<PAGE>
 
                                                                  Exhibit 4.6(b)

                     SECOND AMENDMENT TO CREDIT AGREEMENT

                         dated as of November 12, 1996


          LYONDELL-CITGO REFINING COMPANY LTD., a Texas limited liability
company (the "Borrower"), the LENDERS listed on the signature pages hereof and
any Lender hereafter becoming a party to the below-mentioned Agreement in
accordance with the provisions thereof, ABN AMRO BANK N.V., THE BANK OF NOVA
SCOTIA, CREDIT LYONNAIS, THE FIRST NATIONAL BANK OF CHICAGO and THE INDUSTRIAL
BANK OF JAPAN, LTD., as Co-Agents, and THE BANK OF NEW YORK, as Agent and as
Issuer, agree to this Second Amendment (this "Amendment"), dated as of November
12, 1996 (the "Amendment Date"), to the Credit Agreement, dated as of May 5,
1995, among the Borrower, the Lenders parties thereto, such Co-Agents and such
Agent and Issuer, as previously amended (the "Agreement"; capitalized terms used
but not otherwise defined herein having the meanings assigned to them in the
Agreement, and references herein to Sections being references to Sections of the
Agreement unless indicated otherwise), as follows:

          Section 1.  Amendments.    Subject to the terms and provisions herein
                      ----------
set forth, effective as of the Amendment Date, the Agreement hereby is amended
in the following respects:

          (a)  The following definitions are added to Section 1.01 immediately
following the definition of "Accumulated Funding Deficiency":

               "Adjusted Average Debt to EBITDA Ratio" means (a) as of September
                -------------------------------------                           
     30, 1997, the ratio of (i) Average Consolidated Indebtedness over the
     Borrower's four most recently ended fiscal quarters to (ii) Consolidated
     EBITDA for the Borrower's fiscal quarter ending on such date and for the
     preceding fiscal quarter, multiplied by 2, and (b) as of December 31, 1997,
     the ratio of (i) Average Consolidated Indebtedness over the Borrower's four
     most recently ended fiscal quarters to (ii) Consolidated EBITDA for the
     Borrower's fiscal quarter ending on such date and for the preceding two
     fiscal quarters, multiplied by 4/3.

               "Adjusted Coverage Ratio" means (a) as of September 30, 1997, the
                -----------------------                                         
     ratio of (i) Consolidated EBIT for the Borrower's fiscal quarter ending on
     such date and for the preceding fiscal quarter, multiplied by 2, to (ii)
     Consolidated Interest Expense for the Borrower's four most recently ended
     fiscal quarters and (b) as of December 31, 1997, the ratio of (i)
     Consolidated EBIT for the Borrower's fiscal quarter ending on such date and
     for the preceding two fiscal quarters, multiplied by 4/3, to (ii)
     Consolidated Interest Expense for the Borrower,s four most recently ended

                                      -1-
<PAGE>
 
     fiscal quarters.
 
          (b)  The definition of "Applicable Margin" set forth in Section 1.01
is amended to provide that (i) for the period commencing on the Amendment Date
and ending on the last day of the Pre-Completion Period, the per annum
percentage shall be 0.750%, in lieu of the per annum percentages set forth in
column B of such definition for such period, and (ii) for the period commencing
on the first day of the Post-Completion Period and ending on the Determination
Date next succeeding the fiscal quarter of the Borrower ending September 30,
1997, the per annum percentage shall be 0.650%, in lieu of the per annum
percentages set forth in column C of such definition for such period.

          (c)  The obligation of the Borrower to comply with Section 7.16(b) is
suspended for the fiscal quarters of the Borrower ending December 31, 1996,
March 31, 1997, June 30, 1997, September 30, 1997 and December 31, 1997.

          (d)  The obligation of the Borrower to comply with Section 7.16(d) is
hereby suspended for the fiscal quarters of the Borrower ending September 30,
1996, December 31, 1996, March 31, 1997, June 30, 1997, September 30, 1997 and
December 31, 1997.

