LTT ACFT CLBING TO FL210 HAD TCASII RA. CTLR TOLD FLC TO DSND BACK TO FL200 'DUE TO TFC;' THEN THEY RECEIVED A CLB RA AS INTRUDER ACFT SHOWED 400 FT BELOW THEM.

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WE WERE IN THE CLR; CLBING TO FL210. PASSING THROUGH FL201 WE RECEIVED A TFC ALERT ON THE TCASII AND IT POPPED UP ON THE MULTI-FUNCTION DISPLAY. THE TARGET WAS SHOWING 1400 FT ABOVE US AND WAS ALMOST OVERLAID ON TOP OF OUR POS. AT FL205 WE WERE TOLD BY THE CTLR TO DSND BACK DOWN TO FL200. NO URGENCY WAS STRESSED; JUST 'DUE TO TFC.' PASSING THROUGH FL206 AND WHILE INITIATING A DSCNT BACK DOWN TO FL200; WE RECEIVED AN RA OF 'CLB; CLB.' THE TFC WAS NOW OVERLAID ON TOP OF US AND NOW SHOWED 400 FT BELOW US. WE NEVER SAW THE OTHER ACFT OR HEARD CTR ISSUE ANY TYPE OF CLRNC TO THEM. OBVIOUSLY; IT WAS A VERY CONFUSING 15 SECONDS GOING FROM CLB TO DSND TO CLB! THE CTLR WAS DEALING WITH DATA THAT WAS BEING UPDATED VERY SLOWLY WHILE OUR TCASII SHOWED A MORE REALISTIC PICTURE. OUR FIRST REACTION ON THE TA WAS 'WHERE IS HE?' WITH THE TFC ALMOST ON TOP OF US ON THE MULTI-FUNCTION DISPLAY; AND WITH THE OVERLAYING OF GRAPHICAL DATA; IT MADE IT HARD TO INTERPRET THE DATA RAPIDLY. WITH THE RA WE KNEW WHERE WE STOOD. I JUST WISH IT WOULD HAVE COME QUICKER. OBVIOUSLY; HUMAN ERROR SOMEWHERE IN THE ATC SYS OR THE OTHER ACFT CONTRIBUTED TO THIS SIT. I WAS ALSO UNDER THE MISTAKEN IMPRESSION THAT AN ALARM IN THE ATC COMPUTER WOULD ALERT THE CTLR WHEN 2 JETS WERE GOING TO OCCUPY THE SAME AIRSPACE AND IN THE PAST OUR TCASII HAD GIVEN US CONSIDERABLY MORE WARNING THAN IT DID ON THIS OCCASION. EVIDENTLY; THE VERT CLOSURE RATES WERE TOO HIGH FOR EITHER SYS TO HANDLE AFTER THE HUMAN ERROR HAD BEEN MADE. I WOULD LIKE TO SEE BOTH THE ARTCC AND TCASII SYS UPDATED FURTHER. IN THE MEANTIME; WEAR A RABBIT'S FOOT!