<PAGE>   1
                                                                   Exhibit 10.2

                      SECOND AMENDMENT TO CREDIT AGREEMENT


                  SECOND AMENDMENT TO CREDIT AGREEMENT (this "Amendment"), dated
as of April 30, 1998, among STARWOOD HOTELS & RESORTS, a Maryland real estate
investment trust ("Starwood REIT"), SLT REALTY LIMITED PARTNERSHIP, a Delaware
limited partnership ("SLT RLP"), STARWOOD HOTELS & RESORTS WORLDWIDE, INC., a
Maryland corporation (the "Corporation"), ITT CORPORATION, a Nevada corporation
("ITT" and, together with Starwood REIT, SLT RLP and the Corporation, the
"Borrowers") the lenders from time to time party to the Credit Agreement
referred to below (the "Lenders"), BANKERS TRUST COMPANY and THE CHASE MANHATTAN
BANK, as Administrative Agents (in such capacity, the "Administrative Agents")
and LEHMAN COMMERCIAL PAPER INC. and BANK OF MONTREAL, as Syndication Agents (in
such capacity, the "Syndication Agents"). Unless otherwise defined herein, all
capitalized terms used herein shall have the respective meanings provided such
terms in the Credit Agreement referred to below.


                              W I T N E S S E T H:


                  WHEREAS, the Borrowers, the Lenders, the Administrative Agents
and the Syndication Agents are parties to a Credit Agreement, dated as of
February 23, 1998 (as amended, modified or supplemented to the date hereof, the
"Credit Agreement"); and

                  WHEREAS, the parties hereto wish to amend the Credit Agreement
as herein provided;

                  NOW, THEREFORE, it is agreed:

         I.       AMENDMENTS TO THE CREDIT AGREEMENT

                  A. Section 9.03(iv)(y) of the Credit Agreement is hereby
amended by deleting the $50,000,000 amount set forth therein and inserting in
lieu thereof $135,000,000.

         II.      MISCELLANEOUS PROVISIONS

                  A. In order to induce the Lenders to enter into this
Amendment, each of the Borrowers hereby represents and warrants that:

                           1. no Default or Event of Default exists as of the
         Amendment Effective Date (as hereinafter defined), both before and
         after giving effect to this Amendment; and

                           2. all of the representations and warranties
         contained in the Credit Agreement and the other Credit Documents are
         true and correct in all material respects as of the Amendment Effective
         Date, both before and after giving effect to this Amendment, with the
         same effect as though such representations and warranties had been made
         on and as of the Amendment Effective Date (it being understood that any
         representation or
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         warranty made as of a specific date shall be true and correct in all
         material respects as of such specific date).

                  B. This Amendment is limited as specified and shall not
constitute a modification, acceptance or waiver of any other provision of the
Credit Agreement or any other Credit Document.

                  C. This Amendment may be executed in any number of
counterparts and by the different parties hereto on separate counterparts, each
of which counterparts when executed and delivered shall be an original, but all
of which shall together constitute one and the same instrument. A complete set
of counterparts shall be lodged with the Borrowers and the Paying Agent.

                  D. THIS AMENDMENT AND THE RIGHTS AND OBLIGATIONS OF THE
PARTIES HEREUNDER SHALL BE CONSTRUED IN ACCORDANCE WITH AND GOVERNED BY THE LAWS
OF THE STATE OF NEW YORK.

                  E. This Amendment shall become effective on the date (the
"Amendment Effective Date") when each of the Borrowers and the Required Lenders
shall have signed a counterpart hereof (whatever the same or different
counterparts) and shall have delivered (including by way of facsimile
transmission) the same to the Paying Agent at its Notice Office.

                  F. From and after the Amendment Effective Date, all references
in the Credit Agreement and each of the other Credit Documents to the Credit
Agreement shall be deemed to be references to the Credit Agreement as modified
hereby.


                                      * * *
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                  IN WITNESS WHEREOF, the parties hereto have caused their duly
authorized officers to execute and deliver this Amendment as of the date first
above written.