          (e)  In lieu of the covenants set forth in Sections 7.16(b) and
7.16(d), the Borrower shall not permit, at the end of the relevant fiscal
quarter, (i) Consolidated EBITDA (A) for the fiscal year of the Borrower ending
December 31, 1996 to be less than $40,000,000, (B) for the four fiscal quarters
of the Borrower ending March 31, 1997 to be less than $18,000,000 and (C) for
the four fiscal quarters of the Borrower ending June 30, 1997 to be less than
$60,000,000, (ii) the Adjusted Coverage Ratio as of September 30, 1997 and
December 31, 1997 to be less than 2.00 to 1.00 and (iii) the Adjusted Average
Debt to EBITDA Ratio (A) as of September 30, 1997 to be greater than 4.5 to 1.0
and (B) as of December 31, 1997 to be greater than 4.0 to 1.0.

          Section 2.  Waiver.  (a) The Borrower's failure to comply with Section
                      ------                                                    
7.16(d) as of September 30, 1996 and the resulting Event of Default under
Section 8.01(c)(i) are hereby waived and (b) the Event of Default under Section
8.01(d)(iii) resulting from the Borrower's failure to comply with Section
7.16(d) of the Revolving Credit Agreement is hereby waived, subject to the
Second Amendment to Revolving Credit Agreement of even date herewith, which
amends the Revolving Credit Agreement, becoming effective in accordance with the
terms thereof.

          Section 3.  Amendment Fee; Other Fees and Expenses.  On the Amendment
                      --------------------------------------                   
Date, the Borrower shall pay to the Agent for the account of each Lender
executing and delivering this Amendment an amendment fee equal to .05% of such
Lender's Commitment.  The Borrower agrees to pay to the Agent for the account of
counsel to the Agent all reasonable fees and expenses of such counsel in
connection with this Amendment.

                                      -2-
<PAGE>
 
          Section 4.  Effect of Amendments and Waiver.   Except for the
                      -------------------------------                  
amendments and waivers evidenced hereby, the Agreement and other Loan Documents
remain in full force and effect, and the Agreement, as amended hereby, and the
other Loan Documents are hereby ratified and confirmed by the Borrower.  The
execution and delivery of this Amendment shall not, except as specifically set
forth herein, operate as an amendment or waiver of compliance by the Borrower
with respect to any other provision or condition of the Agreement, as amended
hereby, or any other Loan Document, or of any right, power or remedy of the
Agent, any Co-Agent, any Lender or the Issuer under the Agreement, as amended
hereby, or any other Loan Document, or prejudice any right or remedy that the
Agent, any Co-Agent, any Lender or the Issuer may now have or may have in the
future with respect to any Default, or otherwise, under or in connection with
the Agreement, as amended hereby, or any other Loan Document.

          Section 5.  Conditions to Effectiveness.  The effectiveness of the
                      ---------------------------                           
amendments and waivers made by this Amendment to the Agreement is subject to its
execution by the Agent and the Issuer and the Agent's receipt on or before the
Amendment Date of (a) counterparts of this Amendment signed by the Borrower and
the Required Lenders, (b) receipt by the Agent of the amendment fee provided for
in Section 3 of this Amendment and (c) each of the following, in sufficient
number for each of the Lenders, the Co-Agents and the Issuer and in form and
substance reasonably satisfactory to the Agent: (i) a copy, certified by the
Secretary of the Borrower under date of the Amendment Date, of the resolutions
adopted by Owners Committee Action taken by the Owners Committee in accordance
with the applicable requirements of the Regulations to authorize the execution
and delivery of this Amendment and the carrying out of the provisions hereof and
of the Agreement, as amended hereby; (ii) a certificate of a Responsible
Officer, dated the Amendment Date, to the effect that on and as of the Amendment
Date, after giving effect to this Amendment, (A) the representations and
warranties set forth in Article V of the Agreement are true and correct in all
material respects (unless made as of a specific date as set forth in that
Article) and (B) no Default exists; and (iii) an opinion of the general counsel
of the Borrower, dated the Amendment Date, to the effect that this Amendment has
been duly authorized by Owners Committee Action and validly executed and
delivered by the Borrower.

