AFTER BEING CLRED FOR AN INST APCH; A B757 RECEIVED A TCASII RA; CLB; DUE TO A DC9 700 FT BELOW ON THE SAME APCH. AFTER LEVELING FROM THE TCASII RA; THEY RECEIVED A TCASII RA; DSND; FOR A B767 800 FT XING ABOVE. AT PLT'S REQUEST; THE CTLR RESEQUENCED THE B757 FOR LNDG.

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WE (ACR X) WERE CLRED TO INTERCEPT THE RWY 9 LOC DSNDING TO 7000 FT. AFTER LOC INTERCEPT; A DSCNT TO 2000 FT WAS ISSUED; FOLLOWED BY A CLRED FOR APCH CLRNC. ABOUT 11.1 MI (ILS DME) THE CTLR CALLED US IN A NORMAL TONE OF VOICE. EXPECTING TO BE GIVEN A CONTACT THE TWR; I RESPONDED THE SAME ONLY TO BE TOLD TURN L IMMEDIATELY TO 030 DEGS; THERE IS A DC9 ACR Y BELOW YOU. THE FO MADE AN IMMEDIATE TURN AND STARTED A CLB. THE TCASII THEN WENT ACTIVE SHOWING A TARGET JUST 700 FT BELOW US. WE LEVELED OFF AT 3300 FT AND THE CTLR TOLD US TO TURN R 130 DEGS DSND TO 2000 FT AND REINTERCEPT THE LOC. WE REQUESTED A L TURN TO REINTERCEPT AS WE WERE NOW WITHIN 9 MI OF THE FIELD. JUST THEN THE TCASII WENT ACTIVE AGAIN WITH A DSND WARNING AND WE OBSERVED ACR Z; A B767; JUST 800 FT ABOVE US HDG ABOUT 230 DEGS. I QUESTIONED THE CTLR WHO REPLIED YOU ARE CLR OF THAT TFC NOW. WE REQUESTED AND RECEIVED A L TURN TO REINTERCEPT THE APCH TO RWY 9. ON BOARD IN THE JUMP SEAT WAS AN FAA INSPECTOR. HE WITNESSED THE WHOLE SEQUENCE AND IS SUBMITTING A RPT TO THE FAA ALSO ON HIS RETURN TO THE UNITED STATES. WHEN I HAD QUERIED APCH HE STATED THAT THE DC9 WAS NOT TALKING TO HIM AND HAD RADIO FAILURE; YET THE DC9 WAS PARKED AT GATE WHEN WE ARRIVED. I WOULD LIKE TO COMMEND THE FO ON HIS QUICK SMOOTH AND PROFESSIONAL HANDLING OF THE AIRPLANE DURING THIS INCIDENT.