN ONCOLOGY RESOURCES, INC.


                          (Pursuant to Section 151(g)
                    of the Delaware General Corporation Law)

     It is hereby certified that:

     1.  The name of the corporation is AMERICAN ONCOLOGY RESOURCES, INC.
(hereinafter called the "Corporation").

     2.  That, pursuant to the authority conferred upon the Board of Directors
by the Certificate of Incorporation, as amended to date, of the said Corporation
and pursuant to the provisions of Section 151(a) of the Delaware General
Corporation Law, the Board of Directors on May 16, 1997 duly adopted, by all
necessary action on the part of the Corporation, the following resolution
creating a series of five-hundred thousand (500,000) shares of Preferred Stock
designated as Series A Preferred Stock;
<PAGE>
 
     RESOLVED, that pursuant to the authority granted to and vested in the Board
of Directors of this Corporation in accordance with the provisions of the
Certificate of Incorporation, the Board of Directors hereby creates a series of
Series A Preferred Stock, with a par value of $.01 per share, of the Corporation
and hereby states the designation and number of shares, and fixes the relative
rights, preferences and limitations thereof (in addition to the provisions set
forth in the Certificate of Incorporation which are applicable to the Preferred
Stock of all classes and series) as follows:

     SERIES A PREFERRED STOCK

     Section 1.  Designation, Par Value and Amount.  The shares of such series
shall be designated as "Series A Preferred Stock" (hereinafter referred to as
"Series A Preferred Stock"), the shares of such series shall be with par value
of $.01 per share, and the number of shares constituting such series shall be
500,000; provided, however, that, if more than a total of 500,000 shares of
Series A Preferred Stock shall be issuable upon the exercise of Rights (the
"Rights") issued pursuant to the Rights Agreement, dated as of May 29, 1997
between the Corporation and American Stock Transfer & Trust Company, as Rights
Agent (as amended from time to time) (the "Rights Agreement"), the Board of
Directors of the Corporation, pursuant to Section 151(a) of the Delaware General
Corporation Law, shall direct by resolution or resolutions that a certificate be
properly executed, acknowledged and filed providing for the total number of
shares of Series A Preferred Stock authorized to be issued to be increased (to
the extent that the Certificate of Incorporation then permits) to the largest
number of whole shares (rounded up to the nearest whole number) issuable upon
exercise of the Rights.

                                      A-2
<PAGE>
 
     Section 2.  Dividends and Distributions.

     (A)  Subject to the prior and superior rights of the holders of any shares
of any series of Preferred Stock ranking prior and superior to the shares of
Series A Preferred Stock with respect to dividends, the holders of shares of
Series A Preferred Stock shall be entitled to receive, when, as and if declared
by the Board of Directors out of assets legally available for the purpose,
quarterly dividends payable in cash on the first business day of January, April,
July and October in each year (each such date being referred to herein as a
"Quarterly Dividend Payment Date"), commencing on the first Quarterly Dividend
Payment Date after the first issuance of a share or fraction of a share of
Series A Preferred Stock, in an amount per share (rounded to the nearest cent)
equal to the greater of (a) $10.00 or (b) subject to the provision for
adjustment hereinafter set forth, 1,000 times the aggregate per share amount of
all cash dividends, and 1,000 times the aggregate per share amount (payable in
kind) of all non-cash dividends or other distributions other than a dividend
payable in shares of Common Stock, par value $.01 per share, of the Corporation
(the "Common Stock") or a subdivision of the outstanding shares of Common Stock
(by reclassification or otherwise), declared on the Common Stock since the
immediately preceding Quarterly Dividend Payment Date, or, with respect to the
first Quarterly Dividend Payment Date, since the first issuance of any share or
fraction of a share of Series A Preferred Stock.

     (B)  The Corporation shall declare a dividend or distribution on the Series
A Preferred Stock as provided in paragraph (A) above immediately after it
declares a dividend or distribution on the Common Stock (other than a dividend
payable in shares of Common Stock); provided that, in the event no dividend or
distribution shall have been declared on the Common Stock

                                      A-3
<PAGE>
 
during the period between any Quarterly Dividend Payment Date and the next
subsequent Quarterly Dividend Payment Date, a dividend of $10.00 per share on
the Series A Preferred Stock shall nevertheless be payable on such subsequent
Quarterly Dividend Payment Date.

