SCT CTLR DESCRIBES NMAC AS LAX AND SMO ARR ACFT CONFLICT AFTER SMO TFC DSNDS WITHOUT CLRNC.

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ACFT X WAS ON VECTORS ON DOWNWIND TO ILS RWY 24R. ACFT X WAS APPROX 10 MI NE OF LAX AT 6000 FT WHEN I SLOWED IT TO 180 KTS; REQUIRING ACFT X TO LEVEL OFF AT 6000 FT. ACFT Y (BE40) WAS ON A HDG 280 DEGS; VECTORS TO SMO VISUAL APCH. AT 8000 FT; TFC WAS EXCHANGED BTWN BOTH ACFT. I DSNDED ACFT Y TO 7000 FT AND ADVISED HE WOULD BE STEPPED DOWN REF TFC ON DOWNWIND; A B777. AT 3 MI SEPARATION; I REISSUED TFC INSTRUCTIONS TO ACFT Y AS 'TFC 11:30 O'CLOCK POS; 3 MI; 6000 FT; DSNDING B777.' AS I UNKEYED; I OBSERVED ACFT Y BELOW ASSIGNED ALT AT 6800 FT. ACFT Y RESPONDED THAT HE SAW THE TFC AND WAS DIVING UNDER HIM. I SAW ACFT Y AT 6600 FT. I INSTRUCTED ACFT Y TO LEVEL OFF. OBSERVING ACFT Y CONTINUING HIS DSCNT; I CONTINUED WITH 'TURN R; TURN R.' ACFT Y REPLIED WITH I AM 'DIVING' UNDER TFC OR SOMETHING LIKE THAT; BUT DIVING WAS AGAIN USED. AT THIS POINT THE ACFT WERE ON A COLLISION COURSE APPROX 1/2 MI APART WITH ACFT X AT 6000 FT AND ACFT Y AT 6100 FT. I XMITTED TO ACFT X 'TFC ALERT; TFC DSNDING IN FRONT OF YOU.' ACFT X RESPONDED IN A VERY PANICKED VOICE; AS MINE HAD BEEN; 'TCAS CLB.' TARGETS MERGED WITH NO OBSERVED DIFFERENCE BTWN ALTS. I COULD NOT TELL WHO WENT UNDER WHO. TARGETS CAME APART WITHOUT A COLLISION AND BOTH ACFT PROCEEDED TO THEIR DESTS. I WAS RELIEVED OF MY DUTIES. ACFT Y CALLED ABOUT MY POOR SVC. ACFT X DECLINED TO CALL THE FACILITY. A PLTDEV IS BEING FILED BY THE FAA.