AN LGT ACR CREW HAD A TCASII ALERT AT ALT THAT COMMANDED A CLB. THEY RESPONDED; THEN RETURNED TO THEIR ORIGINAL ALT.

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TCASII PROVIDED A TA DIRECTLY UNDER OUR ACFT WHICH QUICKLY (2 SECONDS) RESOLVED INTO A RA COMMANDING A 'CLB' WHICH IN 1 SECOND CHANGED TO 'INCREASE CLB.' GREEN FLY TO ARC DICTATED A CLB RATE OF 4000 FPM UP. 'CLR OF CONFLICT/MONITOR VERT SPD' ANNUNCIATION CAME AS OUR ACFT APCHED FL310. ATC WAS ADVISED WITH NO RESPONSE. ATC AGAIN ADVISED AND THEY TOLD US TO CHANGE FREQ TO ZFW AND TO ALSO CHK OUR ALT. (INCIDENT OBVIOUSLY OCCURRED AT CTR SECTOR CHANGEOVER; ADDING TO ATC CONFUSION). ADVISED ATC THAT WE HAD ALREADY INFORMED THEM OF ALTDEV DUE TO RA. THEY ROGERED OUR CALL AND SAID ZFW HAD INQUIRED ABOUT OUR ALT AND TO CHANGE FREQ AND TALK TO ZFW. WE SWITCHED TO ZFW AND ADVISED OF SAME; REQUESTED INFO ON TFC. WERE TOLD TFC HAD LEVELED UNDER US AT FL280 AND THAT THERE WAS NO CONFLICT. WE INDICATED TO ATC WE WOULD DOCUMENT THE INCIDENT. CONCLUSION -- TCASII WORKED AS ADVERTISED; HOWEVER; THIS APPEARS TO BE A SITUATION WHERE TCASII OBVIOUSLY CANNOT DETERMINE INTENT. WITHOUT TCASII WE WOULD HAVE NEVER MOVED THE AIRPLANE. A TFC CALLOUT FROM ATC (WITH TFC'S INTENT TO LEVEL AT 280) WOULD HAVE DEFINITELY BEEN APPROPRIATE AND VERY BENEFICIAL. THIS MAY BE EVEN MORE IMPORTANT WITH THE INCREASE IN ACFT EQUIPPED WITH TCASII. TCASII WAS BEING OPERATED IN TA/RA; RANGE 50; NORMAL ALT SEARCH.