     (C)  Dividends shall begin to accrue and be cumulative on outstanding
shares of Series A Preferred Stock from the Quarterly Dividend Payment Date next
preceding the date of issue of such shares of Series A Preferred Stock, unless
the date of issue of such shares is prior to the record date for the first
Quarterly Dividend Payment Date, in which case dividends on such shares shall
begin to accrue from the date of issue of such shares, or unless the date of
issue is a Quarterly Dividend Payment Date or is a date after the record date
for the determination of holders of shares of Series A Preferred Stock entitled
to receive a quarterly dividend and before such Quarterly Dividend Payment Date,
in either of which events such dividends shall begin to accrue and be cumulative
from such Quarterly Dividend Payment Date.  Accrued but unpaid dividends shall
not bear interest.  Dividends paid on the shares of Series A Preferred Stock in
an amount less than the total amount of such dividends at the time accrued and
payable on such shares shall be allocated pro rata on a share by share basis
among all such shares at the time outstanding.  The Board of Directors may fix a
record date for the determination of holders of shares of Series A Preferred
Stock entitled to receive payment of a dividend or distribution declared
thereon, which record date shall be not more than 30 days prior to the date
fixed for the payment thereof.

                                      A-4
<PAGE>
 
     Section 3.  Voting Rights.  The holders of shares of Series A Preferred
Stock shall have the following voting rights:

     (A)  Except as provided in paragraph C of this Section 3 and subject to the
provision for adjustment hereinafter set forth, each share of Series A Preferred
Stock shall entitle the holder thereof to 1,000 votes on all matters submitted
to a vote of the stockholders of the Corporation.

     (B)  Except as otherwise provided herein or by law, the holders of shares
of Series A Preferred Stock and the holders of shares of Common Stock shall vote
together as one class on all matters submitted to a vote of stockholders of the
Corporation.

     (C)  (i) If, on the date used to determine stockholders of record for any
meeting of stockholders for the election of directors, a default in preference
dividends (as defined in subparagraph (v) below) on the Series A Preferred Stock
shall exist, the holders of the Series A Preferred Stock shall have the right,
voting as a class as described in subparagraph (ii) below, to elect two
directors (in addition to the directors elected by holders of Common Stock of
the Corporation).  Such right may be exercised (a) at any meeting of
stockholders for the election of directors or (b) at a meeting of the holders of
shares of Voting Preferred Stock (as hereinafter defined), called for the
purpose in accordance with the Bylaws of the Corporation, until all such
cumulative dividends (referred to above) shall have been paid in full or until
non-cumulative dividends have been paid regularly for at least one year.

     (ii)  The right of the holders of Series A Preferred Stock to elect two
directors, as described above, shall be exercised as a class concurrently with
the rights of holders of any other series of Preferred Stock upon which voting
rights to elect such directors have been conferred and are then exercisable.
The Series A Preferred Stock and any additional series of Preferred

                                      A-5
<PAGE>
 
Stock which the Corporation may issue and which may provide for the right to
vote with the foregoing series of Preferred Stock are collectively referred to
herein as "Voting Preferred Stock."

     (iii) Each director elected by the holders of shares of Voting Preferred
Stock shall be referred to herein as a "Preferred Director."  A Preferred
Director so elected shall continue to serve as such director for a term of one
year, except that upon any termination of the right of all of such holders to
vote as a class for Preferred Directors, the term of office of such directors
shall terminate.  Any Preferred Director may be removed by, and shall not be
removed except by, the vote of the holders of record of a majority of the
outstanding shares of Voting Preferred Stock then entitled to vote for the
election of directors present (in person or by proxy) and voting together as a
single class (a) at a meeting of the stockholders, or (b) at a meeting of the
holders of shares of such Voting Preferred Stock, called for such purpose in
accordance with the Bylaws of the Corporation, or (c) by written consent signed
by the holders of a majority of the then outstanding shares of Voting Preferred
Stock then entitled to vote for the election of directors, taken together as a
single class.

