UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                    -----------------------------------------
                                AMENDMENT NO. 1
                                       to
                                  SCHEDULE 13G
                    Under the Securities Exchange Act of 1934
                    -----------------------------------------


                                   ENZON, INC.
                    -----------------------------------------
                                (Name of Issuer)


                     Common Stock, par value $0.01 per share
                   ------------------------------------------
                         (Title of Class of Securities)

                                    293904108
                                  -------------
                                 (CUSIP Number)


  Check  the  appropriate  box to  designate  the rule  pursuant  to which  this
Schedule is filed:

                                      [ ] Rule 13d-1(b)
                                      [x] Rule 13d-1(c)
                                      [ ] Rule 13d-1(d)

        *The  remainder  of this cover page shall be filled out for a  reporting
person's  initial  filing on this  form with  respect  to the  subject  class of
securities,  and for any subsequent amendment containing information which would
alter disclosures provided in a prior cover page.

        The  information  required in the remainder of this cover page shall not
be deemed to be "filed" for the purpose of Section 18 of the Securities Exchange
Act of 1934 ("Act") or otherwise  subject to the  liabilities of that section of
the Act but shall be subject to all other  provisions of the Act  (however,  see
the Notes to Schedule 13G).



                                        1



- ---------------------                                     ----------------------
CUSIP No.  293904108               13G/A                  Page 2 of 12 Pages
- ---------------------                                     ----------------------

- --------------------------------------------------------------------------------
1        NAMES OF REPORTING PERSONS
         S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

         Paramount Capital Asset Management, Inc.
- --------------------------------------------------------------------------------
2        CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP          (a)[ ] (b)[ ]

- --------------------------------------------------------------------------------
3        SEC USE ONLY

- --------------------------------------------------------------------------------
4        CITIZENSHIP OR PLACE OF ORGANIZATION
         Delaware
- --------------------------------------------------------------------------------
             NUMBER OF             5       SOLE VOTING POWER
              SHARES                       None  
                                   ---------------------------------------------
           BENEFICIALLY            6       SHARED VOTING POWER
             OWNED BY                      1,613,832
                                   ---------------------------------------------
               EACH                7       SOLE DISPOSITIVE POWER
             REPORTING                     None
                                   ---------------------------------------------
              PERSON               8       SHARED DISPOSITIVE POWER
               WITH                        1,613,832
- --------------------------------------------------------------------------------
9        AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
         1,613,832
- --------------------------------------------------------------------------------
10       CHECK BOX IF THE AGGREGATE AMOUNT IN ROW 11 EXCLUDES CERTAIN SHARES*
                                                                             [ ]

- --------------------------------------------------------------------------------
11       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)
         4.5%
- --------------------------------------------------------------------------------
12       TYPE OF REPORTING PERSON*
         CO
- --------------------------------------------------------------------------------




                                        2



- ---------------------                                     ----------------------
CUSIP No.  293904108               13G/A                  Page 3 of 12 Pages
- ---------------------                                     ----------------------

- --------------------------------------------------------------------------------
1        NAMES OF REPORTING PERSONS
         S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

         Aries Domestic Fund, L.P.
- --------------------------------------------------------------------------------
2        CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP          (a)[ ] (b)[ ]

- --------------------------------------------------------------------------------
3        SEC USE ONLY

- --------------------------------------------------------------------------------
4        CITIZENSHIP OR PLACE OF ORGANIZATION
         Delaware
- --------------------------------------------------------------------------------
             NUMBER OF             5       SOLE VOTING POWER
              SHARES                       None  
                                   ---------------------------------------------
           BENEFICIALLY            6       SHARED VOTING POWER
             OWNED BY                      448,564
                                   ---------------------------------------------
               EACH                7       SOLE DISPOSITIVE POWER
             REPORTING                     None
                                   ---------------------------------------------
              PERSON               8       SHARED DISPOSITIVE POWER
               WITH                        448,564
- --------------------------------------------------------------------------------
9        AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
         448,564
- --------------------------------------------------------------------------------
10       CHECK BOX IF THE AGGREGATE AMOUNT IN ROW 11 EXCLUDES CERTAIN SHARES*
                                                                             [ ]

- --------------------------------------------------------------------------------
11       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)
         1.2%
- --------------------------------------------------------------------------------
12       TYPE OF REPORTING PERSON*
         PN
- --------------------------------------------------------------------------------



                                        3



- ---------------------                                     ----------------------
CUSIP No.  293904108               13G/A                  Page 4 of 12 Pages
- ---------------------                                     ----------------------

- --------------------------------------------------------------------------------
1        NAMES OF REPORTING PERSONS
         S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

