AN A320 FLT CREW HAVE TO TAKE EVASIVE ACTION TO AVOID A B737 THAT LINED UP ON THE WRONG RWY AT LAX.

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WHILE DSNDING ON THE MITTS ARR AND ALIGNED WITH THE LOC TO LAX RWY 24R; WE WERE ADVISED BY SOCAL OF TFC AT OUR 9 O'CLOCK POS ON APCH TO RWY 25L. WE CALLED THE TFC IN SIGHT AND WERE ADVISED TO MAINTAIN VISUAL SEPARATION. WE KEPT THE ACFT; B737-200; IN SIGHT AS IT CONTINUED TO GET CLOSER TO US; REMAINING IN OUR 9 O'CLOCK POS. AT ABOUT 30 DME FROM THE RWY; IT APPEARED THAT THE B737 MIGHT BE LINING UP ON OUR RWY AS IT CONTINUED TO CONVERGE WITH OUR PATH. AS WE QUESTIONED SOCAL AS TO THE JET'S CLRNC; IT RAPIDLY CLOSED THE DISTANCE BTWN US UNTIL I WAS FORCED TO TAKE EVASIVE ACTION TO AVOID COLLISION. AS I TURNED ABOUT 15 DEGS TO THE R AND DSNDED APPROX 300-400 FT TO 9600 FT MSL; THE B737 PASSED ALMOST DIRECTLY ABOVE US. I MOMENTARILY LOST SIGHT OF THE B737 IN THE SUN. IT THEN BEGAN A CLBING L TURN AND BEGAN REALIGNING ITSELF SLOWLY WITH RWY 25L; AT WHICH POINT SOCAL ADVISED THAT THE ACFT WAS NOW AT 10900 FT MSL. IT WAS APPARENT TO MY FO AND ME THAT THE B737 WAS LINING UP WITH RWY 24R. THE REMAINDER OF OUR APCH WAS COMPLETED WITHOUT INCIDENT. IT SHOULD BE NOTED THAT AT NO TIME DID THE TCASII SYS IN MY ACFT GIVE ANY TFC OR RA; AND I SUBSEQUENTLY WROTE UP THE SYS FOR MAINT INSPECTION.