     (iv)  So long as a default in any preference dividends on the Series A
Preferred Stock shall exist or the holders of any other series of Voting
Preferred Stock shall be entitled to elect Preferred Directors, (a) any vacancy
in the office of a Preferred Director may be filled (except as provided in the
following clause (b)) by an instrument in writing signed by the remaining
Preferred Director and filed with the Corporation and (b) in the case of the
removal of any Preferred Director, the vacancy may be filled by the vote or
written consent of the holders of a majority of the outstanding shares of Voting
Preferred Stock then entitled to vote for the

                                      A-6
<PAGE>
 
election of directors, present (in person or by proxy) and voting together as a
single class, at such time as the removal shall be effected.  Each director
appointed as aforesaid by the remaining Preferred Director shall be deemed, for
all purposes hereof, to be a Preferred Director.  Whenever (x) no default in
preference dividends on the Series A Preferred Stock shall exist and (y) the
holders of other series of Voting Preferred Stock shall no longer be entitled to
elect such Preferred Directors, then the number of directors constituting the
Board of Directors of the Corporation shall be reduced by two.

     (v)  For purposes hereof, a "default in preference dividends" on the Series
A Preferred Stock shall be deemed to have occurred whenever the amount of
cumulative and unpaid dividends on the Series A Preferred Stock shall be
equivalent to six full quarterly dividends or more (whether or not consecutive),
and, having so occurred, such default shall be deemed to exist thereafter until,
but only until, all cumulative dividends on all shares of the Series A Preferred
Stock then outstanding shall have been paid through the last Quarterly Dividend
Payment Date or until, but only until, non-cumulative dividends have been paid
regularly for at least one year.

     (E)  Except as set forth herein (or as otherwise required by applicable
law), holders of Series A Preferred Stock shall have no general or special
voting rights and their consent shall not be required for taking any corporate
action.

     Section 4.  Certain Restrictions.

     (A)  Whenever quarterly dividends or other dividends or distributions
payable on the Series A Preferred Stock as provided in Section 2 are in arrears,
thereafter and until all accrued

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<PAGE>
 
and unpaid dividends and distributions, whether or not declared, on shares of
Series A Preferred Stock outstanding shall have been paid in full, the
Corporation shall not:

     (i)  declare or pay dividends, or make any other distributions, on any
shares of stock ranking junior (either as to dividends or upon liquidation,
dissolution or winding up) to the Series A Preferred Stock;

     (ii)  declare or pay dividends, or make any other distributions, on any
shares of stock ranking on a parity (either as to dividends or upon liquidation,
dissolution or winding up) with the Series A Preferred Stock, except dividends
paid ratably on the Series A Preferred Stock and all such parity stock on which
dividends are payable or in arrears in proportion to the total amounts to which
the holders of all such shares are then entitled;

     (iii) redeem or purchase or otherwise acquire for consideration (except as
provided in (iv) below) shares of any stock ranking junior (either as to
dividends or upon liquidation, dissolution or winding up) to the Series A
Preferred Stock, provided that the Corporation may at any time redeem, purchase
or otherwise acquire shares of any such junior stock in exchange for shares of
any stock of the Corporation ranking junior (either as to dividends or upon
dissolution, liquidation or winding up) to the Series A Preferred Stock;

     (iv) redeem or purchase or otherwise acquire for consideration any shares
of Series A Preferred Stock, or any shares of stock ranking on a parity (either
as to dividends or upon liquidation, dissolution or winding up) with the Series
A Preferred Stock, except in accordance with a purchase offer made in writing or
by publication (as determined by the Board of Directors) to all holders of such
shares upon such terms as the Board of Directors, after consideration of the
respective annual dividend rates and other relative rights and preferences

                                      A-8
<PAGE>
 
of the respective series and classes, shall determine in good faith will result
in fair and equitable treatment among the respective series or classes.

     (B)  The Corporation shall not permit any subsidiary of the Corporation to
purchase or otherwise acquire for consideration any shares of stock of the
Corporation unless the Corporation could, under paragraph (A) of this Section 4,
purchase or otherwise acquire such shares at such time and in such manner.

