NMAC. FLC OF AN ATX C402 TOOK EVASIVE ACTION BY CLBING; AND TURNING; AFTER OBSERVING A C206 COMING AT THEM FROM THE OPPOSITE DIRECTION WHILE IN TRAINING NEAR A LCL VOR NAVAID.

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I WAS ON A ROUTINE TRAINING FLT IN BOULDER CITY WHEN I EXPERIENCED 2 CLOSE CALLS WITH ANOTHER ACFT. WE LEFT THE BOULDER VOR AT 5500 FT AND HEADED S OF BOULDER ARPT TO PRACTICE SOME MANEUVERS. WE MADE A RADIO CALL ANNOUNCING OUR INTENTIONS UPON LEAVING THE VOR. WE THEN MADE ANOTHER RADIO CALL 5 MI S OF BOULDER AT 5500 FT MANEUVERING. FOLLOWING THE RADIO CALL; WE STARTED A L TURN 90 DEGS FOR CLRING AND THEN ANOTHER 90 DEG TURN TO THE R TO COMPLETE THE 180 DEG TURN TO FULLY CLR THE AREA. ON COMPLETION OF THE R TURN; THE PLT BEING TRAINED SAW A C206 LOWER AND TO THE L. WE THEN CLBED AND IMMEDIATELY TURNED R. WE THEN CALLED 3 TIMES ON 122.7 IN AN ATTEMPT TO CONTACT THE OTHER ACFT. WE NEVER HEARD A RESPONSE AND CHOSE TO CONTINUE TRAINING AFTER CLRING THE AREA AGAIN. APPROX 20 MINS PASSED AND WE DECIDED TO ENTER THE PATTERN FOR A FEW TOUCH-AND-GOES. WE THEN CALLED LEAVING 5500 FT TO ENTER THE PATTERN AT BOULDER. WE THEN MADE ANOTHER CALL WHEN WE WERE ESTABLISHED ON A 45 DEG ANGLE FOR RWY 15 AT BOULDER. WE KNEW THAT THE WINDS WERE ABOUT 20 KTS OUT OF THE S AND TFC HAD BEEN USING RWY 15. AS WE WERE ON A 45 DEG ANGLE; WE HEARD 1 ACFT TAXIING FOR RWY 15 AND THEN I SAW AT OUR 12 O'CLOCK A C206 CLBING THROUGH 3400 FT WHICH WE WERE DSNDING THROUGH. WE THEN MADE A R DSNDING TURN AND TRIED TO CONTACT THE TFC. AGAIN; HE MADE NO RESPONSE BUT THEN MADE A TFC CALL ASKING FOR US. WE RESPONDED AND APOLOGIZED IF WE HAD MISSED A CALL AND EXPLAINED THAT WE WOULD CONTINUE A R TURN AND RE-ENTER ON THE 45 DEG. HE SEEMED FINE AND SAID HE HAD US IN SIGHT FROM TKOF AND THAT WE HAD ROOM TO SPARE AND THAT HE WAS LEAVING THE PATTERN.