         The Aries Master Fund
- --------------------------------------------------------------------------------
2        CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP          (a)[ ] (b)[ ]

- --------------------------------------------------------------------------------
3        SEC USE ONLY

- --------------------------------------------------------------------------------
4        CITIZENSHIP OR PLACE OF ORGANIZATION
         Cayman Islands
- --------------------------------------------------------------------------------
             NUMBER OF             5       SOLE VOTING POWER
              SHARES                       None  
                                   ---------------------------------------------
           BENEFICIALLY            6       SHARED VOTING POWER
             OWNED BY                      1,165,268
                                   ---------------------------------------------
               EACH                7       SOLE DISPOSITIVE POWER
             REPORTING                     None
                                   ---------------------------------------------
              PERSON               8       SHARED DISPOSITIVE POWER
               WITH                        1,165,268
- --------------------------------------------------------------------------------
9        AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
         1,165,268
- --------------------------------------------------------------------------------
10       CHECK BOX IF THE AGGREGATE AMOUNT IN ROW 11 EXCLUDES CERTAIN SHARES*
                                                                             [ ]

- --------------------------------------------------------------------------------
11       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)
         3.2%
- --------------------------------------------------------------------------------
12       TYPE OF REPORTING PERSON*
         OO (see Item 2)
- --------------------------------------------------------------------------------



                                        4



- ---------------------                                     ----------------------
CUSIP No.  293904108               13G/A                  Page 5 of 12 Pages
- ---------------------                                     ----------------------

- --------------------------------------------------------------------------------
1        NAMES OF REPORTING PERSONS
         S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

         Lindsay A. Rosenwald, M.D.
- --------------------------------------------------------------------------------
2        CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP          (a)[ ] (b)[ ]

- --------------------------------------------------------------------------------
3        SEC USE ONLY

- --------------------------------------------------------------------------------
4        CITIZENSHIP OR PLACE OF ORGANIZATION
         United States
 -------------------------------------------------------------------------------
             NUMBER OF             5       SOLE VOTING POWER
              SHARES                       None  
                                   ---------------------------------------------
           BENEFICIALLY            6       SHARED VOTING POWER
             OWNED BY                      1,613,832
                                   ---------------------------------------------
               EACH                7       SOLE DISPOSITIVE POWER
             REPORTING                     None
                                   ---------------------------------------------
              PERSON               8       SHARED DISPOSITIVE POWER
               WITH                        1,613,832
- --------------------------------------------------------------------------------
9        AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
         1,613,832
- --------------------------------------------------------------------------------
10       CHECK BOX IF THE AGGREGATE AMOUNT IN ROW 11 EXCLUDES CERTAIN SHARES*
                                                                             [ ]

- --------------------------------------------------------------------------------
11       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)
         4.5%
- --------------------------------------------------------------------------------
12       TYPE OF REPORTING PERSON*
         IN
- --------------------------------------------------------------------------------




                                        5



Item 1.

        (a)           Name of Issuer:

                      Enzon, Inc.

        (b)           Address of Issuer's Principal Executive Offices:

                      Enzon, Inc.
                      20 Kingsbridge Rd.
                      Piscataway, NJ 08854-3969
                      732-980-5911

Item 2.

        (a)           Name of Person Filing:

                      This  statement  is filed on behalf of  Paramount  Capital
                      Asset  Management,   Inc.  ("Paramount  Capital"),   Aries
                      Domestic Fund, L.P. ("Aries  Domestic"),  The Aries Master
                      Fund, a Cayman  Islands  exempted  company  ("Aries Master
                      Fund"),  Lindsay A. Rosenwald,  M.D. ("Dr.  Rosenwald" and
                      collectively,  "Reporting Parties").  See attached Exhibit
                      A, which is a copy of their  agreement  in writing to file
                      this statement on behalf of each of them.

                      Dr. Rosenwald is an investment banker, venture capitalist,
                      fund manager and sole shareholder of Paramount  Capital, a
                      Subchapter  S   corporation   incorporated   in  Delaware.
                      Paramount   Capital  is  the  General   Partner  of  Aries
                      Domestic, a limited partnership  incorporated in Delaware,
                      and is the  Investment  Manager to Aries  Master  Fund,  a
                      Cayman Islands exempted company.

        (b)           Address  of  Principal   Business   Office  or,  if  None,
                      Residence:

                      Paramount Capital's,  Aries Domestic's and Dr. Rosenwald's
                      business  address is 787 Seventh Avenue,  48th Floor,  New
                      York,  New York,  10019.  The  business  address for Aries
                      Master Fund is c/o MeesPierson (Cayman) Limited,  P.O. Box
                      2003,  British American Centre,  Phase 3, Dr. Roy's Drive,
                      George Town, Grand Cayman.