                                  STARWOOD HOTELS & RESORTS,
                                     a Maryland real estate investment trust




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



                                 STARWOOD HOTELS & RESORTS
                                     WORLDWIDE, INC., a Maryland
                                     corporation




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



                                 SLT REALTY LIMITED PARTNERSHIP,
                                     a Delaware limited partnership

                                  By:  Starwood Hotels & Resorts, a Maryland
                                       real estate investment trust, its general
                                       partner



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




                                 ITT CORPORATION, a Nevada corporation




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


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                                     BANKERS TRUST COMPANY, Individually
                                      and as Administrative Agent and as Paying
                                      Agent



                                     By:__________________________________
                                     Name:
                                     Title:



                                      THE CHASE MANHATTAN BANK,
                                       Individually and as Administrative Agent



                                     By:__________________________________
                                     Name:
                                     Title:



                                     LEHMAN COMMERCIAL PAPER INC.,
                                     Individually and as Syndication Agent


                                     By:__________________________________
                                     Name:
                                     Title:
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                              BANK OF MONTREAL, CHICAGO BRANCH        
                              Individually and as Syndication Agent
                              
                              
                              By:
                              --------------------------------------
                              Name:
                              Title:
                              
                              
                              ARAB BANKING CORPORATION (B.S.C.)
                              
                              
                              By:
                              --------------------------------------
                              Name:
                              Title:
                              
                              BANCA POPOLARE DI MILANO
                              
                              
                              By:
                              --------------------------------------
                              Name:
                              Title:
                              
                              
                              By:
                              --------------------------------------
                              Name:
                              Title:
                              
                              
                              BANKBOSTON, N.A.
                              
                              
                              By:
                              --------------------------------------
                              Name:
                              Title:
                              
                              
                              
                              
                              
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                              BANK LEUMI USA


                              By:
                              --------------------------------------
                              Name:
                              Title:
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                      THE BANK OF TOKYO-MITSUBISHI,     
                      LIMITED, NEW YORK BRANCH
                      
                      
                      By:
                          ----------------------------------
                      Name:
                      Title:
                      
                      BANK POLSKA KASA OPIEKI S.A. -
                      PEKAO S.A. GROUP, NEW YORK
                      BRANCH
                      
                      
                      By:
                          ----------------------------------
                      Name:
                      Title:
                      
                      BANQUE PARIBAS
                      
                      
                      By:
                          ----------------------------------
                      Name:
                      Title:
                      
                      
                      By:
                          ----------------------------------
                      Name:
                      Title:
                      
                      BANQUE WORMS CAPITAL CORP.
                      
                      
                      By:
                          ----------------------------------
                      Name:
                      Title:
                      
                      BEAR STEARNS INVESTMENT
                      PRODUCTS INC.
                      
                      
                      By:
                          ----------------------------------
                      Name:
                      Title:
                      
<PAGE>   8
                        BARCLAYS BANK PLC                 
                        
                        
                        By:
                          ---------------------------
                        Name:
                        Title:
                        
                        
                        
                        CHANG HWA COMMERCIAL BANK,
                        LTD., NEW YORK BRANCH
                        
                        
                        By:
                          ---------------------------
                        Name:
                        Title:
                        
                        CHIAO TUNG BANK CO., LTD. NEW
                        YORK AGENCY
                        
                        
                        By:
                          ---------------------------
                        Name:
                        Title:
                        
                        CIBC INC.
                        
                        
                        By:
                          ---------------------------
                        Name:
                        Title:
                        
                        
<PAGE>   9
                            COMPAGNIE FINANCIERE DE CIC ET DE    
                            L'UNION EUROPEENNE
                            
                            
                            By:
                              ----------------------------------
                            Name:
                            Title:
                            
                            
                            By:
                              ----------------------------------
                            Name:
                            Title:
                            
                            
                            CREDIT LYONNAIS NEW YORK BRANCH
                            
                            
                            By:
                              ----------------------------------
                            Name:
                            Title:
                            
                            
                            
                            CREDIT SUISSE FIRST BOSTON
                            
                            
                            By:
                              ----------------------------------
                            Name:
                            Title:
                            
                            
                            By:
                              ----------------------------------
                            Name:
                            Title:
                            
