B737-300 ACFT ON DEP HAD TCASII RA AND FLC TAKES EVASIVE ACTION. ATC QUESTIONED AND SEES TFC ON RADAR BUT UNIDENTED.

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DEPARTED COS RWY 17L; L TURN TO NNW VECTOR; CLB TO 12000 FT. FO FLYING; LEVELED AT 12000 FT; VMC ENRTE DEN. VICINITY OF COS VOR CAPT ASKS COS DEP CTLR ABOUT SSEBOUND TFC ON CRT TCASII DISPLAY. INDICATED 11900 FT ON COURSE TO MEET OURS. TARGET BECAME TA WHEN CTLR RESPONDED THAT HE NOW SEES THE TARGET ON RADAR AND TO TURN 40 DEGS R. TCASII RA NOW COMMANDS 'CLB' WHICH FO INITIATES WHILE TURNING. ATC WAS NOT TALKING TO SECOND ACFT WHICH WAS NEVER IDENTED. ATC SUSPECTS IT MAY HAVE BEEN MIL TRAINER. UNABLE TO CONFIRM. SUGGEST REMINDER TO MIL TRAINERS TO COMMUNICATE WITH ATC; FLY VFR ALTS. ALSO SUGGESTED TO COMPANY TO PURSUE ALTERNATE ROUTING FURTHER E OF MIL PRACTICE AREA. WITHOUT TCASII; COULD HAVE BEEN A DISASTER. SUPPLEMENTAL INFO FROM ACN 368448: FLEW N THEN NW (340 DEG HDG) UP TO 12000 FT MSL IN VMC. IMMEDIATELY AFTER THE ENCOUNTER; COS DEP INSTRUCTS DIRECT FQF VOR AND HANDS US OFF TO DEN APCH. FIRST OPPORTUNITY TO INQUIRE ABOUT INCIDENT WAS 4 HRS LATER IN DTW (DUE TO 35 MIN TURN IN DEN). CAPT CALLED COS TWR AND SPOKE WITH THE SUPVR. CAPT WAS TOLD SHIFT CHANGE OCCURRED AND WORKING CTLR WAS NOT AVAILABLE. SUPVR SAID HE WOULD REVIEW THE TAPE. CAPT AND SUPVR SPOKE AT CAPT'S HOME THE EVENING AFTER THE TRIP. SUPVR TOLD CAPT THAT TARGET WAS NOT CTLED OR IDENTED BY COS OR DEN. HIS BEST GUESS OF TARGET WAS POSSIBLY A TRAINING FLT FROM MIL. POST ENCOUNTER CONSIDERATIONS: OUR PRIMARY CONCERN WAS TO IDENT THE PROB AND ENSURE AVOIDANCE OF SIMILAR PROB AND POTENTIAL DISASTER. ADDITIONAL CONCERNS INCLUDE 1) WHY DID THE TARGET NOT SHOW UP ON COS DEP RADAR SCREEN UNTIL ENCOUNTER STARTED? AND 2) IF THIS WAS A MIL ACFT; WHY WAS IT AT AN IFR ALT AND IN SUCH CLOSE PROX TO ANOTHER ACFT? CAPT SUGGESTIONS ARE 1) HAVE FOLLOW-UP AND COMMUNICATE TO COS AND MIL TO REINFORCE THE NEED TO COMMUNICATE WITH ATC. 2) FLY VFR ALTS WHEN IN VFR. 3) ESTABLISH ANOTHER ACR RTE FROM COS TO DEN; PREFERABLY FURTHER E AND AWAY FROM MIL INSTITUTE AND OTHER FRONT RANGE AIR TFC. NOTE #1: NASA; TCASII ENCOUNTER AND FSAP FORMS HAVE BEEN COMPLETED. NOTE #2: WITHOUT TCASII; THIS LIKELY WOULD HAVE BEEN A MIDAIR.