FLC OF A CANADAIR; CL65; RESPONDED TO ARTCC CTLR CLRNC FOR DSCNT AND HEARD CTLR USE ANOTHER OF HIS COMPANY'S ACFT CALL SIGNS IN ACKNOWLEDGEMENT TO THEIR READBACK. THE CTLR CONTINUED TO CONFUSE THEIR CALL SIGN WITH THE OTHER ACFT'S CALL SIGN.

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WE CHKED ON WITH CTR (ZDC; I THINK) AT FL290. OUR FLT NUMBER WAS ACR X. AFTER I INITIATED THE FIRST CALL; ATC RESPONDED BY SAYING; 'ROGER; ACR Y AT FL290.' I THEN HEARD ACR Y RESPOND CONFUSINGLY; 'ROGER ACR Y.' I REALIZED THAT CTR HAD MISTAKEN US WITH ACR Y; SO I THEN RESCHEDULED ON AT FL290 AND CTR RESPONDED WITH 'ACR X.' I LATER LOST TRACK OF WHERE ACR Y WAS AT AND WHAT ALT. WE WERE THEN CLRED DOWN TO FL240 AND RESPONDED AS SUCH. OUT OF APPROX FL280; CTR ASKED 'ACR Y TO MAINTAIN FL270.' ACR Y RESPONDED AND I FELT THAT ATC MAY HAVE CONFUSED US AGAIN. I BROUGHT THE TCASII UP ON THE DISPLAY TO MAKE SURE THERE WAS NO CONFLICTING TFC AHEAD OF US. ASSURED THAT EVERYTHING WAS OK; I ASKED THE FO TO MONITOR RADIO #1 AS I CHKED THE WX IN RDU. WHEN I RETURNED TO THE FREQ; THE FO TOLD ME THERE HAD BEEN NO CHANGES. ABOUT THAT TIME; AROUND FL248; WE GOT A TA SHORTLY FOLLOWED BY AN RA FOR A CORRECTIVE CLB. THE CORRECTION WAS INITIATED AND WE LEVELED OFF AT FL250 AFTER TALKING TO ATC. THEY THEN ASKED US TO CONTACT ANOTHER FREQ AND SAID NOTHING OF THE ALT CONFLICT. A FEW MINS LATER I RETURNED TO THAT FREQ AND ASKED THE CTLR WHAT HAD GONE WRONG. HE SAID HE THOUGHT HE HAD ASKED US TO LEVEL OFF AT FL250. I; AS THE CAPT; DID NOT HEAR THIS AND THE FO ASSURED ME THAT HE WAS GIVEN ONLY FL240. THE CTLR THEN IMPLIED THAT EVERYTHING WAS OK AND NOT TO WORRY ABOUT IT. I THANKED HIM AND CHANGED FREQS. I THINK 2 THINGS COULD HAVE BEEN DONE TO AVOID THIS SIT. FIRST OF ALL; I SHOULD HAVE QUESTIONED ATC TELLING TO MAINTAIN FL270; AND SECONDLY; I THINK THE COMPANY SHOULD BE MORE CAUTIOUS ABOUT SCHEDULING 2 FLTS WITH SIMILAR FLT NUMBERS AT THE SAME TIME OF DAY. I WILL TALK WITH THE CHIEF PLT CONCERNING THIS.