FLT CREW OF B767 RECEIVE 2 TCASII RA'S AND EXPERIENCE AN NMAC ON RWY 25R INST APCH TO LAX. OTHER ACFT ON VFR ARR FOR ADJACENT RWY 25L.

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ALL HAD GONE NORMALLY AND WE WERE AT 11000 FT ON THE PARADISE 4 ARR INTO LAX WITH THE TRANSITION TO RWY 25L. APPROX .6 MI FROM ARNES; SOCAL APCH RECLRED US TO THE RWY 25R TRANSITION. THIS TOOK US ABOUT 45 SECONDS TO REPROGRAM THE FMS AND ILS FREQ AND WE HAD A MILD OVERSHOOT FOR RWY 25R LOC SINCE WE HAD BEEN ASSIGNED 230 KTS. AFTER WE HAD INTERCEPTED THE RWY 25R LOC AND WERE ON COURSE INBOUND WITH THE AUTOPLT COUPLED UP; SOCAL APCH TOLD US THAT AN ACR Y BRASILIA WOULD BE FLYING ABEAM US FOR THE VISUAL TO RWY 25L; AND WOULD NOT PULL IN FRONT OF US; AND WE ACKNOWLEDGED. AT ABOUT 2100 FT ON THE APCH; TCASII GAVE US AN RA TO DSND AND WAS REQUESTING ABOUT 1300 FPM DOWN AS A RESULT OF THE OTHER ACFT BEING BEHIND US HIGH AND DSNDING. THE AIRPLANE IMAGES ON OUR TCASII WERE SUPERIMPOSED. WE HAD NOWHERE TO GO AND MAINTAINED GS AND COURSE GUIDANCE. SHORTLY AFTER THAT THE E120 PULLED ABEAM SLIGHTLY HIGH AND THEN FORWARD OF US. THE FO READ 100 FT ON THE TCASII AND I ESTIMATE HIM TO HAVE BEEN IN THE 60-80 FT RANGE FROM MY COCKPIT! (NOT THE WINGTIP!) ON ABOUT A 20 DEG ANGLE FORWARD OF MY 3-9 LINE. THEY SLOWLY DSNDED AFTER THEY GOT AHEAD OF US (I COULD SEE INTO HIS COCKPIT) AND THEN WENT BELOW US TO THE L AND TRIGGERED ANOTHER TCASII RA. WHEN APCH SWITCHED US TO TWR I TOLD THEM I WOULD BE WRITING A RPT.