MD80 FLT CREW OBSERVE LEARJET PASS THEM ON 3 MI FINAL TO SEA RWY 34R DSNDING THROUGH 1400 FT MSL. AFTER INCIDENT CONVERSATION WITH TWR IS ADVISED THAT LEARJET WAS CONDUCTING A CHK NAV APCH TO RWY 34L.

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WE EXPERIENCED A TCASII 'TFC' WARNING (VISUAL AND AURAL) WHILE DSNDING THROUGH 1400 FT MSL (APPROX 1000 FT AGL) ON A VISUAL APCH TO RWY 34R AT SEA. WHEN THIS OCCURRED; WE WERE STABILIZED ON THE ILS GS AND ABOUT 3 NM FROM THE THRESHOLD. THE TCASII DISPLAY INITIALLY INDICATED THAT THE TFC WAS BEHIND OUR ACFT AT OUR 6 O'CLOCK POS; AND 600 FT BELOW US. THE TARGET ON THE TCASII RAPIDLY APCHED OUR ACFT FROM BEHIND UNTIL THE SYMBOL MERGED WITH OUR ACFT SYMBOL. (I ASSUME WE DID NOT RECEIVE A TCASII RA MANEUVER SINCE WE WERE BELOW THE RA INHIBIT5 ALT.) BEFORE I COULD QUERY THE TWR CTLR REGARDING THE TFC; A LEARJET CAME INTO VIEW FROM BENEATH OUR L WING. THE ACFT WAS WITHIN AN ESTIMATED 100 FT LATERALLY; WAS WELL BELOW THE GS FOR EITHER RWY AND WAS ABOUT 600 FT BELOW US (AS INDICATED ON THE TCASII). THE ACFT PASSED US LIKE WE WERE STANDING STILL AND I WOULD ESTIMATE ITS SPD IN EXCESS OF 200 KTS. AS THE ACFT GOT WELL AHEAD OF US; WE COULD SEE THAT IT WAS NOT IN A LNDG CONFIGN. IT WAS CLEAN WITH THE LNDG GEAR RETRACTED. WHEN THE LEAR ARRIVED OVER THE THRESHOLD OF RWY 34L; IT EXECUTED A GAR WITH A VERY STEEP; HIGH SPD; CLBING L TURN OUT OF THE TFC PATTERN. WE IMMEDIATELY QUERIED THE TWR CTLR ABOUT THIS ACFT; WHO INFORMED US THAT THE LEARJET WAS ON A LOW APCH AND HAD BEEN TOLD TO KEEP OUR ACFT IN SIGHT. THE FO CALLED THE TWR AFTER WE ARRIVED AT THE GATE. HE TOLD THE TWR SUPVR THAT HE FELT THAT THERE HAD BEEN A LOSS OF SEPARATION. SINCE WE WERE NEVER ADVISED THAT THERE WAS ANY OTHER TFC IN OUR AREA (OTHER THAN THE DHC-8 WE WERE FOLLOWING TO RWY 34R) HE QUESTIONED WHO WAS RESPONSIBLE FOR MAINTAINING SEPARATION. THE TWR SUPVR SAID THAT THE TWR CTLR HAD US BOTH IN SIGHT AND WAS SUPERVISING THE SEPARATION. SHE DID APOLOGIZE PROFUSELY FOR THIS INCIDENT. SHE TOLD THE FO THAT THE LEARJET WAS AN FAA ACFT DOING NAV FLT CHKS. SUPPLEMENTAL INFO FROM ACN 593534: AT NO TIME WAS TFC GIVEN TO US ABOUT THE LEAR OR ITS INTENTIONS BY EITHER APCH CTL OR THE TWR. THE CTLR IN CHARGE APOLOGIZED FOR THE CONFUSION AND TOLD US THAT TFC SHOULD HAVE BEEN GIVEN TO US. THE LEARJET WAS AN FAA FLT CHK DOING A TEST ON THE RWY 34L ILS.