ARTCC ADVISED B767 FREIGHTER OF VFR TFC. FREIGHTER FLC HAS NEAR MISS WITH LIGHT TWIN DURING DSCNT. IT WAS NOT VISIBLE IN HAZY CONDITIONS. FOLLOWING TCASII RA; RESULTED IN POSITIVE RESULT.

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FO WAS FLYING; AUTOPLT ENGAGED. DSNDING TO 14000 FT OUT OF FL240 APCHING BANDS INTXN. ATC ADVISED WE HAD VFR TFC AT 12 O'CLOCK; OPPOSITE DIRECTION; 15 MI AT 13500 FT UNCONFIRMED. AT A GUESS; WE WERE AT 17000 FT DSNDING RAPIDLY ON THE ARR (SPD BRAKES EXTENDED). WE WERE THEN HANDED OFF TO SOCAL APCH. AT ABOUT 15000 FT WE GOT A TA AND THE TFC APPEARED ON THE TCASII INSIDE THE 6 MI RANGE. ALMOST IMMEDIATELY WE GOT AN RA 'DSND; DSND; DSND.' THE TCASII GAVE US AN ACCURATE LOCATION OF 12:30 - 1 O'CLOCK POS AND LESS THAN 2 MI. THE FO HAD DISCONNECTED THE AUTOPLT AND INCREASED OUR DSCNT RATE TO COMPLY WITH THE RA. APCHING 14000 FT THE TCASII RA CHANGED TO 'CLB; CLB; CLB.' I WAS VISUALLY SCANNING. THE TFC (LIGHT/MEDIUM PROP TWIN) APPEARED AT LESS THAN 1 MI. WE BANKED SLIGHTLY TO THE L AND PASSED IT. WE PASSED WITH LESS THAN 500 FT HORIZ SEPARATION AND APPEARED TO BE LEVEL AT 14000 FT. I NEVER SAW THE TFC TAKE ANY EVASIVE ACTION. WE CHKED IN WITH SOCAL AND ADVISED HIM OF THE NEAR MISS. HE HAD NO COMMENT AT ALL. THE WX IN THE LOS ANGELES BASIN WAS THE USUAL DENSE SMOG; ALMOST UP TO 14000 FT. WITHOUT THE TCASII DEPICTION IT IS UNLIKELY WE WOULD HAVE FOUND THE TFC AT OUR CLOSURE RATE. IF WE HAD HAD TCASII WITH RANGE DEPICTION ON OUR EHSI WE WOULD HAVE HAD CONSIDERABLY MORE TIME TO LOOK FOR THE TFC AND WOULD LIKELY HAVE BEEN ABLE TO AVOID HIM WITH A LARGER MARGIN OF SAFETY. A TCASII DISPLAY OF LARGER RANGE ON ANY TCASII INST WOULD HAVE BEEN MORE USEFUL BUT THE EHSI WOULD HAVE BEEN THE BEST. AS WE ARE ALL AWARE; ADS-B WOULD NOT HAVE GIVEN US ANY WARNING UNLESS THE OTHER ACFT HAD BEEN EQUIPPED WITH ADS-B.