DC9 CREW RECEIVE A CLRNC ZAU ARTCC MEANT FOR ANOTHER FLT WITH A SIMILAR CALL SIGN AND STARTED DSCNT.

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OUR ATC CALL SIGN FOR THIS FLT WAS XXX AND SOMEONE ELSE ON ZAU FREQ HAD A SIMILAR SOUNDING CALL SIGN. WHILE DSNDING FROM FL330 TO FL290; WE WERE FURTHER CLRED TO FL240. AT AROUND FL282; ZAU ASKED US TO SAY ALT. THIS CAUGHT OUR ATTN. WE RESPONDED WITH 'FL282 DSNDING TO FL240' AND CTR TOLD US TO STOP AT FL270. WE THOUGHT THAT THIS WAS ODD; SO WHEN WE NEXT TALKED TO CTR; WE ASKED IF WE HAD BEEN AT THE WRONG ALT. CTR SAID 'YES' AND WE TOLD HIM THAT WE HAD READ BACK OUR DSCNT CLRNC TO FL240 WHEN WE WERE GIVEN IT. CTR RESPONDED THAT WE MUST HAVE READ BACK THE CLRNC AT THE SAME TIME AS SOMEONE ELSE (THUS OUR READBACK WAS NOT HEARD). CTR ADDED THAT NO CONFLICT HAD OCCURRED AND THERE WAS NO CONCERN ON HIS PART. KNOWING THAT THERE WAS ANOTHER SIMILAR SOUNDING CALL SIGN ON FREQ; WE THOUGHT THAT WE WERE EXTRA VIGILANT; BUT OBVIOUSLY COULD HAVE BEEN MORE. ALSO; IT HAD ALREADY BEEN A SEEMINGLY LONG DAY WITH MECHANICAL AND WX ISSUES AFTER A SHORT LAYOVER. I'VE HEARD IT HAPPEN SEVERAL TIMES BEFORE WHERE 2 ACFT READ BACK A FREQ OR ALT CHANGE; BUT USUALLY CTR CATCHES THE FACT THAT 2 ACFT RESPONDED AT THE SAME TIME. BESIDES BEING MORE CAREFUL WHEN ACCEPTING CLRNCS WHEN SIMILAR CALL SIGNS ARE ON FREQ; POSSIBLY HAVING CTR REPEAT THE CALLSIGNS TWICE WOULD HELP.