CTLR JUDGEMENT OF TFC SPACING ACR X SAME ALT ASSIGNED HAD LTSS FROM ACR Y. ACR X TCASII RA CLB EVASIVE ACTION TAKEN.

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ACR X SWBOUND AT FL310 REQUESTING FL350. ACR Y EBOUND AT FL330 REQUIRED BY ATC OPERATING PROCS TO DSND TO FL290. I FELT THERE WAS SUFFICIENT TIME TO SWAY ALTS OF BOTH ACFT BEFORE XING. ACR Y ASSIGNED FL290 AND ASKED TO GIVE BEST RATE THROUGH FL310. ACR X ASSIGNED FL330 AND ASKED TO CLB AT BEST RATE. AFTER A MIN; NO CHANGE WAS NOTICED IN ACR X'S MODE C. ACR X ASSIGNED FL290 AND TOLD TO EXPEDITE. ACR Y WAS TOLD TO STOP DSCNT AT FL310. ACR X WAS ACTUALLY ABOVE FL320 AT THIS TIME. ACR X'S LAG IN STARTING IN CLB AND GAP IN UPDATING OF RADAR DISPLAYED MODE C MISLED ME TO THINK ACR X WAS STILL LEVEL AT FL310. SITUATION WAS RESOLVED BY TCASII. SUPPLEMENTAL INFO FROM ACN 226340: ACR X HAD REQUESTED CLB FROM FL310 TO FL350. WE WERE SUBSEQUENTLY CLRED TO FL330 AND STARTED A CLB TO 330. SUDDENLY; A DIFFERENT CTLR (A MALE INSTEAD OF FEMALE VOICE) ASKED US TO EXPEDITE A DSCNT TO FL290; WHICH WE STARTED TO COMPLY WITH BY DSNDING. THEN WE RECEIVED TCASII ALERT OF TFC 1-2 O'CLOCK EBOUND 1000 FT BELOW US. THE CTLR AGAIN ASKED US TO EXPEDITE DSCNT TO FL290. AFTER HIS LAST REQUEST; WE RECEIVED A TCASII RA TO STOP DSCNT WITH THE LIGHTS IN THE IVSI INDICATED A 2000 FPM CLB; WHICH WE; WITHOUT HESITATION; COMPLIED WITH. THE CAPT ALSO COMMENCED A L TURN. I VISUALLY SAW THE INTRUDER ACFT PASS OFF OF OUR R SIDE IN THE CLOUDS; AT A TCASII ALT OF 100-200 FT. WE ADVISED THE CTLR WE WERE FOLLOWING A TCASII RA AND CLBING THROUGH 32000 FT. HE ASKED US TO MAINTAIN FL330; WHICH WE DID AFTER THE TCASII RA ANNOUNCED CLR OF CONFLICT. THE CAUSE FROM OUR VANTAGE POINT APPEARED TO BE LACK OF COORD WITH A CTLR CHANGE. WE REQUESTED THE ALT CHANGE WITH ONE CTLR (A FEMALE VOICE) AND RECEIVED THE CLRNC TO 330 FROM ANOTHER VOICE (MALE). WE ALSO RECEIVED THE DSCNT AND EXPEDITE CLRNC FROM THE NEW VOICE. PERHAPS ONE DIDN'T ADEQUATELY BRIEF THE OTHER AS TO THE SITUATION? THANK GOODNESS FOR TCASII. THE SYS WORKED IN THIS SITUATION.