AN ACR MD80 FLC RPTS AN ENCOUNTER WITH A TWIN ENGINED ACFT AT 10000 FT WHILE TALKING TO APCH CTL. THE OTHER ACFT WAS NOT ON THE COM FREQ OR; APPARENTLY; REQUIRED TO BE.

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LEVEL AT 10000 FT; 25-30 MI E OF LAS IN CONTACT WITH APCH CTL. TARGET APPEARED ON TCASII AT APPROX 10 O'CLOCK POS; LEVEL AT OUR ALT CLOSE IN ON 20 MI RANGE; I SELECTED 10 MI THEN IMMEDIATELY 5 MI RANGE TO FIX HIS POS WHILE ASKING FO TO ASK APCH ABOUT TFC. AT SAME TIME TARGET WAS RAPIDLY CLOSING GOING TO TA AND THEN IMMEDIATELY TO AN RA. THIS HAPPENED WITHIN A SPAN OF POSSIBLY 4 SECONDS. WE RESPONDED TO THE RA COMMAND TO CLB AFTER WHICH APCH GAVE US A CONFLICT ALERT AND TOLD US TO DSND. WE INFORMED HIM WE WERE CLBING IN RESPONSE TO AN RA AND BEGAN A TURN TO THE R AS TARGET APPEARED TO BE CLBING INTO US. AFTER A FEW SECONDS THE TARGET STOPPED HIS CLB AND BEGAN A DSCNT. WE ENDED OUR MANEUVER. TFC APPEARED AT APPROX 2 MI; POSSIBLY LESS; WAS NOT TALKING WITH APCH OR CTR AND WAS LEVEL AT 10000 FT. APCH PICKED UP TFC ABOUT THE TIME WE BEGAN TO CLB. WE NEVER SAW THE TFC; HOWEVER; SEVERAL PAX ON DEPLANING RPTED SEEING A TWIN ENG ACFT APPROX 1000 FT FROM US. DUE TO THE MANEUVER I'M NOT SURE ABOUT THE ACCURACY OF THEIR ESTIMATE. BASED ON TCASII I WOULD GUESS TFC WAS WITHIN 1/4 MI +/-100 FT AT CLOSEST APCH. TALKING WITH APCH CTL SUPVR; WE WERE TOLD THE ACFT CONTINUED NBOUND AND WAS NOT TALKING WITH ANYONE.