SAAB 340 FLC RECEIVES RA DURING INITIAL APCH TO JFK.

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ENRTE FROM BDL TO JFK; APCH VECTORED US INTO 2 CLBING ACFT. APCH TOLD US TO TURN TO HDG 220 DEGS. AS WE ROLLED OUT; WE RECEIVED AN RA TO DSND. I DISENGAGED THE AUTOPLT AND STARTED TO DSND. WE WERE AT 4000 FT MSL WHEN WE RECEIVED THE RA. AS WE STARTED TO DSND; I OBSERVED THE TFC ON THE TCASII DISPLAY TO BE AT 3900 FT MSL AND CLBING WITH ANOTHER ACFT DIRECTLY BEHIND THE FIRST ACFT ALSO CLBING OUT OF 3600 FT MSL. WE SLOWED THE DSCNT AS THE FIRST ACFT CLBED THROUGH OUR ALT. THE SECOND ACFT WAS DIRECTLY BELOW US AND CLBING. THE TCASII WAS TELLING US TO DSND BUT WE COULD NOT AS WE WERE RIGHT IN BTWN BOTH ACFT AT VERY CLOSE RANGE. I TURNED L AND THE SECOND ACFT CLBED THROUGH OUR ALT. WE CONTINUED THE DSCNT AT THAT POINT AS THE RA WAS STILL CALLING FOR A DSCNT. WE LEVELED OFF AT 3000 FT MSL. THE ATC FREQ THROUGH ALL OF THIS WAS MAXED OUT WITH A LOT OF ACFT/CTLR COMS. WE COULD NOT GET A WORD IN. AT 3000 FT MSL; THE CTLR QUESTIONED US AND WE ADVISED WE WERE RESPONDING TO AN RA. THE CTLR NEVER GAVE ANY WARNING OF THE 2 CLBING ACFT AND TURNED US DIRECTLY INTO THEIR CLBING FLT PATH. AFTER THE INCIDENT THE CTLR TURNED US BACK TO JFK AND THE 2 RA ACFT CONTINUED TO CLB OFF TO THE SSW. NOTE: WE HAD THE FIRST ACFT VISUALLY AFTER HE CLBED THROUGH OUR ALT. WE NEVER SAW THE SECOND ACFT EXCEPT ON THE TCASII DISPLAY.