B757 FLT CREW HAS A TCAS RA AFTER BEING ISSUED A DSCNT CLRNC FROM ATC.

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CROSSED ARG AT FL320; TURNED DIRECT TO FAM. IT WAS VFR AND WE OBSERVED AN ACFT DIRECTLY ABOVE US AT FL330 APPARENTLY ON THE SAME TRACK. SHORTLY AFTER OUR TURN; ATC DIRECTED US TO DSND TO FL310. ALT WAS SET IN ALT WINDOW AND ENTERED INTO FMS AND WE BEGAN OUR DSCNT. ACFT THEN DIRECTED A TURN TO A HDG OF 300 DEGS. AS WE BEGAN OUR TURN WE RECEIVED A TA QUICKLY FOLLOWED BY AN RA COMMANDING A 2000-2500 FPM CLB. I DISCONNECTED THE AUTOPLT; ROLLED WINGS LEVEL AND PULLED THE NOSE UP. AS I DID THIS; FO NOTIFIED ATC THAT WE HAD RECEIVED A TCAS ALERT AND WERE CLBING IN RESPONSE. ATC CTLR RESPONDED 'DON'T CLB TFC ABOVE YOU.' I BEGAN TO LEVEL OFF AND TCAS ALERTED AGAIN; THIS TIME COMMANDING A 2000-2500 FPM DSCNT. I PUSHED THE NOSE OVER TO COMPLY AND AFTER VSI NEEDLE REACHED GREEN BAND; I LOOKED UP AND OBSERVED TFC PASSING FROM R TO L IN MY WINDSCREEN. THE VSI/TCAS SCREEN INDICATED HE PASSED 300 FT ABOVE AND APPROX 1/2 - 1 MI AHEAD. TCAS RPTED CLR OF CONFLICT AND WE LEVELED AT FL310. SUPPLEMENTAL INFO FROM ACN 698802: ANOTHER ACFT ON THE FREQ STATED THAT HE WAS RESPONDING TO AN RA. THE TCAS ISSUED A 'CLR OF CONFLICT' MESSAGE AND THE CAPT RETURNED TO OUR ASSIGNED ALT AND HDG.