B737-300 CREW AND ANOTHER COMPANY ACFT WERE GIVEN A HOLD AT THE SAME POINT; AT THE SAME ALT IN ZOB CLASS A.

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WE WERE GOING FROM WHITE PLAINS TO ORD AND GIVEN A HOLDING CLRNC FROM ZOB TO HOLD E EWC ON J64. R HAND TURNS; 10 MI LEG AT FL350. WE PROGRAMMED THE HOLD IN THE FMC AND MANUALLY ENTERED THE HOLDING INFO ON OUR RADIOS. WE REPORTED ENTERING THE HOLD AT FL350 AT XA50. DURING THIS TIME ACR FLT XXX WAS GIVEN A HOLDING CLRNC TO HOLD E OF WEC ON J64 AT THE 30 DME FIX. R HAND TURNS; 10 MI LEGS. AS WE WERE ENTERING OUR SECOND TURN INBOUND WE RECEIVED A TA. WE LOOKED FOR TFC BUT DIDN'T SEE IT. THIS WAS IMMEDIATELY FOLLOWED BY AN RA TA WHICH TIME WE FOLLOWED THERA AND BEGAN A DESCENT. I REPORTED THE RA TO ZOB. THIS TIME ACR FLT XXX RECEIVE A RA AN BEGAN A CLIMB. THEY REPORTED THIS TO ZOB ATC AS WELL. WE THEN RECEIVED A CLR OF CONFLICT AND WE CLIMBED BACK TO FL350. WE DESCENDED APPROX 500 FT DURING RA. ACR FLT XXX RECEIVED CLR AND DESCENDING BACK TO FL350. I ASKED ZOB CENTER WHAT HEY PLAN TO DO AS THERE WERE TWO FO US IN A HOLDING PATTERN AT 350? THIS TIME HE GAVE ACR FLT XXX A CLRNC TO HOLD AT 40 DME FIX WHICH THEY ACKNOWLEDGED AND DID. WHILE INBOUND TO FIX ZOB CALLED US AND TOLD US TO CALL ZOB ABOUT A POSSIBLE VIOLATION. I WAS TOLD THEY ARE INVESTIGATING A VIOLATION OF PROTECTED AIRSPACE. IT WAS LATER DETERMINED BOTH ACR FLTS WERE ON TRACK AS FAR AS ALT AND AIRSPD IN REGARD TO THE CLRNC. THE UNION REP WAS TOLD BY ZOB INVESTIGATIVE BOARD THAT THEY HAD DETERMINED THAT THIS INCIDENT WAS CTLR ERROR.