B737-500 FLC IGNORES TCASII RA TWICE AND HAS NMAC CLBING OUT OF HPN.

Narrative

WHITE PLAINS; NY; TO CHICAGO; IL. ON CLBOUT FROM WHITE PLANES; UNDER NY TRACON CTL IN VMC CONDITIONS; LEAVING 7000 FT MSL IN 'ROBUST' CLB (MORE THAN 4000 FPM); TCASII TA FOR TFC AT 10 O'CLOCK POS; AND 10 NM 2500 FT ABOVE. OUR HEADING WAS 320 DEGS (RADAR VECTOR) AND WE VISUALLY ACQUIRED AN ACFT ABOVE US; 10 O'CLOCK POS; AND APPROX CORRECT DISTANCE. THIS ACFT WAS SBOUND;; MOVING AWAY FROM US. SECONDS AFTER VISUAL CONTACT TCASII RA SOUNDED WITH 'REDUCE VERT SPD' AURAL WARNING. THE CAPT AND I FELT THIS WAS A NUISANCE RA AND CONTINUED CLB AT SAME RATE. SECONDS LATER TCASII SAYS 'DSND; DSND' AND AGAIN WE FELT THAT THIS WARNING COULD BE DISREGARDED SINCE WE COULD SEE THE TFC; AND IT WAS NO FACTOR (MOVING AWAY FROM US). SECONDS LATER; THE CAPT EXCLAIMS; 'OH S--T; THERE'S ANOTHER GUY OUT HERE.' I LOOKED OUT STRAIGHT AHEAD AND IMMEDIATELY SAW A SINGLE-ENG PROP; OPPOSITE DIRECTION; OUR APPROX ALT. OUR TREMENDOUS VERT SPD CARRIED US OVER HIM TO AVOID THE COLLISION. WE DIDN'T HAVE TO MANEUVER THE ACFT EXCEPT FOR SLIGHT INCREASE IN BACK PRESSURE ON CTLS AND MAYBE 1-2 DEG INCREASE IN PITCH ATTITUDE ONCE WE SAW HIM. ATC NEVER SAID A SINGLE WORD. I THINK A MAJOR CONTRIBUTING FACTOR IN THIS INSTANCE WAS THE ATTITUDE WE ACR PLTS SOMETIMES HAVE ABOUT TCASII RA MANEUVERING. WE OFTEN FEEL THAT IF WE HAVE TFC IN SIGHT THAT IS 'NO FACTOR;' WE CAN AVOID TCASII MANEUVERING THAT MIGHT DISRUPT THE SMOOTH RIDE WE'RE TRYING TO GIVE THE PAX. THIS INCIDENT PROVES THAT THIS ATTITUDE NEEDS TO CHANGE -- AND ALL RA'S REGARDLESS OF SIT; SHOULD BE FOLLOWED.