B757-CREW EXECUTES TCASII MANEUVER ON APCH TO RWY 30 AT MIA WHEN ANOTHER ACFT ON APCH TO RWY 27 CROSSES THEIR ASSIGNED COURSE.

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RA ON APCH TO MIA RWY 30. WE WERE BEING VECTORED FROM THE S OFF THE DUVAL ARR FOR THE LOC TO RWY 30. THE WX WAS CLR WITH NO CLOUDS. MIA APCH INSTRUCTED US TO DSND TO 3000 FT AND TURN L TO 060 DEGS HDG. WE DID SO. AT THE SAME TIME; APCH HAD ANOTHER ACFT AT 2000 FT WHO WAS CLRED TO INTERCEPT THE LOC TO RWY 27. WE HAD THE ACFT IN SIGHT. THE OTHER ACFT FLEW THROUGH THE LOC AT WHICH TIME APCH INSTRUCTED THE ACFT TO MAKE AN IMMEDIATE TURN TO THE E. THE ACFT DID NOT COMPLY. APCH ISSUED ANOTHER IMMEDIATE TURN. THE ACFT DID NOT COMPLY. APCH ISSUED INSTRUCTIONS FOR THE OTHER ACFT TO DSND TO 1500 FT. THE ACFT STARTED A DSCNT; BUT THEN STOPPED AND STARTED A CLBING L-HAND TURN IN OUR DIRECTION. OUR TCASII ISSUED AN RA FOR US TO CLB. AT THE SAME TIME; APCH GAVE US A TURN TO THE W. WE STARTED AN IMMEDIATE CLB WHILE TURNING AND MAINTAINED A VISUAL ON THE TFC. TOTAL CLB WAS 300 TO 500 FT BEFORE THE TCASII TERMINATED THE ALERT. WE INFORMED APCH THAT WE HAD THE TFC AND FIELD IN SIGHT. APCH CLRED US FOR A VISUAL TO RWY 27. WE LANDED WITHOUT INCIDENT AND TAXIED TO THE GATE. I CALLED ATC FROM THE TERMINAL AND TALKED WITH THE CTLR. I WAS ASSURED THAT THE PROB WAS WITH THE OTHER ACFT AND THAT WE WERE NOT AT FAULT.