AN ACR BA31 CLBING ON AN ASSIGNED HDG BY DEP CTL WAS OVERTAKEN BY AN ACR EMB120 WHO WAS MAINTAINING VISUAL SEPARATION. THE EMB120 CAUSED A TCASII AURAL WARNING IN THE BA31 AND THEY SAW HIM PASS OVERHEAD APPROX 200 FT ABOVE. PHONE CALLS TO TRACON AND TWR CONFIRMED THAT THE EMB120 WAS CLRED TO MAINTAIN VISUAL SEPARATION. RPTR SAYS WAS TOO CLOSE.

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WE HAD BEEN CLRED FOR TKOF FROM RWY 24L IMMEDIATELY BEHIND AN ACR TURBOJET. ANOTHER BA31 HAD JUST PRIOR BEEN CLRED FOR TKOF FROM RWY 24R. AN EMB120 WAS CLRED FOR IMMEDIATELY AFTER US. FINAL INSTRUCTION FROM TWR WAS TO MAINTAIN VISUAL ON THE DEPARTING TURBOJET; TURN TO 270 DEGS AT THE SHORELINE AND MAINTAIN 3000 FT. WE WERE TOLD TO CONTACT DEPS. DEP TOLD US TO MAINTAIN 3000 FT AND CALLED THE BA31 TFC AHEAD (THE ACR TURBOJET WAS NO LONGER A FACTOR) WHICH WE RPTED IN SIGHT. SHORTLY AFTER THAT; WE WERE CLRED TO 7000 FT. THERE HAD BEEN NO AURAL TA'S FROM THE TCASII. IMMEDIATELY UPON COMMENCING THE CLB THE TCASII GAVE AN AURAL WARNING AND SHOWED A TARGET DIRECTLY 200 FT ABOVE. THE CAPT IMMEDIATELY BEGAN A DSCNT WHILE WE BOTH LOOKED FOR TFC. SHORTLY AFTER; THE EMB120 BECAME VISIBLE AS IT PULLED AHEAD DIRECTLY ABOVE US. WHEN WE QUERIED THE CTLR HE SAID THE EMB120 HAD RPTED US IN SIGHT AND WAS MAINTAINING VISUAL. LATER WHEN THE CAPT CONTACTED DEP CTL ON THE TELEPHONE; THEY SAID THE LAX TWR HAD CALLED US AS TFC TO THE EMB120 AND INSTRUCTED THEM TO MAINTAIN VISUAL. THE CAPT THEN CALLED THE TWR AND WAS TOLD SEPARATION WAS THE RESPONSIBILITY OF THE EMB120. CONCLUSION: THIS WAS A VERY NEAR CATASTROPHE THAT WAS AVERTED BY THE MARGINAL PERFORMANCE OF TCASII. I BELIEVE ATC SEPARATION STANDARDS SHOULD REQUIRE THAT BOTH CREWS BE ADVISED AND REQUIRED TO MAINTAIN VISUAL WHEN SEPARATION IS LESS THAN 500 FT VERT. PAST EXPERIENCE WITH THE TCASII INSTALLED IN OUR ACFT HAS BEEN ERRATIC DISPLAY OF CLOSE IN (LESS THAN 2.5 MI) TARGETS PARTICULARLY WHEN DIRECTLY IN FRONT OR BEHIND THE ACFT. I PRESUME THAT THE EMB120 CREW DID NOT RECEIVE A TCASII ALERT AND POSSIBLY HAD THE OTHER BA31 IN SIGHT.