EVASIVE ACTION DSCNT COMMANDED BY TCASII RA WAS THE WRONG COMMAND ON UNKNOWN VFR TFC NORAC TFC IN AREA.

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WE DEPARTED ORD AND WERE CLBING OUT OF 8500 FT FOR 13000 FT. ATC ISSUED A TA FOR 12 O'CLOCK AND 8 MI. THE TFC RPTED WAS PREVIOUSLY COMPLAINED ABOUT BY OTHER ACFT SAYING IT WAS NOT IDENTIFIED; COMMUNICATED WITH; AND IN AIRSPACE WHERE IT SHOULD NOT HAVE BEEN. WE RESPONDED NEGATIVE CONTACT. NO TCASII TARGET WAS SHOWN. WE WERE GIVEN A TURN TO 090 DEGS AND WERE IN THE MIDDLE OF A CLBING TURN; IN MODERATE TURB; AND SCATTERED CLOUDS AT 10000 FT. WE RECEIVED A SECOND ADVISORY AND I TOLD MO FO THAT I DID NOT SEE IT. STILL NO TARGET ON TCASII. WE RECEIVED A THIRD ADVISORY FROM ATC RPTING THE TFC AT 1 O'CLOCK AND 3 MI (ATC WAS UNCERTAIN AS THEY RPTED THAT IT WAS NOT BEING TRACKED OR COMMUNICATED WITH). ALSO WE HAD A CLOUD OBSTRUCTING OUR VISION AND STILL COULD NOT SEE THE TFC AND WE RESPONDED NEGATIVE CONTACT. SUDDENLY TCASII SHOWED A TARGET AT 12 O'CLOCK; 2 MI; AND 200 FT BELOW OUR ALT WITH A TA. IT SUDDENLY THEN CHANGED TO AN RA AND ISSUED A DSCNT ADVISORY. I STARTED TO DSND AS INSTRUCTED BY THE TCASII WHEN WE SUDDENLY GOT A VISUAL CONTACT WITH THE INTRUDER. I ALSO REALIZED THAT DSNDING WOULD PUT US CLOSER TO THE COLLISION HAZARD AND NOT AWAY FROM IT AS WE WERE 100 FT VERT AND A MI OR LESS HORIZ SEPARATION AND I IMMEDIATELY STARTED A CLB AND A R TURN AWAY FROM THE INTRUDER (IT WAS 100 FT BELOW OUR PRESENT ALT). AS I STARTED THE CLBING TURN; TCASII SUDDENLY GAVE A CLB RA. THE INTRUDER DID NOT APPEAR TO SEE OR AVOID. I ESTIMATED THE INTRUDER AT OR BELOW 10000 FT. AFTER CLRING CONFLICT WE CONTINUED ON TO EWR. INTRUDER HDG ESTIMATED TO BE 300 TO 330 DEGS AND JUST BELOW CLOUDS (CLOUDS HAD 10000 FT BASES). NO INJURIES OCCURRED. TCASII GAVE NO TARGET INDICATIONS OR ALERTS UNTIL INTRUDER WAS WITHIN 2 MI HORIZ AND 200 FT BELOW OUR ACFT.