B727 FLC CLRED FOR APCH WAS ISSUED ALTERNATE CLRNC TO EXPEDITE DSCNT DUE TO CONFLICTING TFC. TCASII RA INSTRUCTS ACFT TO ARREST DSCNT AND CLB. AS PIC EXECUTED TCASII INSTRUCTIONS; CTLR HAD TO ISSUE EVASIVE TURNS TO CONFLICTING TFC. PIC ALLEGES NMAC. SUBSEQUENT COM WITH TWR SUPVR IDENTS INCIDENT AS OPERROR.

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FLT WAS OPERATING FROM BNA APCH CTL. WE WERE INBOUND TO BNA; APPROX 35 NM NE OF BNA. WE WERE CLRED TO DSND OUT OF 10000 FT FOR 4000 FT; AND CLRED FOR THE ILS APCH RWY 20R. DSNDING THROUGH APPROX 6300 FT; THE CTLR CLRED US TO 3000 FT AND WERE TOLD TO EXPEDITE THROUGH 5000 FT. THE CTLR ADVISED US OF TFC AT 12 O'CLOCK POS; 10 NM; LEVEL AT 5000 FT. AS WE BEGAN TO INCREASE OUR DSCNT RATE; THE TCASII ISSUED A TA. THE TCASII WAS QUICKLY ADJUSTED FOR A BETTER DISPLAY AND IT LOOKED AS THOUGH A DSCNT THROUGH 5000 FT WAS NOT THE SAFEST OPTION. ALMOST SIMULTANEOUSLY THE TCASII BEGAN ISSUING A RESOLUTION ALERT TO 'REDUCE DSCNT;' FOLLOWED BY 'CLB; CLB.' AT SOME POINT DURING THIS OCCURRENCE; THE CTLR ISSUED A TURN TO THE OTHER ACFT SO AS TO AVOID US LATERALLY. AT APPROX 5300 FT WE STOPPED OUR DSCNT AND BEGAN A CLB. AT THAT POINT WE SIGHTED THE OTHER ACFT PASSING OFF OUR R WING ABOUT 2 NM AND 200-300 FT BELOW US. AFTER LNDG; THE CAPT CALLED BNA APCH AND SPOKE TO THE SUPVR. THE SUPVR AGREED TO LOOK INTO THE SIT. AS WE TAXIED OUT FOR THE NEXT LEG; TO DFW; TWR REQUESTED THAT WE CALL BACK TO BNA UPON OUR ARR IN DFW. THE CONVERSATION WITH THE SUPVR CLARIFIED THE EVENT AND THE SUPVR STATED THAT A RPT OF 'OPERROR' WOULD BE MADE.