MLG IN CLASS A AIRSPACE HAS TCASII RA.

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WHILE CRUISE AT FL290; WORKING WITH ZNY; WE HAD BEEN GIVEN CLRNC TO DEV E OF THE AIRWAY DUE TO TSTMS. WE HAD ONLY DEVIATED FROM THE AIRWAY FOR 3 OR 4 MI. WE WERE GIVEN AN ENRTE FREQ FROM VHF 132.87 TO 128.57. THE SECTOR WAS EXTREMELY BUSY FROM THE SOUND OF THE CTLR. WE DO NOT BELIEVE AT THIS TIME THAT WE HAD HAD A CHANCE TO CHK IN WITH THE NEW SECTOR CTLR. AT THAT TIME THE ONBOARD TCASII SYS GAVE US A 'TA' AND SHOWED TFC AT OUR ALT; 12 O'CLOCK POS. 20 MI RANGE AND CLOSING. AT THIS TIME THE CTLR CALLED US TELLING US TO MAKE A L TURN AND DSND; HOWEVER; AT THE SAME TIME THE TCASII SYS HAD GONE INTO A 'RESOLUTION' MODE COMMANDING AN IMMEDIATE CLB. I HAD INITIATED AN IMMEDIATE CLBING L TURN AND CLBED TO FL295. THE CONFLICTING TFC ALSO RPTED THAT HIS TCASII HAD COMMANDED A DSCNT. AFTER INITIATING THE AVOIDANCE MANEUVER; I VISUALLY ACQUIRED THE CONFLICTING TFC AT OUR 1 O'CLOCK POS APPROX 4 MI. WITH OUR RELATIVE POSITIONS; THE CLB AND L TURN WAS THE BEST AVENUE FOR AVOIDANCE. I FEEL THE CTLR MAY HAVE BEEN OVERLOADED WITH TFC AND WX. WE HAD BEEN GETTING STEPPED DOWN FROM CRUISE ALT AND BEEN GIVEN NUMEROUS HDG CHANGES AND RTE CHANGES.