ACR X UNAUTH DSCNT FROM ASSIGNED ALT TCASII RA HAD LTSS FROM ACR Y. SYS ERROR ALTDEV. EVASIVE ACTION TAKEN.

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ENRTE TO CVG WE HAD BEEN GETTING STEPPED DOWN A COUPLE THOUSAND FT AT A TIME. LEVEL AT FL240 ON THE SWEED A ARR PAST THE HENDERSON VOR; ZID ADVISED ACR X DSND AND MAINTAIN FL200. I READ BACK THE CLRNC TO ATC. I THEN SET THE MODE CTL PANEL ALT TO 20000 FT AND ANNOUNCED '20000 FT SET' AS PER COMPANY PROC. THE CAPT RESPONDED; '20000 FT CHKED' AS PER COMPANY PROC. THE CAPT THEN INITIATED A DSCNT USING THE VERT SPD WHEEL ON THE MODE CTL PANEL. THE RATE WAS 1000 FPM. DSNDING THROUGH 23800 FT WHEN AN AIRPLANE SHOWED UP ON TCASII DIRECTLY BELOW US SHOWING MINUS 8. THE CAPT IMMEDIATELY BEGAN TO LEVEL OFF USING THE VERT SPD WHEEL. I LOOKED OUT THE R WINDSHIELD AND OBSERVED WHAT APPEARED TO BE A FOKKER JET PASSING BELOW US AND TO THE R. AT THIS TIME THE TCASII COMMANDED A CLB AND WE BEGAN A GRADUAL CLB. ZID THEN INQUIRED AS TO WHAT ALT WE WERE AT. WE ADVISED THE CTLR HE HAD CLRED US TO FL200. HE TOLD US TO CLB BACK TO FL240; AND THAT THE FL200 WAS FOR ANOTHER ACFT. ADVISED HIM I HAD READ BACK 'ACR X CLRED TO FL200.' HE TOLD US TO LISTEN UP. THE CAPT AND I BOTH HEARD THE CLRNC. THE CAPT HEARD ME READ BACK THE CLRNC AND CONFIRMED THE ALT WAS RESET PROPERLY ON THE MCP. I DO NOT KNOW HOW THIS COULD HAVE HAPPENED OTHER THAN THE ATC CTLR ISSUED US A CLRNC HE HAD INTENDED FOR ANOTHER ACFT. THE WX IN CVG WAS BAD AND THINGS WERE BACKED UP AND BUSY. SUPPLEMENTAL INFO FROM ACN 294505: ACR X TOOK THE CLRNC OF ANOTHER ACFT AND DSNDED TO FL235 IN CONFLICT WITH AN ACFT AT FL240.