B727 CAPT SPOTS SEL ACFT 300 FT BELOW WHILE ON FINAL TO GEG THEN RECEIVES A TFC ALERT FROM THE CTLR AND A TCASII RA.

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WE WERE DSNDING THROUGH 5500 FT MSL TO 4000 FT AS ASSIGNED BY GEG APCH CTL FOR VECTOR TO THE ILS TO RWY 21 AT GEG WHEN OUR TCASII GAVE AN RA TO 'CLB; CLB NOW.' THE VSI INDICATED A 'GREEN BAND' CLB OF APPROX 1800-2000 FPM RATE. JUST PRIOR TO THE ALERT; I (THE CAPT) HAD SPOTTED WHAT APPEARED TO BE A SINGLE ENG/GA TYPE ACFT IN A TURN AT APPROX OUR ALT AT 12 O'CLOCK POS AND AN ESTIMATED DISTANCE OF 1 MI. I IMMEDIATELY LOOKED AT OUR DISPLAY AND SAW A TARGET AT 12 O'CLOCK POS AND APPROX 300 FT BELOW. AT THAT MOMENT; WE WERE GIVEN A TFC ALERT AND A FEW SECONDS LATER A 'CLB; CLB NOW' ALERT. THE FO; WHO WAS FLYING; DISCONNECTED THE AUTOPLT AND INITIATED THE CLB WHILE I FOLLOWED THROUGH WITH HIM ADVANCING THE THRUST LEVERS TO GAR EPR'S; AND LOOKING OUTSIDE TO RE-ESTABLISH VISUAL CONTACT WITH THE TARGET. AFTER THE CLR OF CONFLICT ANNUNCIATION AND ESTABLISHING VISUAL CONTACT; WE PROCEEDED WITH OUR DSCNT AND ADVISED APCH CTL WHO HAD ADVISED US OF TFC AT 12 O'CLOCK AFTER WE WERE GIVEN THE RA ALERT AND HAD INITIATED THE AVOIDANCE MANEUVER.