AN ACR MDT HAS A LESS SEVERE NMAC WHILE FLYING IN ZMP CTL AREA.

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ENRTE FROM GFK-TVF FLT XX OPERATED BY ACR. WE DSNDED TO 3000 FT AFTER INITIAL CRUISE OF 7000 FT. TVF AWOS RPTED ZZ40Z; 2200 FT OVCST; 10 MI; -04/-15; 3006; ALTIMETER 30.28. WE WERE OPTING FOR A VISUAL APCH. LEVEL AT 3000 FT (200 FT BELOW THE OVCST) WE NOTICED A TCASII TARGET (BLUE; PROXIMATE TFC) INDICATING LEVEL WITH US AT 3000 FT AT OUR 12 O'CLOCK POS; VARYING TO 1 O'CLOCK POS. THIS TURNED TO A YELLOW TA ON TCASII 'TFC; TFC.' I SAW INTRUDER ACFT IN A L WING DOWN POS AT 12 O'CLOCK LEVEL WITH US. I INSTRUCTED THE FO TO IMMEDIATELY 'TURN L NOW.' WE PASSED OFF THE R SIDE OF THIS ACFT WAY TOO CLOSE. I FILED AN NMAC RPT WITH ZMP BECAUSE I FELT THE INTRUDER ACFT WAS IN THE WRONG. CRUISING WBOUND VFR AT 3000 FT; 200 FT BELOW THE OVCST ON A PUBLISHED AIRWAY. AS WE WERE DEVIATING THE TCASII ISSUED AN RA TO DSND; BUT WE ALREADY HAD TFC IN SIGHT AND WE DEVIATED TO HIS R (OUR L). AT ABOUT THIS TIME ZMP CTR ADVISED US OF TFC AT 12 O'CLOCK (HE ALREADY PASSED) AND CTR SAID HE JUST 'POPPED UP.' TCASII DID A NICE JOB ON THIS DAY.