FLC OF AN LGT ACR ACFT CLBED AND STARTED A GAR DURING A VISUAL APCH TO PARALLEL RWYS IN RESPONSE TO A TCASII RA.

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APCH CLRED US TO CROSS FUELR AT 8000 FT THEN DSND TO 5000 FT. AFTER FUELR ATC CLRED US FOR A VISUAL TO 25R. ATC ADVISED TFC ON VISUAL TO 25L. WE HAD A TCASII BUT NOT VISUALLY. TFC BEHIND LOWER. WE WERE SLOWED TO 170 KTS. ADVISED DSNDING OUT OF 5000 FT; WE GOT AN RA ON TCASII TO CLB. CAPT ELECTED TO FOLLOW AND EXECUTE A GAR. CLBED. I ADVISED APCH; THEN TWR. TWR TOLD US TO DSND TO 2000 FT. STARTING THE DSCNT; APCHING RWY BEYOND LIMMA; DSNDED TO 4000 FT. TWR ADVISED TFC (IN LAX CORRIDOR). GOT ANOTHER RA TO CLB; GOT VISUAL ON TFC. HE PASSED BENEATH US. ADVISED TWR. THEY CLRED US TO 3000 FT. WE WERE VECTORED FOR VISUAL TO 24R WITHOUT INCIDENT. DURING TAXI IN; TWR SUPVR REQUESTED CREW CALL. CAPT CALLED. HEARING ONLY ONE SID; I DETERMINED SUPVR AND CAPT WERE AT ODDS ON DECISION TO GAR AND PROCS WE FOLLOWED. WE ARE TRAINED TO REACT TO AN RA. HOWEVER; IN TERMINAL AREAS; VFR CONDITIONS; ATC CTL; PARALLEL APCHS; WE HAVE AUTH TO TURN TCASII TO TA ONLY. FEEL CONTRIBUTING FACTORS WERE CONFUSING ON ACR PROC. AS WE WERE SLOWED TO 170 KTS; TO DSND ON VISUAL THE OTHER ACFT WAS FASTER AT A STEADY ALT. BEING PARALLEL APCHS; TCASII COMPUTER READ A POSSIBLE CONFLICT. COMPUTER HAS NO WAY OF KNOWING PARTICULAR UNUSUAL CIRCUMSTANCES. BETTER COORD BTWN CREW AND ATC (I.E.; ATC ADVISING US ACFT IN BACK OF US HAD US IN SIGHT -- NO PROB). SECOND CONFLICT I FEEL MORE DANGEROUS SINCE WE WERE IN VFR CORRIDOR OVER LAX. CONFLICT AVOIDED BECAUSE OF VISUAL CONTACT.