ACFT 1 ON AN ILS APCH IS ALERTED BY TCASII OF CLBING OPPOSITE DIRECTION TFC (ACFT 2). ACFT 1 DID NOT SIGHT THE TFC AND THEN TAKES EVASIVE ACTION AS DIRECTED BY TCASII. AFTER THE CLR ADVISORY FROM TCASII; ACFT 1 RESUMES THE ILS. ACFT 2 WAS NEVER SIGHTED.

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EXECUTING AN ILS APCH TO RWY 16R AT SEATAC INTL ARPT UNDER IFR; MY ACFT WAS ON LOC AND GS FROM ABOUT 3000 FT MSL. BOTH BOEING FIELD (BFI) AND SEA WERE INTERMITTENTLY VISIBLE THROUGH A SCATTERED TO BROKEN CLOUD DECK 200-300 FT THICK; WITH A BASE AT 1100 FT AGL (1500 FT MSL). APCHING OVERHEAD BFI; THE TCASII INDICATED LOWER TFC (MANY ACFT); NON-CONFLICTING; APPARENTLY IN THE BFI TFC PATTERN BELOW. AS WE PASSED BFI; ANOTHER TCASII TARGET APPEARED; LOW AT OUR 12 O'CLOCK POS AND CLBING THROUGH ABOUT 1000 FT BELOW OUR ALT; ABOUT 1 MI AHEAD. NEITHER I NOR MY COPLT COULD ACQUIRE THE TFC VISUALLY. THE TCASII WARNED; 'TFC.' THE COPLT OBSERVED THE TARGET CHANGE COLOR FROM OLIVE TO AMBER TO RED RAPIDLY; AND THE TCASII GAVE A RA; 'CLB... CLB...' WHILE COMMANDING A MINIMUM CLB RATE OF 1500 FPM. THE COPLT SAW THE TARGET CLOSE TO ABOUT 200 FT DIRECTLY BELOW US JUST AFTER I HAD ADDED PWR AND STARTED CLBING. AFTER WE HAD CLBED ABOUT 700 FT; THE TCASII ANNOUNCED 'CLR OF TFC;' AND I DID MY BEST TO TRANSITION SMOOTHLY BACK TO THE GS FOR A NORMAL LNDG ON RWY 16R. AT NO TIME BEFORE OR AFTER THE TCASII WARNING COULD WE ACQUIRE THE OTHER ACFT VISUALLY; DUE TO A COMBINATION OF CIRCUMSTANCES; E.G.; THE NOSE HIGH APCH ATTITUDE OF MY ACFT; PARTIAL VISIBILITY LOSS DUE TO THE BROKEN CLOUD DECK; AND THE VISUAL CLUTTER OF TREES; ROADS; CARS; HOUSES; ETC.; IN THE BACKGROUND. ABOUT 45 MIN LATER IN A CONFERENCE PHONE CALL BTWN ME; MY AIRLINES' DISPATCH AND SAFETY STAFF; AND SEA TWR SUPVR (ATC); THE LATTER SAID THAT THE TFC 'POPPED UP' WITHOUT WARNING; AND WAS STILL UNIDENT. HE ALSO INDICATED THAT THE 'CLASS B' AIRSPACE BOUNDARY IS ONLY 100 FT BELOW THE ILS GS. NOTWITHSTANDING THIS FACT; IT SEEMS THAT ANY ACFT IN THAT AREA IS REQUIRED TO BE IDENTED; CLRED AND IN RADIO CONTACT WITH ATC. THIS IS MY SECOND NEAR MISS IN 3 MONTHS WITH AN ACFT (UNKNOWN) ENCROACHING ON APCH AIRSPACE (THE FIRST WAS AN EMER ENG OUT APCH TO RWY 8L AT HNL). APPARENTLY; THE SYS NEEDS WORK. IN THIS CASE; I BELIEVE THAT THE TCASII MAY WELL HAVE PREVENTED A MIDAIR COLLISION.