B767 FLC CLRED TO DSND AND CLRED FOR APCH RECEIVED TCASII TA ON ACFT WHICH THEY SEE AFTER BREAKING OUT OF CLOUDS. THE OTHER ACFT'S FLC CONTACTED RPTR ON GND BECAUSE THEY TOO HAD A TCASII TA. APPARENTLY THEY DSNDED LATE; BUT CTLR DIDN'T SAY ANYTHING.

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RECEIVED RWY CHANGE CLOSE IN TO VOR DME RWY 35. CLRED TO DSND TO 6000 FT. CLRED VOR DME RWY 35 APCH; DSND AT PLT'S DISCRETION. WE WERE GIVEN NO INDICATION OF TFC AHEAD ON THE APCH. RECEIVED TA JUST PRIOR TO 10 DME OUTBOUND FOR COURSE REVERSAL AND BROKE OUT OF CLOUDS AT 6000 FT. HAD TFC IN SIGHT AT 12 O'CLOCK; STARTED TURN TO R; NOTED 900 FT ON TCASII -- ACFT GOING BELOW US AS WE WERE TURNING AND BEGAN DSCNT TO 5000 FT. ON GND; ACR X CALLED AND ASKED IF WE HAD SEEN HIM ON THE APCH AND THAT HE HAD RECEIVED A TCASII ALERT. WE DETERMINED THAT ACR X WAS LATE IN DSNDING TO 4500 FT PER THE APCH AND THAT OUR DSCNT RATE MUST HAVE TRIGGERED THE TA. WE NEVER RECEIVED AN RA. WE WERE FLYING THE PROC AS SHOWN -- AT ABOVE 6000 FT AT 10 DME -- WHEN WE CONTINUED THE DSCNT TO 5000 FT ENTERING THE OUTBOUND TURN TO BE AT 5000 FT AT 14 DME. THE REST OF THE APCH WAS NORMAL. THE FLT WAS NEVER IN JEOPARDY; HOWEVER; WE COULD SEE HOW THIS COULD BE POTENTIAL FUTURE PROB; IE; 2 ACFT AT SAME ALT IN THE HOLDING PATTERN/PROC TURN IN THIS SIT.