ACFT EQUIP PROB TCASII LOGIC. ACR X TCASII RA WITH VFR ACFT EVASIVE ACTION DSND CAUSED CLOSE PROX OF ACFT.

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ACR X; A T/DC9/A; WAS INBOUND TO BNA ON A FLT FROM MEM. X WAS ON THE GRAHAM 2 ARR AND HAD BEEN CLRED TO CROSS THE GHM VORTAC AT 10000 AND HAD RPTED LEAVING FL230. X WAS ISSUED TFC AT 1 O'CLOCK; 15 NM; NWBOUND; ALT INDICATING 14400 FT; UNVERIFIED. X ACKNOWLEDGED THE TFC AND ADVISED HE HAD IT ON TCASII. AN ADDITIONAL TFC CALL WAS ISSUED ABOUT 2 MIN LATER; X WAS ADVISED HE COULD STOP THE DSCNT AT HIS DISCRETION. AT THIS TIME X WAS DSNDING THROUGH FL188 AT ABOUT 1800-2000 FPM. X ADVISED HE WOULD STOP AT 15000 FT. ZME CONCURRED AND X LEVELED OFF AT 15000 FT. X THEN CALLED ADVISING HE HAD A RED/WHITE HIGH WING TWIN ACFT AT THE PREVIOUSLY ISSUED POS AND ALT. DURING THIS XMISSION; X HAD A TCASII ALERT TELLING HIM TO DSND. X COMPLIED WITH THE ALERT TURNING R TO MISS THE TWIN ACFT. THE TARGETS MERGED ON THE RADAR DISPLAY AT 14400 FT. LATERAL DISTANCE COULD NOT BE DETERMINED. THE PLT ADVISED THE 15000 FT ALT WAS THE BEST CALL AND TCASII HAD PUT THE 2 ACFT IN EXTREMELY CLOSE PROX. IT IS MY FIRM BELIEF THAT IF X HAD NOT MAINTAINED VISUAL SEPARATION WHILE RESPONDING TO THE TCASII ALERT; THE ACFT WOULD HAVE COLLIDED. THE ONLY SAVING FACTOR HERE WAS THE VISIBILITY; THE TCASII OBVIOUSLY MALFUNCTIONED.