NMAC IN CLOSE PROX OF AIRSPACE BOUNDARIES.

Narrative

WE HAD BEEN VECTORED FOR A PRACTICE CAT III APCH TO RWY 16R AT SEA. WE INTERCEPTED FINAL OVER PARKK OM ABOVE THE GLIDE PATH AT 3000 FT MSL. SINCE WE WERE HIGH ON THE GLIDE PATH AND NEEDED TO MAINTAIN 170 KTS DUE TO FASTER TFC IN TRAIL; WE DISCONTINUED THE PRACTICE APCH. ON AN APPROX 3.5 MI FINAL AT 2000 FT MSL; STILL ABOVE THE GLIDE PATH; WE RECEIVED A TCASII RA INSTRUCTING US TO DSND AT APPROX 2500 FPM. WE ACCOMPLISHED THIS PER TCASII PROCS AND SIGHTED A BEECHCRAFT BARON XING OUR PATH FROM L TO R ON AN APPROX HDG OF 330 DEGS. OUR HDG WAS 160 DEGS; OUR FLT PATHS CROSSED AND THE TCASII INDICATED THAT THE BEECHCRAFT WAS 100 FT ABOVE US. UPON CHKING IN WITH SEA TWR AND ADVISING THEM OF THE RA; WE WERE TOLD THERE WERE NUMEROUS TARGETS IN THE VICINITY OF BOEING FIELD. WE WERE NEVER ADVISED OF THE TFC IN OUR VICINITY. SEA TWR DID NOT KNOW THE TFC WAS THERE EITHER. WE DID RECEIVE 2 PRIOR TA'S ON OTHER TFC IN THE BOEING PATTERN. WE DID NOT RECEIVE A TA ON THE BEECHCRAFT; ONLY AN INSTANTANEOUS RA. IT APPEARS THE BEECHCRAFT CLBED ABOVE THE BOEING AIRSPACE INTO THE SEA AIRSPACE WITH NO CLRNC TO DO SO. HAD OUR ACFT NOT HAD TCASII A SEVERE MID-AIR COLLISION WOULD HAVE HAPPENED.