     Section 5.  Reacquired Shares.  Any shares of Series A Preferred Stock
purchased or otherwise acquired by the Corporation in any manner whatsoever
shall be retired and cancelled promptly after the acquisition thereof.  All such
shares shall upon their cancellation become authorized but unissued shares of
Preferred Stock and may be reissued as part of a new series of Preferred Stock
subject to the conditions and restrictions on issuance set forth herein, in the
Certificate of Incorporation, in any other Certificate of Designation creating a
series of Preferred Stock or as otherwise required by law.

     Section 6.  Liquidation, Dissolution or Winding Up.

     (A) Subject to the prior and superior rights of holders of any shares of
any series of Preferred Stock ranking prior and superior to the shares of Series
A Preferred Stock with respect to rights upon liquidation, dissolution or
winding up (voluntary or otherwise), no distribution shall be made to the
holders of shares of stock ranking junior (either as to dividends or upon
liquidation, dissolution or winding up) to the Series A Preferred Stock unless,
prior thereto, the holders of shares of Series A Preferred Stock shall have
received $1,000 per share, plus an amount equal to accrued and unpaid dividends
and distributions thereon, whether or not declared, to the date of such payment
(the "Series A Liquidation Preference").  Following the

                                      A-9
<PAGE>
 
payment of the full amount of the Series A Liquidation Preference, no additional
distributions shall be made to the holders of shares of Series A Preferred Stock
unless, prior thereto, the holders of shares of Common Stock shall have received
an amount per share (the "Capital Adjustment") equal to the quotient obtained by
dividing (i) the Series A Liquidation Preference by (ii) (such number in clause
(ii), the "Adjustment Number").  Following the payment of the full amount of the
Series A Liquidation Preference and the Capital Adjustment in respect of all
outstanding shares of Series A Preferred Stock and Common Stock, respectively,
holders of Series A Preferred Stock and holders of Common Stock shall receive
their ratable and proportionate share of the remaining assets to be distributed
in the ratio of the Adjustment Number to 1 with respect to such Preferred Stock
and Common Stock, on a per share basis, respectively.

     (B) In the event, however, that there are not sufficient assets available
to permit payment in full of the Series A Liquidation Preference and the
liquidation preferences of all other series of preferred stock, if any, which
rank on a parity with the Series A Preferred Stock, then such remaining assets
shall be distributed ratably to the holders of Series A Preferred Stock and the
holders of such parity shares in proportion to their respective liquidation
preferences.  In the event, however, that there are not sufficient assets
available to permit payment in full of the Capital Adjustment, then such
remaining assets shall be distributed ratably to the holders of Common Stock.

     Section 7.  Consolidation, Merger, etc.  In case the Corporation shall
enter into any consolidation, merger, combination or other transaction in which
the shares of Common Stock are exchanged for or changed into other stock or
securities, cash and/or any other property, then

                                     A-10
<PAGE>
 
in any such case the shares of Series A Preferred Stock shall at the same time
be similarly exchanged or changed in an amount per share (subject to the
provision for adjustment hereinafter set forth) equal to 1,000 times the
aggregate amount of stock, securities, cash and/or any other property (payable
in kind), as the case may be, into which or for which each share of Common Stock
is changed or exchanged.

     Section 8.  No Redemption.  The shares of Series A Preferred Stock shall
not be redeemable.

     Section 9.  Ranking.  The Series A Preferred Stock shall rank junior to all
other series of the Corporation's Preferred Stock as to the payment of dividends
and the distribution of assets, unless the terms of any such series shall
provide otherwise.

     Section 10.  Amendment.  The Certificate of Incorporation of the
Corporation shall not be further amended in any manner which would materially
alter or change the powers, preferences or special rights of the Series A
Preferred Stock so as to affect them adversely without the affirmative vote of
the holders of a majority or more of the outstanding shares of Series A
Preferred Stock, voting separately as a class.

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<PAGE>
 
     IN WITNESS WHEREOF, this Certificate of Designations is executed on behalf
of the Corporation by its Chairman of the Board and Chief Executive Officer this
29th day of May, 1997.


                              AMERICAN ONCOLOGY RESOURCES, INC.

                              By: /s/ R. Dale Ross
                                 ----------------------------------------------
                              R. Dale Ross
                              Chairman of the Board and Chief Executive Officer


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