MD80 CREW HAD A TCASII RA IN ZOB CLASS A AIRSPACE.

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WE WERE LEVEL AT FL350 AND HAD JUST TRANSITIONED FROM J64 TO J78 WHEN WE WERE INSTRUCTED TO TURN R TO 360 DEGS. WE STARTED OUR TURN WHEN WE HEARD THE CTLR INSTRUCT ANOTHER ACFT TO TURN. WE SENSED CONCERN WITH THAT CALL. HE THEN GAVE US SOMETHING LIKE 'TURN IMMEDIATELY'; OR 'GIVE ME A HARD TURN.' MIND YOU; WE WERE HDG FROM WHAT I CAN REMEMBER ABOUT 240 DEGS AT FL310 AT MACH .76. I SAW THE ACFT; BUT IT WAS HARD TO TELL AT NIGHT HOW CLOSE HE WAS VISUALLY. I QUICKLY LOOKED AT MY SPD AND PUT THE BANK TO 30 DEGS. WHILE WE WERE ABOUT 1/2 WAY THROUGH THE TURN; WE RECEIVED A TA ALERT; FOLLOWED IMMEDIATELY BY AN RA ALERT TO CLB. I CLOCKED OFF THE AUTOPLT AND STARTED CLBING. WE TOLD ATC WE WERE RESPONDING TO AN RA. I THINK HE KNEW IT; AND WE CLBED ABOUT 700 FT AND THEN GOT 'MONITOR VERT SPD' AND THEN 'CLR OF CONFLICT.' I WOULD ESTIMATE ELAPSED TIME FROM THE FIRST INSTRUCTION TO TURN TO THE RA ALERT WAS LESS THAN 90 SECONDS. DURING THIS TIME; BELIEVE IT OR NOT; MY #1 FLT ATTENDANT WAS DELIVERING THE MEALS. SHE DID A GREAT JOB AND REALIZED WE WERE BUSY AND RESPONDED ACCORDINGLY.