C130 ON IAP IN VMC HAS AN NMAC WITH PA32 NOT IN CONTACT WITH THE TWR WITHIN NQA CLASS D AIRSPACE.

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DURING A ROUTINE TRAINING FLT IN A MIL C130E (NON TCASII EQUIPPED); A NEAR MISS OCCURRED NEAR NQA (MILLINGTON; TN). OUR ACFT WAS A C130E ON AN IFR FLT PLAN. WE HAD COMPLETED HOLDING OVER MNFRD (MEM 015/027) AND WERE CLRED FOR THE VOR RWY 22 FULL PROC TURN BY ZME. AFTER RPTING PROC TURN INBOUND TO MEMPHIS APCH CTL; WE WERE GIVEN THE FREQ CHANGE TO MILLINGTON TWR PRIOR TO THE FINAL APCH FIX. WE RPTED GEAR DOWN APCHING THE FINAL APCH FIX TO MILLINGTON TWR APPROX 3 MI FROM MNFRD (THE FINAL APCH FIX). OUR ACFT WAS FULLY CONFIGURED FOR LNDG (FLAPS AT 50%; GEAR DOWN; 150 KIAS; LNDG LIGHTS ON; WINGTIP TAXI LIGHTS ON; ANTI-COLLISION AND POS LIGHTS ON). WE WERE AT ALT 2000 FT MSL (APPROX 1700 FT AGL) COORDINATES 5.25.45N 089.50.25W; AIRSPD 150 KIAS. THIS POINT IS CLASS E AIRSPACE; UNDERNEATH THE LATERAL LIMITS OF THE CLASS B AIRSPACE OF MEM; WITH FLOOR 700 FT ABOVE THE SURFACE. THE FE CALLED THE TFC AND BOTH THE STUDENT AND INSTRUCTOR (ACFT COMMANDER) INITIATED AN EVASIVE MANEUVER TO PULL UP. THE OFFENDING ACFT (A PROP-DRIVEN CIVILIAN ACFT) PASSED 50 FT BELOW AND 75 FT R OF OUR ACFT DURING THE MANEUVER. THE ACFT CLBED 200+ FT DURING THE MANEUVER. WE CALLED MILLINGTON TWR AND ASKED IF THEY KNEW THAT WE JUST EXPERIENCED A NEAR MISS AND IF THEY WERE TALKING TO THE ACFT? THE CIVILIAN ACFT CALLED BACK TO RPT THAT HE WAS 'SORRY' AND THAT HE 'TRIED TO AVOID US.' TWR DID NOT KNOW OF THE NEAR MISS.