        (c)           Citizenship:

                      Dr. Rosenwald is a citizen of the United States.

        (d)           Title of Class of Securities:

                      Common Stock, $0.01 par value ("Common Stock").

        (e)           CUSIP#:

                      293904108



                                        6



Item 3.               Check the box if this  statement is filed pursuant to Rule
                      13d-1(c)                                               [x]

Item 4.               Ownership:

                      For  information  concerning the ownership of Common Stock
                      of the  Company  by the  Reporting  Persons,  see  Items 5
                      through 9 and 11 of the cover pages to this  schedule 13G.

Item 5.               Ownership of Five Percent or Less of a Class:

                      As of the date of this filing,  the Reporting  Parties are
                      no  longer  the  beneficial  owners of more than 5% of the
                      Common Stock of the Issuer.

Item 6.               Ownership  of More than Five  Percent on Behalf of Another
                      Person:

                      Not applicable.

Item 7.               Identification  and Classification of the Subsidiary Which
                      Acquired  the  Security  Being  Reported  On By the Parent
                      Holding Company:

                      Not applicable.

Item 8.               Identification and Classification of Members of the Group:

                      Not applicable.

Item 9.               Notice of Dissolution of Group:

                      Not applicable.

Item 10.              Certification:

                      By  signing  below  I  certify  that,  to the  best  of my
        knowledge and belief, the securities referred to above were not acquired
        and are not held for the  purpose of or with the effect of  changing  or
        influencing  the  control of the issuer of the  securities  and were not
        acquired and are not held in connection  with or as a participant in any
        transaction having that purpose or effect.

               Material to be Filed as Exhibits:
               ---------------------------------

Exhibit A -    Copy  of  an  Agreement  between  Dr.  Rosenwald,  Paramount
               Capital,  Aries  Domestic  and  Aries  Master  Fund to file  this
               Statement on Schedule 13G on behalf of each of them.

Exhibit B -    List of executive officers and directors of Paramount Capital
               and  information  called  for  by  Items  2-6 of  this  statement
               relating to said officers and directors.

Exhibit C -    List of executive  officers and  directors of Aries  Domestic
               and  information  called  for  by  Items  2-6 of  this  statement
               relating to said officers and directors.

Exhibit D -    List of executive officers and directors of Aries Master Fund
               and  information  called  for  by  Items  2-6 of  this  statement
               relating to said officers and directors.



                                        7



                                   SIGNATURES
                                   ----------

               After  reasonable  inquiry  and to the best of my  knowledge  and
belief,  I certify  that the  information  set forth in this  statement is true,
complete and correct.


                                    PARAMOUNT CAPITAL ASSET MANAGEMENT, INC.

Dated:  February 16, 1999
        New York, NY                 By /s/ Lindsay A. Rosenwald, M.D.
                                        ------------------------------
                                        Lindsay A. Rosenwald, M.D.
                                        Chairman


                                    ARIES DOMESTIC FUND, L.P.
                                    By Paramount Capital Asset Management, Inc.
                                    General Partner

Dated:  February 16, 1999
        New York, NY                 By /s/ Lindsay A. Rosenwald, M.D.
                                        ------------------------------
                                        Lindsay A. Rosenwald, M.D.
                                        Chairman


                                    THE ARIES MASTER FUND
                                    By Paramount Capital Asset Management, Inc.
                                    Investment Manager

Dated:  February 16, 1999
        New York, NY                By /s/ Lindsay A. Rosenwald, M.D. 
                                       ------------------------------
                                       Lindsay A. Rosenwald, M.D.
                                       Chairman


Dated:  February 16, 1999
        New York, NY                By  /s/ Lindsay A. Rosenwald, M.D.  
                                        ------------------------------
                                        Lindsay A. Rosenwald, M.D.






                                        8



                                    EXHIBIT A

                                    AGREEMENT

                          JOINT FILING OF SCHEDULE 13G



               The  undersigned  hereby agrees to jointly  prepare and file with
regulatory  authorities  a  Schedule  13G  and  any  future  amendments  thereto
reporting each of the undersigned's  ownership of securities of Enzon, Inc., and
hereby  affirm  that such  Schedule  13G is being filed on behalf of each of the
undersigned.


                                    PARAMOUNT CAPITAL ASSET MANAGEMENT, INC.

