FLC OF LGT IS CLRED TO 31000 FT FROM 35000 FT. TFC IS CALLED AT THE ALT TO WHICH THEY ARE CLRED. PRIOR TO QUERYING ATC TCASII ISSUES ALERT. CTLR ALSO VECTORS BOTH ACFT. TAPE REPLAY INDICATES CTLR ERROR.

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WE WERE CLRED TO DSND TO FL310 FROM FL350. THE FO READ BACK FL310; SET THE ALT ALERT AT 31000 FT AND I CONFIRMED THE ALT BY POINTING AT THE SET ALT AND SPEAKING '310' AS PER OUR SOP. DURING THE DSCNT AND JUST BELOW FL330; ATC CALLED TFC FOR US AT 12 O'CLOCK POS AND FL310. THEY CONCLUDED THEIR XMISSION WITH; 'WHEN CLR OF THIS TFC; YOU'LL BE CLRED TO A LOWER ALT.' I IMMEDIATELY ASKED THE FO TO ASK ATC TO CONFIRM THE TFC WAS AT FL310; BECAUSE THAT WAS OUR CLRED ALT AND IT DIDN'T MAKE SENSE. AT THAT TIME; ONE OF OUR FLT ATTENDANTS KNOCKED AND ENTERED THE COCKPIT. THE FO WAS DISTRACTED MOMENTARILY BY THE FLT ATTENDANT BEGINNING TO TALK; BUT ATC HAD BEEN TOO BUSY FOR HIM TO ASK THE CTLR ABOUT THE TFC ANYWAY. I AGAIN ASKED HIM TO CONFIRM THE TFC. DSNDING THROUGH FL319 AND BEFORE THE FO WAS ABLE TO ASK ATC ABOUT THE TFC; THE CTLR ASKED US TO VERIFY OUR ALT AND TO CLB TO FL330 BECAUSE WE HAD TFC AT FL310. WITHIN SEVERAL SECONDS; THE FOLLOWING TRANSPIRED: TCASII CALLED 'TFC' (WE NEVER RECEIVED AN RA). I DISCONNECTED THE AUTOPLT AND BEGAN A CLB. THE CONFLICTING TFC WAS TOLD TO TURN L 20 DEGS. THE CONFLICTING TFC TOLD ATC THEY WERE FOLLOWING A 'DSND' RA. WE WERE TOLD TO TURN L 20 DEGS. ATC TOLD THE CONFLICTING TFC TO DISREGARD THE 'DSND' RA AS THEIR TFC CONFLICT (US) WAS NOW CLBING. WE RESET THE ALT ALERT AND CLBED TO FL330. I DIDN'T GET A GOOD LOOK AT THE TCASII DURING THE FINAL SECONDS OF THIS EVENT; BUT I BELIEVE THE VERT SEPARATION BTWN US AND THE OTHER ACFT WAS 400 FT AND THE HORIZ SEPARATION WAS ABOUT 1-2 MI. AFTER WE LANDED; I CALLED ATC AND SPOKE WITH THE SUPVR ABOUT THE CONFLICT. HE SAID THAT AFTER THE EVENT OCCURRED; THEY PULLED THE TAPE AND WE HAD INDEED BEEN ERRONEOUSLY CLRED TO FL310 INSTEAD OF FL330.