POTENTIAL CONFLICT OCCURS WHEN A B737 FLT IS CLRED TO CLB BY ZDC CTLR THROUGH ANOTHER B737'S ALT WHILE PROCEEDING DIRECT TO ACY; NJ.

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WE WERE FILED FOR FL350; BUT UPON REACHING FL310; WE WERE TOLD THAT WE WOULD BE THERE FOR A WHILE. I WAS THINKING ABOUT OPENING MY CREW MEAL AND GETTING PREPARED FOR THE NEXT 2 HRS OF CRUISE WHEN ATC GAVE US A HDG FOR DIRECT ACY AND TOLD US TO CLB NOW TO FL350. WE WERE 110 NM N OF ACY ON THE 039 DEG RADIAL. I BELIEVE I HAD THE TCASII IN THE 40 MI SCALE AND DID NOT NOTICE ANY TFC AT FL330. I COMMENCED OUR CLB AND RECEIVED AN AURAL TA AND NOTICED TFC OFF THE NOSE 1500 FT ABOVE US. THE TCASII SYMBOLOGY WAS YELLOW. I IMMEDIATELY ORDERED FO TO QUERY ATC ABOUT THE TFC; BUT ATC WAS TALKING ON THE FREQ; WHICH WAS ZDC ON 128.52. SHORTLY THEREAFTER; THE TCASII COMMANDED 'DON'T CLB!' OR SOMETHING TO THAT EFFECT; WHILE AT THE SAME TIME MY BRAIN WAS ENGAGING AND FIGURING OUT THAT I NEEDED TO STOP OUR CLB! ALMOST SIMULTANEOUSLY; I DISCONNECTED THE AUTOPLT/AUTOTHROTTLES AND BEGAN A SHALLOW L DSNDING TURN. I BELIEVE THE HIGHEST ALT WE REACHED WAS FL324. THE CONFLICTING TFC; ANOTHER B737 AT FL330; PASSED BY VISUALLY OFF OUR R SIDE AT AN ESTIMATED 2 MI. BY THIS TIME ATC HAD GIVEN US AN ORDER TO DSND IMMEDIATELY TO FL310; BUT I HAD ALREADY TAKEN THAT COURSE OF ACTION. I DO NOT KNOW IF THE OTHER B737 TOOK ANY ACTION. ATC SEEMED TO HAVE BEEN CAUGHT TOTALLY OFF GUARD. TCASII AND AN ALERT CREW SAVED THE DAY HERE. THE FLT ATTENDANTS CALLED LATER IN THE FLT AND ASKED ABOUT THE EARLIER 'AEROBATICS;' BUT SAID THAT THE PITCH DOWN WAS RELATIVELY SMOOTH AND THE PAX DIDN'T NOTICE OR COMMENT.