LGT HAS NMAC WITH SMA ON DSCNT.

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APPROX 20 NM W OF MIA ON A 120 DEG HDG TO INTERCEPT THE 9L LOC AND DSNDING TO 3000 MSL; MIA APCH REQUESTED WE TURN TO 090 DEGS AND RPTED TFC AT OUR 11 O'CLOCK ALT UNKNOWN. AS WE ROLLED OUT 090 DEGS; WE HAD NEITHER A VISUAL SIGHTING NOR TCASII CONTACT WITH THE TFC. PASSING 4000 MSL; TCASII GAVE A TA AND SUDDENLY DISPLAYED AN AMBER TARGET AT 11 O'CLOCK -- 800 FT AND 4 NM. THIS WAS FOLLOWED IMMEDIATELY WITH AN RA COMMANDING A LEVEL-OFF ON THE VVI. THE FO WAS FLYING AND RESPONDED IMMEDIATELY BY LEVELING THE ACFT AT 3200 MSL. SIMULTANEOUS WITH THE 'MONITOR VERT SPD' RA I ACQUIRED THE TFC VISUALLY 2-3 NM AND CONVERGING. AS IT APPEARED WE WOULD PASS CLOSE; I TOLD MY FO TO 'CLB TO 3500.' AS HE LEVELED AT 3500 MSL THE TFC PASSED DIRECTLY BENEATH US WITH 500 FT OF VERT SEPARATION ACCORDING TO THE TCASII. WHEN I ADVISED MIA APCH WE HAD A TCASII RA ON THE TFC THEY REPLIED THAT THEY WERE RECEIVING NO XPONDER CODE FROM THE ACFT. I SUSPECT THE TFC'S XPONDER WAS NOT OPERATING PROPERLY; RESPONDING TO INTERROGATIONS WITH A WEAK REPLY THAT COULD NOT BE RECEIVED BY APCH CTL AND WAS NOT PICKED UP BY OUR TCASII UNTIL INSIDE OF 4 NM. THE TFC WAS A SINGLE ENG LOW WING; LIGHT BROWN WITH DARK MARKINGS. ITS PLT APPARENTLY NEVER SAW US AS HE TOOK NO EVASIVE ACTION. CLR OF TFC; WE CONTINUED OUR DSCNT; AND WERE CLRED BY APCH TO RETURN TO OUR INTERCEPT OF THE LOC. TCASII GETS MY VOTE. STILL; 'SEE AND AVOID' IS THE BEST COURSE OF ACTION.