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                                                                  EXHIBIT 4.9(b)


                               SECOND AMENDMENT TO
                        STERLING CHEMICALS HOLDINGS, INC.
                             STOCKHOLDERS AGREEMENT

              THIS SECOND AMENDMENT TO STERLING CHEMICALS HOLDINGS, INC.
STOCKHOLDERS AGREEMENT (this "Amendment") dated effective as of May 1, 1998 is
by and among STERLING CHEMICALS HOLDINGS, INC., a Delaware corporation (the
"Corporation"), STERLING CHEMICALS, INC. EMPLOYEE STOCK OWNERSHIP TRUST, an
employee stock ownership trust created pursuant to the Sterling Chemicals, Inc.,
Employee Stock Ownership Plan (the "ESOT"), and the other persons and entities
whose signatures appear on the signature pages hereof (the "Other Parties" and,
together with the Corporation and the ESOT, the "Parties"). Capitalized terms
used but not defined herein shall have the respective meanings ascribed to such
terms in the Existing Agreement referred to below.

                             PRELIMINARY STATEMENTS

       A.     The Parties, together with certain other Holders, are parties to
              that certain Sterling Chemicals Holdings, Inc. Stockholders
              Agreement dated effective as of August 21, 1996 (the "Original
              Agreement").

       B.     The Original Agreement was amended by that certain First Amendment
              to Sterling Chemicals Holdings, Inc. Stockholders Agreement dated
              effective as of December 31, 1997 (the Original Agreement, as so
              amended, the "Existing Agreement").

       C.     The Parties desire to amend the Existing Agreement in certain
              respects in order to exclude certain shares of Stock from the
              coverage of the Existing Agreement.

              NOW, THEREFORE, in consideration of the premises and the mutual
covenants contained herein and in the Existing Agreement, and for other good and
valuable consideration, the receipt and sufficiency of which are hereby
acknowledged, the parties hereto, intending to be legally bound, hereby agree as
follows:

              Section 1. Amendment of Section 2.16 of the Existing Agreement.
Section 2.16 of the Existing Agreement is hereby amended to read in its entirety
as follows:

              2.16. Except as provided below, the term "Stock" shall mean (1)
       all shares of Common Stock owned by each Holder and the ESOT on the
       Effective Date; (2) all shares of Common Stock issued by the Company to
       or acquired by any Holder or the ESOT after the Effective Date, whether
       in connection with a purchase, issuance, grant, stock split, stock
       dividend, reorganization, warrant, option, convertible security, right to
       acquire or otherwise; (3) all securities of the Company or any other
       corporation or entity which any Holder or the ESOT acquires after the
       Effective Date in respect of his, her or its shares of Common Stock in
       connection with any exchange, merger, consolidation, recapitalization,
       reorganization or other transaction



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       to which the Company is a party; and (4) all shares of Common Stock owned
       by any person or entity who becomes subject to this Agreement pursuant to
       the terms of this Agreement. Notwithstanding the foregoing, the term
       "Stock" shall not include (a) any shares of Common Stock which were
       retained by a Holder or any other person or entity on the Effective Date
       by virtue of a "Rollover Election" made in connection with the Merger
       (other than any such shares held on the Effective Date by a person who
       was a Holder on the Effective Date and who is a party to the Inducement
       Agreement); (b) any shares of Common Stock purchased after the Effective
       Date in the open market through a broker or in a transaction directly
       with a market maker (as defined in section 3(a)(38) of the Securities
       Exchange Act of 1934, as amended); (c) any shares of Common Stock
       distributed by the ESOT; (d) any shares of Common Stock distributed under
       the Sterling Chemicals, Inc. Amended and Restated Employees' Stock
       Ownership Plan, as amended, or any trust created pursuant thereto; or (e)
       any securities of the Company or any other corporation or entity which
       any Holder or the ESOT acquires in respect of any shares of Common Stock
       referred to in clauses (a) through (d) above in connection with any
       exchange, merger, consolidation, recapitalization, reorganization or
       other transaction to which the Company is a party. All references herein
       to the Stock owned by a Holder include the community interest or similar
       marital property interest, if any, of the spouse of such Holder in such
       Stock.

              Section 2. Effect of Amendments. Except as amended and modified by
this Amendment, the Existing Agreement shall continue in full force and effect.
The Existing Agreement and this Amendment shall be read, taken and construed as
one and the same instrument. Upon the effectiveness of this Amendment, each
reference in the Existing Agreement to "this Agreement" shall mean and be a
reference to the Existing Agreement as amended hereby.

              Section 3. Effectiveness. This Amendment shall not be or become
effective unless and until it has been duly executed and delivered by the
Corporation and Holders constituting a Required Voting Percentage.

              Section 4. Binding Effect. This Amendment shall inure to the
benefit of, and shall be binding upon (i) the Corporation and its successors and
permitted assigns and (ii) the Holders and their respective heirs, legatees,
executors, personal representatives, administrators, successors and permitted
assigns.

              Section 5. Counterparts. This Amendment may be executed in two or
more counterparts, each of which shall be deemed an original but all of which
taken together shall constitute one and the same agreement. It shall not be
necessary in making proof of this Amendment to produce or account for more than
one such counterpart.

              Section 6. Severability. Should any clause, sentence, paragraph,
subsection or Section of this Amendment be judicially declared to be invalid,
unenforceable or void, such decision will not have the effect of invalidating or
voiding the remainder of this Amendment, and the Parties agree that the part or
parts of this Amendment so held to be invalid, unenforceable or

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void will be deemed to have been stricken herefrom as if such stricken part or
parts had never been included herein.

              Section 7. Governing Law. THIS AMENDMENT SHALL BE CONSTRUED AND
ENFORCED IN ACCORDANCE WITH, AND THE RIGHTS OF THE PARTIES SHALL BE GOVERNED BY,
THE INTERNAL LAWS OF THE STATE OF DELAWARE, WITHOUT REFERENCE TO PRINCIPLES OF
CONFLICTS OF LAW.

              Section 8. Entire Agreement. This Amendment and the Existing
Agreement set forth all of the promises, agreements, conditions, understandings,
warranties and representations among the Parties with respect to the matters
cover hereby, and supersede all prior agreements, arrangements and
understandings among the Parties, whether written, oral or otherwise. There are
no promises, agreements, conditions, understandings, warranties or
representations, oral or written, express or implied, among the Parties
concerning the subject matter hereof or thereof except as set forth herein or
therein.

              IN WITNESS WHEREOF, the Parties have executed this Amendment
effective as of the date first written above.


                                       STERLING CHEMICALS HOLDINGS, INC.



                                       By:
                                          ---------------------------------
                                       Printed Name:
                                                    -----------------------
                                       Title:
                                             ------------------------------


                                       STERLING CHEMICALS, INC.
                                       EMPLOYEE STOCK OWNERSHIP TRUST

                                       By: Merrill  Lynch Trust Co. of Texas,
                                           solely in its capacity as Trustee



                                           By:
                                              -----------------------------
                                           Printed Name:
                                                        -------------------
                                           Title:
                                                 --------------------------


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                                       OTHER PARTIES:


                                       Individual:




                                       ------------------------------------
                                       Printed Name:
                                                    -----------------------


                                       Entity:


                                       ------------------------------------
                                       (Print Name of Entity)



                                       By:
                                          ---------------------------------
                                       Printed Name:
                                                    -----------------------
                                       Title:
                                             ------------------------------


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