NMAC BETWEEN ACR-MDT AND BMB. OPERATIONAL ERROR.

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LEVEL AT 8000' MSP CENTER TURNED US OVER TO SAW APCH. ON INITIAL CONTACT WE WERE CLRED FROM 8000 TO 3000' AT PLT'S DISCRETION. CAPT WAS FLYING THIS LEG. OUR CLRNC DIRECT TO MQT TOOK US OVER SAWYER AFB JUST OFF THE N END OF RWY 1/19. AS WE WERE DSNDING THROUGH APPROX 4000' APCH ASKED IF WE HAD A BMB WHICH JUST DEPARTED TO THE N. MY REPLY WAS 'NEGATIVE.' UPON RECEIPT OF MY REPLY APCH INSTRUCTED US TO TURN RIGHT TO A HDG OF 030 DEGS FROM THE 330 DEG HDG WE WERE ON. I READ BACK CLRNC AND LOOKED OUT THE RIGHT WINDOW JUST AS CAPT WAS STARTING TURN. THE BMB CAME INTO VIEW JUST FORWARD OF THE RIGHT WING; APPROX 200-400' AND CLBING; IMMEDIATELY UPON VISUAL CONTACT I STARTED A LEFT TURN. CAPT THEN SAW THE ACFT AND CONTINUED THE LEFT TURN. THE BMB ALSO STARTED A LEFT TURN. AT THIS POINT I DON'T BELIEVE THEY COULD SEE US. I THEN LOST SIGHT OF THEM AS THEY APPARENTLY PASSED OVER THE TOP OF US. WE FLEW TO DEST AND RPTED INCIDENT TO COMPANY MGMNT THEN FLEW THE REMAINING PORTION OF OUR SCHEDULE. IN LATER DISCUSSION IT WAS DETERMINED THAT 2 CTLRS WERE WORKING APCH AT THE TIME. I BELIEVE ONE WAS XMITTING SIMULTANEOUSLY ON CIVIL AND MIL FREQ WHILE THE OTHER WAS STRICTLY XMITTING ON MIL FREQ. APCH GAVE BMB CLB CLRNC TO FL180 AND HAD TO REPEAT IT SEVERAL TIMES. DURING THIS TIME BOTH ACFT CROSSED OVER RADAR SIGHT AND WERE TEMPORARILY 'LOST.' WHEN RADAR CONTACT WAS RE-ESTABLISHED (PRIMARY ONLY) APCH INSTRUCTED US TO TURN RIGHT AND INSTRUCTED THE BMB TO TURN LEFT. I BELIEVE THEY HAD THE TARGETS CONFUSED AND WERE ACTUALLY TURNING US INTO EACH OTHER.