NMAC. A TRAINING FLT IS OVERTAKEN ON FINAL BY ANOTHER ACFT MAKING AN APCH TO THE SAME RWY.

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NEAR COMPLETION OF ROUTINE TRAINING FLT; WE REQUESTED AND RECEIVED CLRNC FOR A PRACTICE ILS RWY 15 APCH TO ADDISON ARPT. WE WERE GIVEN A SQUAWK CODE AND TOLD TO RPT AT THE OM INBOUND. WE SUBSEQUENTLY RPTED TO THE TWR THAT WE WERE OVER BRONZE (OM) AND WERE CLRED TO LAND. TFC VOLUME WAS VERY HVY AT THIS TIME AND 1-2 MINS AFTER WE RPTED AT BRONZE; ANOTHER ACFT RPTED AT BRONZE. ADDISON TWR THEN ASKED US WHERE WE WERE. WE RPTED THAT WE WERE INSIDE BRONZE OM. A FEW SECONDS LATER WHILE STILL ON DSCNT APPROX 2 MI FROM THE RWY; AN ACFT PASSED DIRECTLY BELOW US; ALSO ON APCH TO LAND. AT THIS POINT WE APPLIED FULL PWR AND INITIATED A TURNING CLB; NARROWLY AVOIDING CONTACT WITH THE OTHER ACFT. AFTER LNDG WE CALLED ADDISON TWR AND ASKED IF THEY KNEW WHAT HAPPENED. WE WERE ADVISED THAT WHEN 2 ACFT GET VERY CLOSE TOGETHER IT CAN APPEAR AS ONE ON THE RADAR. THEY WERE APPARENTLY AWARE OF THE NEAR MISS INCIDENT AND WOULD NOT ELABORATE FURTHER. I HAVE TO PRESUME THAT THE ACFT THAT PASSED UNDER US WAS THE SAME ONE THAT RPTED AT THE OM JUST BEHIND US; IE; ON THE RWY CTRLINE. IF AN ACFT IS LINED UP ON APCH TO THE RWY AS WE WERE; HOW COULD THEY NOT SEE ANOTHER ACFT (US) DIRECTLY IN FRONT AND ONLY SLIGHTLY ABOVE THEIR ALT? I HAVE REQUESTED THE TWR TAPES IN AN ATTEMPT TO ANSWER THIS QUESTION.