AN ACR MLG CLBED IN RESPONSE TO A TCASII COMMAND.

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RADAR VECTORS FOR VISUAL APCH AT GEG; RWY 7 (3-21 CLOSED);HDG 270 DEGS CLRED TO DSND TO 5500 FT MSL. APCH POINTED OUT VFR TFC (SMALL ACFT) AT APPROX 1 O'CLOCK CLBING THROUGH 3500 FT. WE COULD NOT MAKE VISUAL CONTACT; BUT WERE ABLE TO OBSERVE HIM ON OUR TCASII (INCORPORATED IN EHSI). APCH WAS TALKING TO HIM ON DIFFERENT FREQ. WE HEARD APCH ASK HIM TO WHAT ALT HE WAS CLBING. SINCE WE WERE ON A DIFFERENT FREQ; WE DID NOT HEAR RESPONSE. HIS READOUT ON OUR TCASII WAS A CLBING READOUT 3800 FT; 3900 FT; 4000 FT. OUR TCASII GAVE YELLOW TFC WARNING. SUDDENLY HIS READOUT WENT TO 5000 FT (WE WERE AT 5700-5800 FT) AND WE RECEIVED A 'CLB; CLB' RA. WE FOLLOWED RA AND RECEIVED 'CLR OF CONFLICT' AT 5900 FT. WE RPTED THE RA TO ATC. HE STATED THAT IN ACCORDANCE WITH HIS RADAR; ADEQUATE SEPARATION WAS AVAILABLE. WE DID NOT LEAVE ASSIGNED ALT NOR DID WE DEVIATE FROM ANY CLRNC. UNEVENTFUL LNDG MADE. I TELEPHONED APCH CTL AFTER ARR AND WE AGREED THAT THERE WAS NO PROB. HOWEVER; SMALL ACFT LATER STATED HE WAS FILING A NASA RPT. SO; HERE IS MINE. RECOMMENDATION: APCH CTL WAS NOT BUSY. ALL ACFT SHOULD BE ON SAME FREQ IF APCHING AN ARPT ON A VFR DAY.