EXHIBIT 3.3(b) Second Amendment to Amended and Restated Limited Partnership Agreement This Second Amendment to the Amended and Restated Limited Partnership Agreement of Equistar Chemicals, LP, dated as of February 16, 1999 (this "Second Amendment"), is entered into by and among Lyondell Petrochemical G.P. Inc., Lyondell Petrochemical L.P. Inc., Millennium Petrochemicals GP LLC, Millennium Petrochemicals LP LLC, Occidental Petrochem Partner 1, Inc., Occidental Petrochem Partner 2, Inc., and Occidental Petrochem Partner GP, Inc. ("Occidental GP"). Whereas, on May 15, 1998, PDG Chemical Inc. and the parties hereto other than Occidental GP entered into the Amended and Restated Limited Partnership Agreement of Equistar Chemicals, LP; Whereas, as of June 30, 1998, PDG Chemical Inc. and the parties hereto entered into the First Amendment to Amended and Restated Limited Partnership Agreement of Equistar Chemicals, LP (the "First Amendment"; the Amended and Restated Limited Partnership Agreement of Equistar Chemicals, LP, as amended by the First Amendment is herein referred to as the "1998 Partnership Agreement"), whereby, among other things, PDG Chemical Inc. withdrew from Equistar Chemicals, LP, and Occidental GP became a general partner thereof; and Whereas, the parties hereto wish to amend the 1998 Partnership Agreement to, among other things, revise the definition of "Oxy Guaranteed Debt" in the Appendix thereof. Now, Therefore, the parties to this Second Amendment agree as follows: 1. All capitalized terms that are defined in the 1998 Partnership Agreement, but are not defined in this Second Amendment, shall have the same meanings as defined in the 1998 Partnership Agreement. 2. Clause (xxii) of Section 6.7 of the 1998 Partnership Agreement is amended (a) to delete the words "Oxy Guaranteed Debt" the four times they appear in such clause (xxii) and substitute the words "Oxy Reference Debt" in their place and (b) to add in the proviso, after the words "or its successors", the following words: "or the reference for determination of the amount of the obligation of OCC to contribute to the Partnership pursuant to an indemnity by OCC in favor of the Partnership issued pursuant to the Letter Agreement, dated as of February 16, 1999, between OCC and the Partnership,". 3. The definition of "Amended and Restated Indemnity Agreement" in Appendix A of the 1998 Partnership Agreement is deleted and the following definition is substituted in its place" "Amended and Restated Indemnity Agreement. The Second Amended and Restated Indemnity Agreement, dated as of February 16, 1999, among Lyondell GP, -1- Lyondell LP, Millennium GP, Millennium LP, Millennium America, PDG Chemical Inc., Occidental LP1, Occidental LP2, OCC, and Occidental GP, as amended from time to time." 4. The definition of "Oxy Guaranteed Debt" in Appendix A of the 1998 Partnership Agreement is deleted and the following definition is substituted in its place: "Oxy Reference Debt. The $419,700,000 drawdown under the Bank Credit Agreement pursuant to Section 8.6(a) and the portion, if any, of any debt that refinances the $419,700,000 drawdown under the Bank Credit Agreement or any subsequent refinancing thereof (in any case, not to exceed an aggregate of $419,700,000 principal amount), in each case to the extent (a) (i) such debt is guaranteed by OCC or an Affiliate thereof and (ii) and the proceeds thereof have been distributed to Occidental LP2 pursuant to Section 3.1(g) or (b) such debt is the reference for determination of the amount of the obligation of OCC to contribute to the Partnership pursuant to an indemnity by OCC in favor of the Partnership issued pursuant to the Amended and Restated Letter Agreement, dated as of February 16, 1999, between OCC and the Partnership. 5. Except as amended by this Second Amendment, all the terms and provisions of the 1998 Partnership Agreement shall remain in full force and effect. 6. This Second Amendment may be executed by one or more of the parties hereto in any number of separate counterparts, and all of such counterparts taken together shall be deemed to constitute one and the same instrument. 7. This Second Amendment shall be governed by and construed in accordance with the laws of the State of Delaware, without giving effect to any conflicts of law principles. -2- In Witness Whereof, the parties hereto have executed and delivered this Second Amendment as of the date first above written. LYONDELL PETROCHEMICAL G.P. INC. By: /s/ Edward W. Rich ---------------------------------- Name: Edward W. Rich Title: Vice President and Treasurer LYONDELL PETROCHEMICAL L.P. INC. By: /s/ Edward W. Rich ---------------------------------- Name: Edward W. Rich Title: Vice President and Treasurer MILLENNIUM PETROCHEMICALS GP LLC By: MILLENNIUM PETROCHEMICALS INC. as manager By: /s/ C. William Carmean ---------------------------------- Name: C. William Carmean Title: Vice President--Legal MILLENNIUM PETROCHEMICALS LP LLC By: MILLENNIUM PETROCHEMICALS INC. as manager By: /s/ C. William Carmean ---------------------------------- Name: C. William Carmean Title: Vice President--Legal OCCIDENTAL PETROCHEM PARTNER 1, INC. By: /s/ J.R. Havert ---------------------------------- Name: J.R. Havert Title: Assistant Treasurer -3- OCCIDENTAL PETROCHEM PARTNER 2, INC. By: /s/ J.R. Havert ---------------------------------- Name: J.R. Havert Title: Vice President and Treasurer OCCIDENTAL PETROCHEM PARTNER GP, INC. By: /s/ J.R. Havert ---------------------------------- Name: J.R. Havert Title: Assistant Treasurer -4-