B757 FO FOLLOWED TCASII RESOLUTIONS SHORTLY AFTER TKOF THAT PROVED TO BE FALSE SINCE NEITHER TCASII NOR DEP CTL RADAR SHOWED ANY ACFT IN THEIR AREA.

Narrative

SHORTLY AFTER TKOF FROM BOS RWY 22R; WE WERE IN A L TURN AND CLBING AND RECEIVED A TCASII RA TO 'DSND.' I COMPLIED WITH THE ADVISORY AS MANDATED TO DO SO. ATC ADVISED US THAT THERE WAS NO TFC THAT WAS A FACTOR. TCASII CONTINUED TO GIVE A 'DSND; DSND NOW' ADVISORY. THE TCASII DISPLAY WAS SHOWING TFC ON OUR NOSE AT OUR ALT. AFTER BEING NOTIFIED AGAIN FROM ATC THAT TFC WAS NOT A FACTOR; I STARTED A CLBING L TURN AGAIN AND RECEIVED A 'DSND; XING DSND' ADVISORY. AFTER APPROX 6000 FT MSL; THE TCASII DISPLAY WENT TO A NORMAL; NO TFC CONDITION. I NEVER DID RECEIVE A CLR OF CONFLICT ADVISORY. I BELIEVE THIS WAS A FALSE TCASII RA. THE TCASII DISPLAY SHOWED TFC ON OUR NOSE; AT OUR ALT; THAT WAS NOT MOVING ON THE DISPLAY DURING THE WARNINGS. I DON'T KNOW WHAT CAUSED THE FALSE WARNINGS. THE ACFT WAS DEICED WITH TYPE 1 PRIOR TO DEP AND THE TCASII SYS TESTED OK DURING PREFLT. THE PROB WAS ENTERED INTO THE MAINT LOGBOOK AND THE SYS (TCASII) WAS DEFERRED FOR REPAIR. NO PREVIOUS HISTORY OF THIS PROB COULD BE FOUND IN THE MAINT LOGBOOK. IT WAS VERY HARD TO START A CLB AS ADVISED BY ATC WHEN THE TCASII IS TELLING US TO DSND. NOT A GOOD SIT.