ACR Y UNCOORD UNAUTH AIRSPACE PENETRATION HAD LTSS FROM ACR X TCASII RA EVASIVE ACTION DSND. SYS ERROR.

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ACR X ON THE MILTON ARR INTO LA GUARDIA AND ON A LEVEL FLT ON OUR ASSIGNED ALT. OUR TCASII SHOWED TFC COMING AT US AT OUR ALT AND SHOWED UP 4 1/2 - 5 MI AWAY. TCASII IMMEDIATELY STARTED SAYING 'TFC; TFC.' WE ASKED THE ZNY CTLR IF HE SHOWED ANY TFC. TCASII STARTED SAYING; 'DSND; DSND.' DSND WHILE WE STILL DIDN'T SEE THE TFC AND STILL SHOWING 00 OR R AT OUR ALT AND GETTING CLOSER. AT THIS TIME I STARTED A SMOOTH BUT POSITIVE DSCNT TO 500 FT BELOW OUR ALT WHILE THE FO TOLD ATC WHAT WE WERE DOING. BY THE TIME I REACHED ABOUT 500 FT BELOW ASSIGNED ALT I SPOTTED ACR Y WHOM APPEARED TO BE CLBING AND ABOUT 1 MI AWAY XING DIAGONALLY IN FRONT OF US. AT THIS TIME; TCASII SHOWED PLUS 1000 FT AND THE 'DSND; DSND' STOPPED. THEN A FEW SECONDS LATER A CLR OF CONFLICT WAS ANNOUNCED BY TCASII. WE QUICKLY RETURNED TO OUR ASSIGNED ALT. I SPOKE TO THE ZNY LGA SECTOR'S SUPVR. HE INFORMED ME A LACK OF COM BTWN THE 2 CTLRS OF THE SECTOR ADJACENT TO US WAS HANDLING THE AREA DEPS FROM NEWARK. THE ACR Y WAS ISSUED A CLRNC TO CLB THROUGH OUR ALT WITH MAINTAINING VISUAL CONTACT ON US. HOWEVER; OUR SECTOR'S CTLR WAS NOT INFORMED OF THIS; THUS; WE DID NOT KNOW OR EXPECT IT.