NMAC WHILE CONDUCTING A VISUAL APCH.

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AT SEATTLE TACOMA INTL ARPT; APCH CTL PLACED US; VIA RADAR VECTORS; ON L BASE TO RWY 16L. WE WERE ASSIGNED 210 KTS AT 5000 FT AND 250 DEG HDG TFC FOR A VISUAL APCH WAS CALLED TO US. WE DID NOT HAVE THE TFC TO FOLLOW BUT WE SEARCHED FOR THE MD-80 AND FOUND HIM. BY THE TIME WE FOUND THE TFC OUR ASSIGNED VECTOR (250 DEGS) HAD US PERPENDICULAR AND ABEAM THE EXTENDED CTRLINE OF RWY 16L. SO WE ARE N OF THE ARPT HDG W AND BEGAN OUR VISUAL. WE APCHED FINAL FROM R TO L. APCH ADVISED MAINTAIN 180 KTS TO BOEING FIELD; AND CALL TWR. JUST PAST BOEING FIELD ON APCH TO RWY 16L AT SEA I OBSERVED A TCASII ALERT. THE TCASII SHOWED PLUS 01 (100 FT) AND THE TARGET WAS DIRECTLY OVERHEAD. I ADDED FORWARD PRESSURE TO THE YOKE AND SEARCHED FOR THE TARGET. WITHIN SECONDS A B-737 APPEARED ON MY R APPROX 200-300 FT. HIS SPD WAS FASTER THAN OURS. I WATCHED HIS GEAR EXTEND. THE 737 WAS NEVER IN FRONT OF US; AND NEVER CALLED AS TFC TO US. WHEN THE 'EVENT' HAPPENED WE WERE CONFIGURED; ON SPD; AND JUST PAST BOEING FIELD. WE WERE ON GS. THE APCH AND LNDG AFTER THE EVENT WAS NORMAL. THE CAPT AND I DEBRIEFED THE CHIEF PLT.