A POTENTIAL CONFLICT OCCURS BTWN A CLBING DA10 FALCON AND A CRUISING MD80 WHILE IN ZLA AIRSPACE AT FL280. TCASII WAS AN AID IN THE EVASIVE MANEUVER.

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NO SIGNIFICANT WX; NIGHT CLR SKIES. ZLA POINTED OUT TFC AT OUR 9:30 O'CLOCK POS AT FL270; PASSING L TO R. SECONDS LATER OUR TCASII SOUNDS 'TFC' ALERT AND IT APPEARS AT 10:30 O'CLOCK POS BUT ONLY 500 FT BELOW OUR ALT. THE ACFT IS SIGHTED; BUT CONTINUES TO CLB TO FL280 AS OUR TCASII INDICATES ZERO ZERO ON THE ALT DIFFERENTIAL. THE TCASII NOW SHOWS THE ACFT AT FL280 AND WITHIN LESS THAN 1 1/2 MI FROM US. THE RA CALLS OUT 'CLB; CLB' AS WE ABRUPTLY TURN L AND CLB (APPROX 200 FT) TO AVOID THE ACFT. THE ACFT PASSED WITHIN APPROX 200 FT BELOW AND BTWN 1 1/2 MI LATERALLY TO OUR ACFT. WE NOTIFY ATC OF OUR REQUIRED DEV. AS THE ACFT MOVED FROM OUR 9:30 O'CLOCK POS TO 12 O'CLOCK POS; THE CTLR REPEATEDLY ASKED TO CONFIRM HE WAS AT FL270; BUT WITH NO REPLY. THE SHARP L TURN AND CLB TO EVADE CAUSED NO INJURY TO CREW OR PAX; HOWEVER; A BRIEF DESCRIPTION OF THE CAUSE OF THE MANEUVER WAS GIVEN OVER THE PA. LAX ATC WAS NOTIFIED AND A CALL TO MR X (OPS SUPVR) WAS MADE AFTER LNDG AT LAX. HE SAID RADAR TAPES INDICATED THE 2 ACFT PASSED WITHIN 200 FT AND 1 1/2 MI; ALTHOUGH THE RADAR SWEEP IS ONLY EVERY 12 SECONDS. I INDICATED IT WAS MUCH CLOSER AND CONSIDERED IT A 'NEAR MISS.'