S80 FLC HAS TCASII RA AND TAKES EVASIVE ACTION AS THEY SIGHT A HOMEBUILT TAKING EVASIVE ACTION.

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WE FLEW AN LAX TURNAROUND TODAY AND HAD AN RA ON EACH LEG. THIS ONE WAS DURING THE CLBOUT EBOUND. THERE WAS AN ACR B757 AHEAD OF US THAT HAD THE SAME TFC CALLED OUT TO HIM THAT GAVE US OUR RA; AND TO MY KNOWLEDGE; THE ACR DID NOT SEE THE TFC. WE WERE GIVEN A CLB TO 17000 FT MSL AND TA AT 10 O'CLOCK AND APPROX 5 MI. WE HAD NEGATIVE CONTACT WITH THE TFC. DURING THIS TIME THE TARGET ACFT SYMBOL BECAME A YELLOW SQUARE CONVERGING WITH OUR COURSE. WE WERE GIVEN AMENDED INSTRUCTIONS TO LEVEL OFF AT 13000 FT MSL AND THE TFC CALLED OUT AGAIN AT 10-11 O'CLOCK AND 1 MI. DURING THIS TIME WE GOT AN RA OF 'DSND; DSND' AND AN IVSI INDICATION TO DSND AT APPROX 200-300 FPM AS WE APCHED LEVELOFF AT 13000 FT MSL. STARING AT MY 10-11 O'CLOCK POS I COULD SEE NOTHING IN CLR AIR. THEN A SINGLE SEAT SINGLE ENG HOMEBUILT TYPE ACFT BROKE TO OUR 6 O'CLOCK POS WITHIN ABOUT 1/2 MI. DURING THIS TIME THE COPLT HAD DISCONNECTED THE AUTOPLT AND WAS SMOOTHLY BUT FIRMLY PUSHING THE ACFT YOKE FORWARD TO COMPLY WITH THE RA INSTRUCTIONS. I WAS ASSISTING HIM WITH FORWARD PRESSURE ON THE YOKE. THE ENCOUNTER WAS NOT A NEAR MISS BY ANY MEANS. IT SIMPLY WAS THE CASE THAT I COULD NOT SEE THE TARGET ACFT UNTIL HE BROKE AWAY FROM US; HAVING PREVIOUSLY BEEN ON A HEAD-ON COURSE TO OUR ACFT AT ABOUT A 90 DEG ANGLE.