C550 FLC INITIATES TCASII EVASIVE MANEUVER WHEN ENCOUNTERING XING TFC WHILE IN DSCNT.

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I (ACFT X) WAS ON IFR FLT PLAN ON JUN/XA/99 FROM GTF TO UKF. ON MY DSCNT TO UKF FROM FL410; WE WERE STEPPED DOWN THROUGH DIFFERENT FLT LEVELS THEN RECEIVED A CLRNC TO 15000 FT THEN CLRNC TO 11000 FT. THERE WAS A BROKEN LAYER OF CLOUDS AT APPROX 10000 FT MSL. AT APPROX 14000 FT; I NOTICED AN AIRPLANE ON TCASII. AS I LOOKED OUT THE WINDOW; A PLANE (ACFT Y) APPEARED TO BE AT MY ALT. IT WAS DARK; SO IT WAS HARD TO BE SURE. THE TCASII GAVE A WARNING SO I STARTED TO TAKE CORRECTIVE ACTION; THEN I REALIZED WE WOULD MISS. I WAS SURPRISED THAT THE CTLR NEVER CALLED OUT TFC. I CONTACTED THE CTLR TO RPT TO HIM THE TFC. HE ASKED ME WHAT MY ASSIGNED ALT WAS. I TOLD HIM 11000 FT. HE SAID; 'NO; YOU WERE CLRED TO 15000 FT.' I RPTED TO THE CTLR THAT MY CLRNC WAS 11000 FT AND REPEATED 11000 FT BACK TO HIM. WE WERE STILL DSNDING. I ASKED THE CTLR IF HE WANTED ME AT 11000 FT OR TO GO BACK TO 15000 FT. HE TOLD ME TO CONTINUE MY DSCNT TO 11000 FT. I DON'T KNOW WHO WAS AT FAULT. COM WILL ALWAYS BE A MAJOR CAUSE FOR AVIATION ACCIDENTS; WHETHER PLT OR CTLR ERROR. NO MATTER HOW HARD WE LISTEN OR CONCENTRATE THERE STILL SEEMS TO BE FAILURES IN COM.