B733 FLC INITIATE EVASIVE TCASII ACTION DUE TO ZNY ISSUED; VFR TFC OPERATING IN VICINITY OF PHL DEP ROUTING.

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DEPARTED PHL AND SWITCHED TO ZNY AT 10000 FT. NEW YORK CLBED US TO 15000 FT AND CALLED OUT TFC (VFR) IN FRONT OF US AT 15500 FT. WE REQUESTED A VECTOR AWAY FROM THE TFC WHICH WAS WITHIN 10 DEGS OF OUR 12 O'CLOCK POS AT 20 MI ON OUR TCASII DISPLAY. THE REQUEST WAS DENIED WITH THE EXPLANATION THAT THE TFC WAS AT 15500 FT AND WE WERE CLRED TO 15000 FT. AS WE CLBED; THE TFC DRIFTED APPROX 30 DEGS TO THE L ON THE TCASII DISPLAY (NO LONGER A FACTOR; I THOUGHT) AND WITH THE CONGESTION ON THE FREQ; WE REMAINED ON OUR NW HDG WITHOUT FURTHER COMMENT TO THE CTLR. IT APPEARED THAT THE TFC WAS ON A DIVERGING COURSE AT THIS POINT. OUR NEXT CLRNC WAS TO TURN L TO A HDG OF 280 DEGS; FOLLOWED SHORTLY BY A CLB CLRNC TO FL190; THEN FL230. THIS BROUGHT THE TFC WITHIN 10 DEGS L OF OUR 12 O'CLOCK POS AT APPROX 10 MI AND AS WE STARTED THE CLB WE GOT AN ALMOST IMMEDIATE TA; RA AND 'DSND; DSND' AURAL AND SIGHTED THE TFC SLIGHTLY HIGH AND L OF OUR NOSE MOVING L TO R AT AN ESTIMATED 5-7 MI; APPARENTLY DSNDING. WE INITIATED THE TCASII COMMANDED DSCNT (I WAS FLYING) AND WHEN IT APPEARED THAT WE WOULD NOT BE ABLE TO MAINTAIN VERT CLRNC; MANEUVERED L TO GAIN LATERAL SEPARATION AND ADVISED ATC. I SPOKE TO THE ZNY WATCH SUPVR AFTER LNDG. THE VFR TFC WAS APPARENTLY MONITORING THE FREQ WHILE MANEUVERING VFR IN THIS PARTICULAR AIRSPACE. ZNY QUALITY ASSURANCE WILL REVIEW THE TAPES.