C182 ACFT ON ILS APCH WAS UNDER FLOWN BY C172 VFR. POSTFLT REVIEW WITH THE OTHER PLT REVEALED THAT HE HAD TAKEN EVASIVE ACTION. APPARENTLY THERE WAS LACK OF TWR COORD WITH THE TFC SINCE ONE ACFT WAS ON AN IFR FLT PLAN AND EXECUTING AN ILS WHILE THE OTHER ACFT ENTERED THE TFC PATTERN FLYING UNDER AND CLOSE TO RPTR ACFT.

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AS WE RPTED TO THE TWR; WITHIN SECONDS THE TWR REQUESTED THE LOCATION OF A VFR ACFT THAT HAD APPARENTLY RPTED 5-6 MI OUT OVER THE CAPITAL AT 1500 FT. WE HAD NOT HEARD THAT RPT; BUT THE LOCATION CAUGHT MY ATTN AS IT WOULD PLACE THAT ACFT IN OUR SAME RELATIVE AREA; VERY CLOSE TO THE APCH PATH; AND I INCREASED MY OUTSIDE SCAN TO THE MAX. I RECALL NOTING OUR ALT A FEW SECONDS BEFORE AT 2100 FT AND DSNDING AT APPROX 500 FPM. WITHIN A FEW SECONDS OF OUR SWITCH TO TWR AND RPT; THE TWR ASKED THE OTHER ACFT WHAT THEIR LOCATION WAS; AND THEIR REPLY WAS THAT WE HAD JUST OVERFLOWN THEM AT 100 FT. I RECOGNIZED THE PLT'S VOICE AS THAT OF AN EXPERIENCED LCL FLT INSTRUCTOR AND FBO OWNER. I DID NOT SEE THE OTHER ACFT UNTIL WE WERE ON SHORT FINAL; AT WHICH TIME THAT ACFT WAS APPROX 1.5 MI IN TRAIL. AS I CAN BEST RECONSTRUCT THE CHAIN OF EVENTS; THE OTHER ACFT WAS APCHING THE ARPT ALONG THE LOC INBOUND COURSE AT 1500 FT; STRAIGHT-IN. IT IS UNKNOWN TO ME WHAT ACFT HE WAS IN; BUT AS HE ONLY HAS C150'S AND A C172 IN HIS RENTAL/INSTRUCTIONAL FLEET; I BELIEVE IT IS REASONABLY TO SURMISE THAT HE WAS IN ONE OF THOSE ACFT; WITH A CRUISE SPD OF APPROX 90-100 KTS. WE WERE APCHING THE ARPT AT 2500 FT; ON THE ILS INBOUND AS INSTRUCTED BY ATC; AND AS NOTED EARLIER; AT APPROX 90 KTS INDICATED. ATC HAD GIVEN US NO ACFT ADVISORIES; NOR HAD I SEEN ANY ACFT IN THE IMMEDIATE AREA AS WE MADE THE INTERCEPT. GIVEN THAT SCENARIO; THE PRIMARY CAUSE OF THE ALLEGED NEAR MISS WOULD APPEAR TO BE THAT THE OTHER ACFT WOULD HAVE BEEN VIRTUALLY BENEATH US; AND NOT VISIBLE TO US SHORT OF AEROBATIC MANEUVERS ON OUR PART. THE CONTRIBUTING FACTORS LEADING TO THE EVENT WOULD INCLUDE THE FACT THAT THE OTHER ACFT WAS BELOW US AND WOULD HAVE BEEN DIFFICULT TO SPOT IN GND CLUTTER; THE OTHER ACFT WAS VFR ON A BUSY APCH PATH KNOWING THAT IT WOULD BE IN CONSIDERABLE USE; WE DID NOT MONITOR BOTH APCH AND TWR FREQS; MY ATTN TO OUTSIDE SCANNING WOULD HAVE BEEN SLIGHTLY LESS THAN NORMAL DUE TO THE STUDENT/INSTRUCTOR RELATIONSHIP; THE OTHER CFI WOULD HAVE HAD THE SAME DIFFICULTY AND APPARENTLY FAILED TO SCAN APPROPRIATELY AS HE USED THE APCH COURSE. AS TO ACTIONS OR INACTIONS; WE TOOK NO EVASIVE ACTION AS WE WERE UNAWARE OF ANY PROB; BUT THE OTHER CFI LATER CLAIMED THAT THEY VEERED SHARPLY AWAY FROM US. HAD WE BEEN MONITORING TWR (DIFFICULT TO DO ON A DAY WHEN RADIO TFC IS HVY); WE PERHAPS WOULD HAVE HEARD THE OTHER ACFT RPT HIS POS AND COULD HAVE TAKEN THE INITIAL ACTION TO RESTRICT OUR DSCNT UNTIL THE LOCATION OF THE OTHER ACFT WAS FULLY DETERMINED. (EASY TO SAY IN HINDSIGHT!) THE OTHER CFI COULD HAVE APCHED THE ARPT AT AN OFFSET FROM THE APCH COURSE; AND/OR COULD HAVE BEEN MONITORING APCH TO DETERMINE IF OTHER ACFT WERE ON THE APCH COURSE. IT WOULD SEEM APPROPRIATE TO PROVIDE RECOMMENDATIONS TO THE CFI COMMUNITY TO AVOID IFR APCH PATHS DURING A VFR APCH. OFFSETS FOR VFR TFC ARE SIMPLE; WHERE IFR TFC IS RESTR TO THE COURSE UNLESS A CONFLICT IS DETECTED. I DID NOT RPT THE EVENT AS A NEAR MISS AS PREVIOUS ENCOUNTERS WITH THIS INDIVIDUAL HAD CAUSED ME TO BELIEVE HIS BEHAVIOR ERRATIC; WITH LESS THAN PROFESSIONAL DEMEANOR. I DID NOT KNOW IF THIS WAS ANOTHER 'SIT' WITH HIM OR IF THERE ACTUALLY HAD BEEN A NEAR MISS. I HAD NO OTHER WAY TO KNOW IF THERE HAD BEEN A NEAR MISS; SO PERHAPS DISMISSED THE EVENT TOO QUICKLY. IT WAS NOT UNTIL ABOUT 1/2 HR OR MORE LATER THAT THIS INDIVIDUAL APCHED ME ON THE GND VERY AGITATED AND ACCUSATORY THAT I BECAME QUITE CONCERNED ABOUT THE EVENT. MY REACTION TO THE OTHER CFI; HOWEVER; WOULD HAVE BEEN IRRELEVANT AS TO THE EVENTS THAT APPARENTLY TRANSPIRED; AS I WAS UNAWARE OF HIS PRESENCE AT THE TIME OF THE EVENT.