B757 CREW IN THE VICINITY OF IRK VOR RECEIVED A TCASII TA; VISUALLY SPOTTED THE TFC AND TOOK EVASIVE ACTION BY TURNING AND GOING AROUND THE OTHER ACFT.

Narrative

WE WERE OPERATING ACR X IN LEVEL CRUISE AT FL370. THE CTR FREQ WAS RELATIVELY QUIET. WE HEARD ATC CALL ACR X. THE FLT NUMBER WAS BLOCKED BY OUR TCASII CALLING 'TFC; TFC.' AT OUR 2 O'CLOCK POS; WE HAD A TARGET SHOWING A RELATIVE ALT OF '00.' WE LOOKED AND IMMEDIATELY HAD THE TFC IN SIGHT AT ABOUT 6 OR 7 MI. ATC CALLED ACR Y (DON'T REMEMBER THEIR FLT NUMBER) TFC AT 10 O'CLOCK; I'M NOT TALKING TO HIM. AT THIS POINT WE MADE A DECISION TO START A R TURN TO PASS BEHIND THE TFC. ATC AGAIN CALLED ACR X. WE RESPONDED ACR X 'GO AHEAD' AND RECEIVED NO RESPONSE. ATC THEN CALLED 'ACR Y DSND AND MAINTAIN FL350 AND HURRY DOWN. ACR X START A 15 DEG R TURN FOR TFC.' BY THE TIME WE GOT THAT CALL WE WERE ALREADY IN THE TURN. WE GOT A MOMENTARY RA THAT SAID 'DSND; XING; DSND;' BUT IT CLRED BEFORE WE COULD TAKE ANY ACTION. AFTER WE PASSED BEHIND THE TFC; WE WERE CLRED TO RESUME OUR OWN NAV. NOTHING WAS SAID BY ATC; ALTHOUGH THERE WAS A CTLR CHANGE. FORTUNATELY THIS HAPPENED DURING DAYLIGHT. IF IT HAD BEEN NIGHT OR IMC; AND WE HAD NOT STARTED AN EARLY TURN; I THINK THIS COULD HAVE BEEN A VERY CLOSE CALL; OR POSSIBLY A COLLISION. FORTUNATELY; SEE AND AVOID; ALONG WITH THE CTLR'S INPUTS; WORKED.