ACR X AND Y OPPOSITE DIRECTION TFC SAME ALT ASSIGNED HAD LTSS. SYS ERROR.

Narrative

ACR X ASSIGNED BY PREVIOUS CTR TO FL350 EBOUND ON RADAR VECTORS FROM NEAR FMN TO MRV VOR AND WHILE MANEUVERING WITH MKC ARTCC CONCURRENCE TO AVOID WX WE ACCEPTED A HDG OF 075 TO ASSIST IN TFC SEPARATION. WE WERE SUDDENLY AND URGENTLY DIRECTED BY MKC ARTCC TO 'TURN R 30 DEGS IMMEDIATELY'. THIS COMMAND WAS REPEATED RAPIDLY AND STRIDENTLY AT LEAST 3 TIMES. THE SAME DIRECTIVE WAS ISSUED TO ACR Y APPARENTLY APCHING US FROM HEADON. WE BOTH ACKNOWLEDGED AT WHICH POINT WE WERE ALREADY IN AN EMER TURN AT A 45 DEG BANK; TURNED ON LNDG LIGHTS. WE THEN SPOTTED TFC IN OUR 11 O'CLOCK POS AND RECEIVED ANOTHER URGENT CALL FROM CTR DIRECTING US TO 'DSND IMMEDIATELY TO FL310'. THIS WAS REPEATED AT LEAST TWICE. WE CUT PWR TO IDLE STOPS; PITCHED DOWN 20 DEGS AND DSNDED AT MAX RATE TO FL310. CONFLICTING TFC PASSED ABOVE AND TO THE L OF OUR ACFT. MKE CTR APOLOGIZED. WE REQUESTED CLB TO 330 WHICH WAS APPROVED. WE THANKED MKC FOR ALERT. WE OVERHEARD CONFLICTING TFC RPT US IN SIGHT AND ADVISE THAT THEIR TCASII WAS OPERATING NORMALLY.