                            
                            
<PAGE>   10
                           CREDITO ITALIANO                      
                           
                           
                           By:
                              ------------------------------
                           Name:
                           Title:
                           
                           
                           By:
                              ------------------------------
                           Name:
                           Title:
                           
                           
                           
                           
                           DEUTSCHE BANK AG NEW YORK
                           AND/OR CAYMAN ISLANDS BRANCH
                           
                           
                           By:
                              ------------------------------
                           Name:
                           Title:
                           
                           
                           By:
                              ------------------------------
                           Name:
                           Title:
                           
                           ERSTE BANK DER OESTERREICHISCHEN
                           SPARKASSEN AG
                           
                           
                           By:
                              ------------------------------
                           Name:
                           Title:
                           
                           
                           By:
                              ------------------------------
                           Name:
                           Title:
                           
                           
<PAGE>   11

                              FIRST COMMERCIAL BANK                     
                              
                              
                              By:
                                 -----------------------------------
                              Name:
                              Title:
                              
                              FIRST SECURITY BANK, N.A.
                              
                              
                              By:
                                 -----------------------------------
                              Name:
                              Title:
                              
                              
                              
                              FLEET BANK, N.A.
                              
                              
                              By:
                                 -----------------------------------
                              Name:
                              Title:
                              
                              GENERAL ELECTRIC CAPITAL
                              CORPORATION
                              
                              
                              By:
                                 -----------------------------------
                              Name:
                              Title:
                              
                              GOLDMAN SACHS CREDIT PARTNERS
                              L.P.
                              
                              
                              By:
                                 -----------------------------------
                              Name:
                              Title:
                              
<PAGE>   12
                                  GULF INTERNATIONAL BANK B.S.C.          
                                  
                                  
                                  By:
                                     ------------------------------------
                                  Name:
                                  Title:
                                  
                                  
                                  
                                  HUA NAN COMMERCIAL BANK, LTD.
                                  NEW YORK AGENCY
                                  
                                  
                                  By:
                                     ------------------------------------
                                  Name:
                                  Title:
                                  
                                  THE INDUSTRIAL BANK OF JAPAN,
                                  LIMITED, NEW YORK BRANCH
                                  
                                  
                                  By:
                                     ------------------------------------
                                  Name:
                                  Title:
                                  
                                  ISTITUTO BANCARIO DI TORINO SpA
                                  
                                  
                                  By:
                                     ------------------------------------
                                  Name:
                                  Title:
                                  
                                  
                                  LAND BANK OF TAWAIN, LOS ANGELES
                                  BRANCH
                                  
                                  
                                  By:
                                     ------------------------------------
                                  Name:
                                  Title:
                                  
                               
<PAGE>   13
                             THE LONG-TERM CREDIT BANK OF         
                             JAPAN, LTD
                             
                             
                             By:
                                ----------------------------------------
                             Name:
                             Title:
                             
                             MITSUBISHI TRUST & BANKING
                             CORPORATION
                             
                             
                             By:
                                ----------------------------------------
                             Name:
                             Title:
                             
                             NATIONSBANK, N.A.
                             
                             
                             By:
                                ----------------------------------------
                             Name:
                             Title:
                             
                             
<PAGE>   14
                               THE ROYAL BANK OF SCOTLAND, PLC          
                               
                               
                               By:
                                 ----------------------------------
                               Name:
                               Title:
                               
                               SOCIETE GENERALE, SOUTHWEST
                               AGENCY
                               
                               
                               By:
                                 ----------------------------------
                               Name:
                               Title:
                               
                               SOUTHERN PACIFIC BANK
                               
                               
                               By:
                                 ----------------------------------
                               Name:
                               Title:
                               
                               THE SUMITOMO BANK, LIMITED, NEW
                               YORK BRANCH
                               
                               
                               By:
                                 ----------------------------------
                               Name:
                               Title:
                               
                               WACHOVIA BANK, N.A.
                               
                               
                               By:
                                 ----------------------------------
                               Name:
                               Title:
                               
                               
<PAGE>   15
                                      WESTDEUTSCHE LANDESBANK
                                      GIROZENTRALE


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


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