ACR FLC REACTS TO A TCASII RA DUE TO UNIDENTED VFR TWIN ENG ACFT ON OPPOSITE DIRECTION COURSE WHILE ACR IS IN DSCNT. ATC GIVES A LATE TA.

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LETTING DOWN ON THE MINKS ARR APCHING MINKS INTXN AT 11000 FT AT AN ASSIGNED SPD OF 250 KTS. TOLD TO DSND TO 9000 FT. I SELECTED LEVEL CHANGE AND RETARDED THE THROTTLES. ALMOST IMMEDIATELY THE TCASII TA WAS HEARD. A YELLOW DOT WAS ON THE WX RADAR DISPLAY AT OUR 12 O'CLOCK POS IMMEDIATELY IN FRONT OF THE NOSE. WITHIN NO MORE THAN 4 SECONDS AN RA WARNING OF 'CLB; CLB' SOUNDED. I IMMEDIATELY DISCONNECTED THE AUTOPLT AND AUTOTHROTTLES; ROTATED THE NOSE TO 15 DEGS NOSE UP; ADVANCED THE THROTTLES. ALL THE WHILE 'CLB; CLB' WAS BEING HEARD. APPROX 10 SECONDS LATER; THE RA CHANGED TO 'MONITOR VERT SPD.' DURING THE CLB; THE AIR TFC CTLR STATED THAT HE HAD UNIDENTED TFC AT 10500 FT AND WE WERE CLRED TO CLB. MY FO INFORMED THE CTLR THAT IS WHAT WE WERE DOING. MY FO VISUALLY ACQUIRED THE ACFT; A TWIN ENG CIVILIAN ACFT. WE ESTIMATE WE CLRED THE UNIDENTED ACFT WHICH WAS FLYING FROM OUR L TO OUR R BY NO MORE THAN 400 FT VERTLY. IF WE HADN'T ACCOMPLISHED THE MANEUVER WE DID; IT WOULD HAVE BEEN VERY CLOSE.