ACR X TCASII TA RA EVASIVE ACTION TAKEN CLB WITH ACR Y. NON ADHERENCE TO ATC CLRNC.

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ENRTE FROM ABQ-PIT; ACR X WAS CLRED TO BEGIN DSCNT FROM 370 TO 330 AND TURN R 20 DEGS. AFTER PASSING FL360 WE OBSERVED A TARGET ON TCASII AT 12 O'CLOCK AND APPROX 700 FT BELOW US. TCASII THEN ADVISED A 500 FPM CLB WHICH WE INITIATED WHILE STILL TURNING. WE RECEIVED A 'CLR OF CONFLICT' ADVISORY JUST AS WE ARRIVED AT FL360 AND WE LEVELED OFF. DURING THE EARLY STAGES OF THIS EVENT THE CTLR STATED THAT HE DID NOT OBSERVE US TURNING AND TO MAKE THE TURN 40 DEGS. I ADVISED HIM WE HAD BEEN TURNING PER HIS ORIGINAL INSTRUCTIONS. AT THAT POINT WE RECEIVED THE TCASII ADVISORY. I ADVISED HIM WE WERE NOW CLBING PER TCASII; AS WELL AS CONTINUING THE TURN. THE CONFLICT WAS APPARENTLY A WBOUND ACR Y AT FL350. THE CTLR APPARENTLY HAD TRIED TO GIVE ACR Y A R TURN ALSO; BUT HAD EVIDENTLY NOT RECEIVED THE CLRNC (POSSIBLY FREQ BLOCKAGE). AFTER SOME DISCUSSION WITH THE CTLR; WE WERE CLRED ON COURSE. SUPPLEMENTAL INFO FROM ACN 202084: TCASII ALERT AS WE DSNDED FROM 370 TO 330. PASSING 35900 TA AT 35600 'CLB'. AT 35900 'CLR OF CONFLICT.' CTR GAVE US DSCNT AND A 20 DEG R TURN. APPARENTLY NOT ENOUGH TURN. AS WE ADVISED ATC HE SAID HE WAS TRYING TO TELL US TO TURN 40 DEGS R. I SAW ACR Y AFTER THE TA. THE CTR CTLR WAS CONCERNED ABOUT THE 5 MI SEPARATION BUT SAID THERE WAS NO CONFLICT.