A B737-300 FLC ACCEPTS A CLB CLRNC MEANT FOR ANOTHER ACFT AND IS TURNED OFF COURSE AND ASKED TO DSND WHEN ATC BECOMES AWARE OF THE ALTDEV 71 MI E OF CRL; MI.

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IN CRUISE FLT AT FL330; ZOB (133.37) CLRED US TO FL350. FL350 WAS READ BACK AND WE STARTED THE CLB. AT APPROX 34700 FT ZOB ASKED OUR ALT. WHEN WE READ BACK 34700 FT; CLE SAID DSND IMMEDIATELY TO FL330 AND THEN TURN R. ZOB SAID WE ACCEPTED SOMEONE ELSE'S CLRNC TO FL350. THE FO AND MYSELF ARE QUITE SURE CLE CLRED US TO FL350; AS WE READ IT BACK; SET FL350 IN THE ALT WINDOW AND BOTH OF US VERIFIED FL350. THERE WAS NO TFC CONFLICT AND AFTER APPROX 8-10 MINS WE WERE CLRED BACK TO FL350. CLE HANDED US OFF TO NEXT CTLR AND SAID; 'THANKS FOR THE HELP.' THE CTLR SAID THAT HE NEVER HEARD OUR READBACK TO CLB TO FL350. I BELIEVE THIS EVENT OCCURRED DUE TO THE LACK OF COM. IF WE DID ACCEPT SOMEONE ELSE'S ALT CHANGE THEN WHEN WE READ IT BACK; THE CTLR SHOULD HAVE CAUGHT THE ERROR; HOWEVER; THEY ARE SOMETIMES OVERLOADED OR THE RADIO FREQ MAY BE BLOCKED. THE CTLR DID SEE THE ALT CHANGE AND CORRECTED IT -- THIS IS GOOD. ALSO TCASII IS A GREAT SAFETY DEVICE AS IT WILL SHOW A PENDING TFC CONFLICT. THERE CANNOT BE ENOUGH VERIFYING AND CONFIRMING WHEN THERE ARE ALT CHANGES INVOLVED.