RPTED NMAC LTSS WHEN RPTR'S ACFT CONFLICTS WITH OTHER TFC BELOW IT DURING DSCNT FROM 6000 FT. FLC MADE AN EVASIVE ACTION CLB AFTER RECEIVING A TCASII RA. CTLR DID NOT RESPOND WHEN QUESTIONED BY THE RPTR ABOUT THE TFC. ON DEP; THE SUPVR ADMITTED TO KNOWING ABOUT THE TFC CONFLICT ON THE PREVIOUS FLT. SUPVR DID NOT INTERVENE DUE TO CTLR TRAINING AND WANTED TO KNOW IF THEY (FLC) WERE GOING TO RPT THIS.

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DURING DSCNT FROM CRUISE INTO LYH ARPT; ZDC 127.92 REQUESTED WE SLOW AS MUCH AS POSSIBLE AS WE WERE #2 FOR THE ARPT. AT THE SAME TIME WE WERE INSTRUCTED TO DSND TO 5000 FT MSL. CTLR CALLED TFC TO FOLLOW 12 O'CLOCK AND 15 MI. WE WERE UNABLE TO SEE THIS TFC DUE TO DISTANCE AND A CLOUD DECK BELOW US. AS WE DSNDED TO THE TOP OF THE CLOUD DECK TCASII ALERTED US TO TFC (WE WERE PASSING 6000 FT MSL). THE DISPLAY DID NOT RESOLVE THE TFC UNTIL WE WERE WITHIN 200 FT OF THE TFC. WE CLBED BACK UP TO 6000 FT UNTIL TCASII SHOWED 1 1/2 MI SEPARATION. THEN RESUMED DSCNT TO 5000 FT MSL. WHEN QUERIED ABOUT THE CONFLICTING TARGET ATC ADMITTED ONLY TO THE TFC 12 O'CLOCK AND NOW 11 MI. DSCNT AND APCH TO LNDG CONTINUED UNEVENTFULLY. WHEN WE DEPARTED LYH TO RETURN TO CLT; A NEW VOICE WAS ON 127.92 CLAIMING TO BE A SUPVR AND ASKED IF WE WERE THE CREW ON THE PREVIOUS FLT. WE SAID YES AND HE ADMITTED TO KNOWING ABOUT THE TFC CONFLICT ON THE PREVIOUS FLT AND DID NOT INTERVENE BECAUSE OF CTLR TRAINING AND WANTED TO KNOW IF WE WERE GOING TO RPT THIS.