MD80 FLT CREW HAS A TCAS RA DURING APCH TO FLL.

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WE POSSIBLY HAD AN NMAC WITH A LOW WING SINGLE ENG ACFT WHILE ON THE FINAL APCH SEGMENT TO RWY 9L IN FLL. (UNSURE OF NEAREST PROX TO OTHER ACFT; BUT IT MAY HAVE BEEN AS CLOSE AS 500 FT.) WE WERE UNDER THE CTL OF MIA APCH CTL AND HAD RECENTLY BEEN GIVEN CLRNC TO FLY A 120 DEG HDG; DSND TO 1800 FT; AND CLRED THE ILS RWY 9L APCH IN FLL. I WAS THE CAPT ON THIS FLT AND ALSO FLYING THE APCH. I HAD ALREADY INTERCEPTED THE LOC AND WAS MAKING AN APPROX 1000 FPM DSCNT TO 1800 FT ON AUTOPLT. ABOUT 2 MI OUTSIDE OF THE FAF; NOVAE (APPROX 9 MI FROM FLL); APCH CTL ALERTED US TO NEARBY TFC CLOSE TO OUR ALT. NEITHER OF US SAW HIM OUTSIDE INITIALLY; AND GLANCING DOWN AT THE TCAS DISPLAY; I SAW THAT THEY WERE ABOUT 300 FT BELOW US AT 2 O'CLOCK AND ABOUT 2 MI. JUST AFTER RECEIVING THE WARNING FROM ATC AND GLANCING DOWN AT THE TCAS DISPLAY; WE RECEIVED A TCAS TFC WARNING AT WHICH TIME I DISCONNECTED THE AUTOPLT AND STARTED ADDING PWR AND SHALLOWING THE DSCNT ANTICIPATING A TCAS CLB COMMAND; BUT THE INITIAL TFC WARNING WAS CLOSELY FOLLOWED BY A DSND COMMAND (TCAS RA) WHICH I STARTED DOING IMMEDIATELY AND AGGRESSIVELY. SECONDS AFTER I HAD INITIATED THE DSCNT; ATC THEN CALLED US BACK TELLING US TO CLB; BUT OUR PROCS INSTRUCT US TO FOLLOW TCAS DIRECTIONS WHEN WE RECEIVE TCAS RA'S. ABOUT THE SAME TIME THAT ATC HAD CALLED US BACK; THE FO SPOTTED AND POINTED OUT THE TFC AT OUR 2:30 O'CLOCK POS; CONTINUING TO HEAD N AND CLOSE TO OUR ALT (I'M GUESSING THIS WAS ABOUT 2300 FT). AFTER SEEING THE TFC; I TURNED N WHILE CONTINUING TO DSND TO INCREASE SEPARATION. THE NBOUND ACFT APPEARED NOT TO SEE US UNTIL WE WERE DIRECTLY IN FRONT OF THEM AT WHICH TIME THEY ENTERED A STEEP TURN WBOUND. (ALL THE EVENTS ABOVE OCCURRED WITHIN A VERY SHORT TIME SPAN.) AFTER CLRING THE TFC; I CORRECTED BACK TO THE ILS COURSE AND GS; AND COMPLETED THE APCH AND LNDG WITHOUT FURTHER INCIDENT. THE FLT ATTENDANTS HAD BEEN GIVEN LNDG NOTIFICATION WELL PRIOR TO THIS AND WERE SEATED ALONG WITH THE PAX; AND NO ONE RPTED ANY INJURIES. WE CAME CLOSE TO THE OTHER ACFT; BUT AREN'T SURE EXACTLY HOW CLOSE -- IT MAY HAVE BEEN AS CLOSE AS 500 FT.