MD80 CREW HAD NMAC ON DSCNT INTO RDU.

Narrative

TCASII RA AT FL330. DURING CRUISE AT FL330; WE RECEIVED A TCASII RA FOR CONVERGING CO-ALT TFC AT 11 O'CLOCK POS. TCASII SOUNDED 'TFC; TFC' AND THEN ATC DIRECTED A 30 DEG R TURN. TCASII THEN COMMANDED A 2000 FPM CLB. MAX CRUISE ALT WITH 1.3 'G' BUFFET WAS FL330 SO WE WERE UNABLE TO ESCAPE VERTLY. WE ENTERED A CLBING R TURN TO INCREASE LATERAL SEPARATION AS OUR ONLY OPTION. OTHER AIRPLANE RESPONDED WITH A TCASII RA TO DSND. ESTIMATE MISS DISTANCE 3 MI. OUR ALTDEV WAS 300 FT HIGH. NO PAX OR CABIN CREW RPTED ANY PROBS OR INJURIES. INCIDENT MAY HAVE CAUSED IN PART WITH A SUDDEN RERTE FROM BNA J42 BKW TO BNA DIRECT IIU. SUPPLEMENTAL INFO FROM ACN 474051: IMC IN HIGH LEVEL CLOUDS. JUST PRIOR TO PASSING BNA VOR; WE RECEIVED A RERTE DUE TO FLOW CTL; WHICH REQUIRED A R TURN AT BNA TO IIU INSTEAD OF PROCEEDING ON J42. AFTER MAKING THE TURN; WE IMMEDIATELY WERE ALERTED 'TFC; TFC.' THEN ATC GAVE US A 30 DEG TURN R. WE THEN WERE ALERTED 'CLB; CLB.' WE TRIED TO CLB; BUT WERE AT THE BUFFET LIMIT DUE TO WT AND ONLY MANAGED 300 FT; BUT INCREASED THE TURN TO ASSURE LATERAL SEPARATION. THE OTHER ACFT ALSO WAS GIVEN A 30 DEG TURN BY ATC AND RPTED AN RA REQUIRING A DSCNT. PAX ON OUR FLT DID NOT SEEM TO NOTICE THE MANEUVER THOUGH FLT ATTENDANTS DID NOTICE. TOTAL ALTDEV WAS 300 FT HIGH.