DURING DSCNT INTO A COMPLEX HIGH TFC VOLUME ARPT'S TERMINAL AREA; FLC OF AN MLG ACR ACFT WERE DIRECTED TO DSND RAPIDLY BY ATC TO AVOID UNEXPECTED TFC AND AT THE SAME TIME A TCASII DIRECTED A CLB. THE FLC OBSERVED THE OTHER ACFT AND DSNDED.

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WE WERE APCHING BUR ARPT FROM THE W IN LATE AFTERNOON SMOG. WE WERE OUTSIDE OF VNY ARPT BEING VECTORED TO THE LOC COURSE. THERE HAD BEEN MULTIPLE TA'S FROM ATC; SEVERAL TA'S FROM TCASII; AND I HAD VISUALLY ACQUIRED MOST OF THEM. I WAS TALKING ON THE RADIO; RUNNING THE CHKLISTS; AND MAINLY LOOKING OUTSIDE FOR TFC AND THE ARPT. THE FO WAS FLYING THE ACFT AND LOOKING OUT FOR TFC. WITHIN AN APPROX 10 SECOND PERIOD THE CTLR GAVE US 'DSND; DSND; IMMEDIATELY CANCEL APCH CLRNC.' THE TCASII THEN GAVE AN RA AND 'CLB; CLB.' I SAW THE TFC AT 1 O'CLOCK POS MOVING L TO R; AT OUR ALT; AND ABOUT 1 MI AWAY. THE CTLR SAID 'CLR OF TFC; MAINTAIN 3000 FT; CLRED TO INTERCEPT FINAL.' THE FO HAD STARTED TO DSND WHEN THE TCASII GAVE CONFLICTING SIGNALS AND THEN WE WERE CLR. IF THE TCASII HAD BEEN FIRST; WE WOULD HAVE FOLLOWED IT. THE CTLR APOLOGIZED FOR THE CONFUSION AND SAID THAT 'THE GUY HAD JUST POPPED UP ON HIS SCREEN AND THAT HE WOULD TRY TO TRACK HIM DOWN AND TALK TO HIM.' WE DIDN'T THINK THAT THE TFC WAS IN ERROR. HE WAS OUTSIDE THE TCA; SW OF BUR FINAL; IN VFR CONDITIONS. THE CTLR DID AN EXCELLENT JOB IN ISSUING ADVISORIES. THE PROBS IN OUR MINDS ARE: CONTINUING CONFLICT BTWN TCASII AND ATC CLRNCS.