Dated:  February 16, 1999
        New York, NY                 By /s/ Lindsay A. Rosenwald, M.D.
                                        ------------------------------
                                        Lindsay A. Rosenwald, M.D.
                                        Chairman


                                    ARIES DOMESTIC FUND, L.P.
                                    By Paramount Capital Asset Management, Inc.
                                    General Partner

Dated:  February 16, 1999
        New York, NY                 By /s/ Lindsay A. Rosenwald, M.D.
                                        ------------------------------
                                        Lindsay A. Rosenwald, M.D.
                                        Chairman


                                    THE ARIES MASTER FUND
                                    By Paramount Capital Asset Management, Inc.
                                    Investment Manager

Dated:  February 16, 1999
        New York, NY                By /s/ Lindsay A. Rosenwald, M.D. 
                                       ------------------------------
                                       Lindsay A. Rosenwald, M.D.
                                       Chairman


Dated:  February 16, 1999
        New York, NY                By  /s/ Lindsay A. Rosenwald, M.D.  
                                        ------------------------------
                                        Lindsay A. Rosenwald, M.D.




                                        9



                                    EXHIBIT B

        The name and principal occupation or employment,  which in each instance
is with Paramount Capital Asset Management,  Inc. ("Paramount  Capital") located
at 787 Seventh Avenue,  48th Floor, New York, New York, 10019, of each executive
officer and director of Paramount Capital is as follows:

PRINCIPAL OCCUPATION NAME OR EMPLOYMENT ---- ------------- Lindsay A. Rosenwald, M.D. Chairman of the Board of Paramount Capital Asset Management, Inc., Paramount Capital Investments LLC and Paramount Capital, Inc. Mark C. Rogers, M.D. President of Paramount Capital Asset Management, Inc., Paramount Capital Investments LLC and Paramount Capital, Inc. Peter Morgan Kash Director of Paramount Capital Asset Management, Inc., Inc., Senior Managing Director, Paramount Capital, Inc. Dr. Yuichi Iwaki Director of Paramount Capital Asset Management, Inc., Inc., Professor, University of Southern Califor nia School of Medicine
Item 2. During the five years prior to the date hereof, none of the above persons (to the best of Paramount Capital's knowledge) was convicted in a criminal proceeding (excluding traffic violations or similar misdemeanors) or was a party to a civil proceeding of a judicial or administrative body of competent jurisdiction, as a result of which such person was or is subject to a judgment, decree or final order enjoining future violations of, or prohibiting or mandating activities subject to, Federal or State securities laws or finding any violation with respect to such laws. Items 3-6. Please refer to Items 3-6 herein reporting the beneficial ownership. 10 EXHIBIT C The name and principal occupation or employment of the General Partner of Aries Domestic, which is located at 787 Seventh Avenue, 48th Floor, New York, New York, 10019, is as follows:
PRINCIPAL OCCUPATION NAME OR EMPLOYMENT ---- ------------- Paramount Capital Asset Management, Inc. General Partner; Investment Manager
Exhibit B is hereby incorporated by reference. Item 2. During the five years prior to the date hereof, the above person (to the best of Aries Domestic's knowledge) has not been convicted in a criminal proceeding (excluding traffic violations or similar misdemeanors) or was a party to a civil proceeding of a judicial or administrative body of competent jurisdiction, as a result of which such person was or is subject to a judgment, decree or final order enjoining future violations of, or prohibiting or mandating activities subject to, Federal or State securities laws or finding any violation with respect to such laws. Items 3-6. Please refer to Items 3-6 herein reporting the beneficial ownership. 11 EXHIBIT D The name and principal occupation or employment, which in the case of Paramount Capital Asset Management, Inc. is located at 787 Seventh Avenue, 48th Floor, New York, New York, 10019, of each executive officer and director of Aries Master Fund is as follows: PRINCIPAL OCCUPATION NAME OR EMPLOYMENT ---- ------------- Paramount Capital Asset Management, Inc. Investment Manager MeesPierson (Cayman) Limited Administrator P.O. Box 2003 British American Centre Phase 3, Dr. Roy's Drive George Town, Grand Cayman Exhibit B is hereby incorporated by reference. Item 2. During the five years prior to the date hereof, neither of the above persons (to the best of Aries Master Fund's knowledge) have been convicted in a criminal proceeding (excluding traffic violations or similar misdemeanors) or was a party to a civil proceeding of a judicial or administrative body of competent jurisdiction, as a result of which such person was or is subject to a judgment, decree or final order enjoining future violations of, or prohibiting or mandating activities subject to, Federal or State securities laws or finding any violation with respect to such laws. Items 3-6. Please refer to Items 3-6 herein reporting the beneficial ownership. 12