B757-200 FLT CREW RECEIVES TWO APPARENTLY FALSE TCAS RESOLUTION ADVISORIES DURING INITIAL CLIMB; FOLLOWED SHORTLY BY A TCAS FAIL MESSAGE.

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TCAS FAILURE. SHORTLY AFTER TKOF AND BEFORE REACHING 1400 FT; WE GOT A DSNDING RA. SKIES WERE CLR WITH GOOD VISIBILITY AND BOTH PLTS HAD SCANNED THE DEP AREA. WE SAW NO TFC BUT RESPONDED TO THE RA. SHORTLY AFTERWARDS; THE RA CHANGED TO A CLBING RA WITH A RED TARGET X MI AT 12 O'CLOCK POS DISPLAYED WITHIN 100 FT OF OUR ALT AND THEN LEVEL WITH US. WE SAW NO TFC BUT AGAIN RESPONDED TO THE RA. ATC WAS INFORMED AND THEY TOO SAW NO TFC OR KNEW OF ANY TFC IN THE VICINITY. ABOUT 15 MINS LATER WE GOT A TCAS FAIL MESSAGE. ENTERING CONGESTED AIRSPACE; WE TURNED OFF THE RA FUNCTION TO AVOID MORE FALSE RA'S. WE DID GET A FALSE TA AND; THEREFORE; TURNED THE TCAS SYS OFF. THE DISTURBING PART OF THIS MALFUNCTIONING SYS WAS THAT IT GUIDED US TOWARDS THE GND AT A LOW ALT. FURTHER; THERE WAS NO REASON TO THINK THAT IT COULD NOT ALSO GUIDE US INTO OTHER TFC. I HAVE SEEN MALFUNCTIONING TCAS SYS BEFORE; BUT NEVER ONE LIKE THIS THAT GAVE RA GUIDANCE THAT WAS NOT ONLY FALSE BUT ALSO CLEARLY AFFECTED SAFETY OF FLT NEGATIVELY.