LEAR 35 WAS INVOLVED IN A NMAC WHILE CONDUCTING AN INST APCH. EVASIVE ACTION WAS TAKEN.

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PART 91 FLT FROM ELP DIRECT MFE. IFR FLT PLAN. APCH FACILITY WAS VECTORING US FOR MFE RWY 31 BACK COURSE. HE CLRED US TO 2000 FT ON A HDG OF 130 DEGS (HDG IS APPROX). HE CALLED TFC VFR 5 MI AWAY AT 3000 FT. I RESPONDED WITH 'OK; WE ARE THROUGH 2700 FT; THANK YOU.' WE LEVELED OFF AT 2000 FT. 2 MINS LATER; AFTER COMPLETING THE APCH CHKLIST; I LOOKED UP AND SAW TFC 1-2 O'CLOCK POS; SAME ALT; LESS THAN 500 FT. I GRABBED THE AIRPLANE; SHOVED THE THROTTLE LEVERS UP TO THEIR MAX; AND YANKED BACK ON THE YOKE AS HARD AS I COULD TO AVOID THE OTHER ACFT. THE AIRPLANE ALSO HAD TO BE BANKED APPROX 20 DEGS R TO AVOID THE VFR TFC. I BELIEVE THE OTHER TFC WAS A MOONEY. I IMMEDIATELY INFORMED ATC WE INITIATED A CLB TO 2700 FT IN ORDER TO MISS THE COLLISION. I ASKED HIM IF HE HAD ANY NEARBY TARGETS. HIS RESPONSE WAS 'NO...WELL THERE IS ONE; 2 MI AND 3000 FT.' I INFORMED HIM THE TARGET WAS NOT AT 3000 FT BECAUSE WE HAD TO TAKE EVASIVE ACTION TO MISS HIM AT 2000 FT. THE APCH SUPVR WAS CALLED ON THE GND AND NOTIFIED OF THE NMAC BY ME. HE SINCERELY APOLOGIZED FOR THE INCIDENT SINCE WE WERE IFR FLT PLAN AND TOLD ME HE WAS GOING TO LOOK INTO THE TAPES TO SEE WHAT HAPPENED.