AN ACR ACFT DSNDING INTO JFK RESPONDED TO A TCAS RA. THE FLT HAD A NMAC WITH VFR TFC AT 17500 FT THAT ATC CALLED AS LATE TFC.

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WHILE FLYING THE KINGSTON 8 ARR INTO JFK; WE EXPERIENCED AN NMAC OVER LGA. WE EXECUTED THE TCAS RA AND AVOIDED THE INTRUDER ACFT. BACKGROUND: AFTER AN INITIAL CLRNC TO CROSS THE LENDY INTXN AT FL190; WE WERE CLRED TO DSND TO 13000 FT AND DEPART LGA HDG 150 DEGS. AS WE APCHED LGA FROM THE NW; WE NOTICED A TCAS TARGET ON AN INTERCEPT COURSE FROM OUR 2 O'CLOCK POS. THAT TARGET WAS BELOW US; BUT WAS CLBING AS WE DSNDED. THE TCAS SOUNDED A TA; THEN QUICKLY CONVERTED TO AN RA; COMMANDING US TO CLB. I QUICKLY DISCONNECTED THE AUTOPLT AND ARRESTED OUR DSCNT AND SMOOTHLY TRANSITIONED TO CLB IN ACCORDANCE WITH THE RA. THE FO HAD BEEN VISUALLY SEARCHING FOR THE TARGET WITH NO LUCK UNTIL THE LAST MOMENT -- WHEN HE SAW A SINGLE ENG GA ACFT PASS BELOW OUR R WINGTIP AT APPROX 500 FT HORIZ AND 300 FT VERT SEPARATION. I NEVER SAW THE TARGET (POSSIBLY A CIRRUS?). THE ATC CTLR CALLED POP-UP 'VFR' TFC JUST AS WE WERE EXECUTING THE RA. THE FO RESPONDED 'WE'RE ALREADY CLBING WITH AN RA.' THE CTLR REPLIED 'HE'S STILL CLBING TOO.' THE INCIDENT WAS OVER IN SECONDS AND WE RESUMED OUR DSCNT WITH AN UNEVENTFUL LNDG AT JFK. IN DEPLANING; NO PAX MADE ANY COMMENT AND THE FLT ATTENDANT SAID SHE BELIEVES THAT NO ONE NOTICED AN ABNORMALITY. MY FO WAS VERY DILIGENT IN HIS TFC SCANNING; BUT THE TARGET ACFT WAS JUST TOO SMALL; FLYING HEAD ON; AND WAS MASKED BELOW IN THE PATTERNS OF THE CITY. OUR CRM AND TCAS RESPONSE TRAINING HELPED CONTRIBUTE TO A RAPID; APPROPRIATE RESPONSE TO THE THREAT.