ACR HAS LTSS WITH MLG WHEN CLRED TO DSND THROUGH MLG ALT.

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FLT PROCEEDING ENRTE FROM HHH TO CLT. VIA DIRECT FLO WHEN ATC CLRED OUR FLT TO TURN L TO HDG OF 300 DEGS AND DSND OUT OF 15000 TO AN ALT OF 11000 FT. WHILE DSNDING THROUGH 14300 FT WE WERE GIVEN AN ORDER BY ATC TO CLB IMMEDIATELY TO 15000 FT. ATC THEN TOLD AN ACR FLT TO TURN L IMMEDIATELY. THE CTLR THEN ASKED IF WE WERE CLRED TO 11000 FT. WE ANSWERED IN THE AFFIRMATIVE. WE THEN PICKED UP THE ACR SET ON OUR TCASII APCHING FROM THE REAR AT ABOUT 7 O'CLOCK. WE WERE AT 15000 FT WHEN THE JET PASSED OFF OUR L SIDE. WE ASKED ATC TO CONFIRM THAT WE WERE IN FACT CLRED TO 11000 FT. ATC DID CONFIRM THAT THERE WAS A CTLR MISTAKE. NOTE: WHEN WE WERE GIVEN THE URGENT ORDER TO CLB BACK TO 15000 FT AND HEARD THE JET GIVING TURN INSTRUCTION; WE OF COURSE SUSPECTED AN ALT CONFLICT. THE FO WAS FLYING THE AIRPLANE; AND I WAS SEARCHING THE SKY AND THE TCASII FOR TFC. I THOUGHT SURELY TCASII WOULD SHOW CONFLICTING TFC; BUT BECAUSE THE TCASII HAS LIMITED REARWARD LOOKING CAPABILITY; THE JET ACFT WAS NOT SEEN UNTIL WITHIN 2 MI BEHIND US. THE JET'S CLOSURE RATE WAS FAST ENOUGH TO GIVE LITTLE TIME FOR CORRECTIVE ACTION.