FLC OF AN MLG DSNDED IN RESPONSE TO A TCASII RA AND OBSERVATION OF THE TFC DSNDING TOWARD THEM. ATC SUBSEQUENTLY INSTRUCTED THE RPTR AND THE OTHER ACFT TO TURN AND THE OTHER ACFT TO STOP DSNDING AND MAINTAIN THEIR ALT.

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WHILE CRUISING AT FL330 ON A DIRECT TO ALB ROUTING IN THE IMMEDIATE VICINITY OF ECK VOR AND UNDER THE CTL OF ZOB; I NOTICED TFC ON OUR TCASII DISPLAY AT OUR 2 O'CLOCK POS DSNDING OUT OF FL350. SHORTLY AFTER THIS OBSERVATION WE RECEIVED A TCASII TA AND OBSERVED THE PREVIOUSLY NOTICED TFC DSNDING TOWARD OUR ACFT AT APPROX FL346. THIS ALERT WAS FOLLOWED IMMEDIATELY BY A TCASII RA 'DSND' ADVISORY. AT THIS TIME I ASSUMED CTL OF THE ACFT AND FLEW THE ACFT IN ACCORDANCE WITH THE COMMANDED TCASII PARAMETERS. AT THIS TIME ZOB DIRECTED US TO TURN 20 DEGS L FOR TFC AND DIRECTED THE OTHER ACFT (ACR Y) TO ALSO TURN 20 DEGS L AND TO MAINTAIN THEIR DSCNT ALT WHICH WE OBSERVED ON OUR TCASII TO BE APPROX FL344. AFTER A DSCNT OF APPROX 250 FT TO FL327.5 WE RECEIVED A 'CLR OF CONFLICT' TCASII ADVISORY. AS WE STARTED OUR TCASII DSCNT WE NOTIFIED ZOB WE WERE DSNDING ON A TCASII RA. AFTER 'CLR OF CONFLICT' ADVISORY WE CLBED BACK TO FL330 AND ADVISED CTR. WHEN I QUESTIONED ZOB ON WHAT HAD HAPPENED; THEY RESPONDED THAT THEY DID NOT KNOW.