          Section 6.  Miscellaneous.  This Amendment is governed by the terms
                      -------------                                          
and other provisions of Sections 1.02, 1.03, 10.05, 10.07, 10.10 (the first
sentence thereof) and 10.12 as if this Amendment were the Agreement.

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<PAGE>
 
          IN WITNESS WHEREOF, the parties hereto have caused this Amendment to
be executed and delivered by their duly authorized officers all as of the
Amendment Date.

                              LYONDELL-CITGO REFINING COMPANY LTD.



                              By:______________________________________________
                                   Name:  D. Lyndon James
                                   Title: Vice President and Controller


                              THE BANK OF NEW YORK,
                                   As Agent, as Issuer and as a Lender



                              By:______________________________________________
                                   Name:_______________________________________
                                   Title:______________________________________


                              OTHER LENDERS:
 
                              ABN AMRO BANK N.V. HOUSTON AGENCY

                              By:      ABN AMRO North America, Inc., as agent



                              By:______________________________________________
                                   Name:_______________________________________
                                   Title:______________________________________



                              By:______________________________________________
                                   Name:_______________________________________
                                   Title:______________________________________
                                                                               

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<PAGE>
 
                              THE BANK OF NOVA SCOTIA



                              By:______________________________________________
                                   Name:_______________________________________
                                   Title:______________________________________


                              BANK POLSKA KASA OPIEKI, S.A.



                              By:_____________________________________________
                                   Name:______________________________________
                                   Title:_____________________________________


                              BANQUE NATIONALE DE PARIS,
                                  HOUSTON AGENCY



                              By:_____________________________________________
                                   Name:______________________________________
                                   Title:_____________________________________


                              CAISSE NATIONALE DE CREDIT AGRICOLE



                              By:_____________________________________________
                                   Name:______________________________________
                                   Title:_____________________________________

                                      -5-
<PAGE>
 
                              COBANK, ACB
                              

                              By:_____________________________________________
                                   Name:______________________________________
                                   Title:_____________________________________
     

                              CREDIT LYONNAIS CAYMAN ISLAND BRANCH



                              By:_____________________________________________
                                   Name:______________________________________
                                   Title:_____________________________________



                              DG BANK DEUTSCHE GENOSSENSCHAFTSBANK



                              By:_____________________________________________
                                   Name:______________________________________
                                   Title:_____________________________________



                              THE FIRST NATIONAL BANK OF CHICAGO



                              By:_____________________________________________
                                   Name:______________________________________
                                   Title:_____________________________________


                              THE INDUSTRIAL BANK OF JAPAN, LTD.



                              By:_____________________________________________
                                   Name:______________________________________
                                   Title:_____________________________________

                                      -6-
<PAGE>
 
                              NATIONSBANK OF TEXAS, N.A.



                              By:_____________________________________________
                                   Name:______________________________________
                                   Title:_____________________________________


                              THE NIPPON CREDIT BANK, LTD.
                                   NEW YORK BRANCH



                              By:_____________________________________________
                                   Name:______________________________________
                                   Title:_____________________________________



                              PNC BANK, NATIONAL ASSOCIATION



                              By:_____________________________________________
                                   Name:______________________________________
                                   Title:_____________________________________



                              ROYAL BANK OF CANADA



                              By:_____________________________________________
                                   Name:______________________________________
                                   Title:_____________________________________

                                      -7-
<PAGE>
 
                              SOCIETE GENERALE, SOUTHWEST AGENCY



                              By:_____________________________________________
                                   Name:______________________________________
                                   Title:_____________________________________

                                                                               


                              THE TOYO TRUST & BANKING CO., LTD.
                                   NEW YORK BRANCH



                              By:_____________________________________________
                                   Name:______________________________________
                                   Title:_____________________________________



                              WESTDEUTSCHE LANDESBANK GIROZENTRALE,
                                  NEW YORK AND CAYMAN
                                  ISLANDS BRANCHES



                              By:_____________________________________________
                                   Name:______________________________________
                                   Title:_____________________________________




                              By:_____________________________________________
                                   Name:______________________________________
                                   Title:_____________________________________

                                      -8-