VISUAL SEPARATION. ATC CLRED RPTR AND LTT FOR TKOF ON PARALLEL RWYS. ATC HAD ALLEGEDLY ADVISED LTT TO MAINTAIN VISUAL SEPARATION (IN TRAIL CLB) FROM RPTR'S FLT. LTT FAILED TO REMAIN IN TRAIL AND ACTIVATED TCASII. RPTR MAINTAINED VISUAL AFTER LTT BECAME THE LEAD ACFT.

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MY FLT WAS CLRED FOR TKOF ON RWY 25R AT LAX FROM INTXN 8J. IMMEDIATELY THEREAFTER YYY WAS CLRED FOR TKOF ON RWY 25L -- I DID NOT HEAR OR UNDERSTAND THIS AT THE TIME. AT APPROX 1200 FT MSL WE RECEIVED THE FIRST OF 2 TCASII RA'S DUE TO OUR CLOSE PROX TO YYY. IT WAS AT THIS TIME THAT I FIRST OBSERVED YYY AT MY 10 O'CLOCK LOW POS -- I WAS STILL CLBING VERY STEEPLY. APCHING OUR CLRED ALT OF 2000 FT I SHALLOWED THE CLB AND RECEIVED A SECOND RA. YYY HAD BEEN ISSUED A VISUAL SEPARATION 'IN TRAIL' CLB; REF MY AIRPLANE. 2 IMPORTANT POINTS: I WAS VERY INVOLVED MANAGING MY OWN AIRPLANE DURING THE HIGH WORKLOAD TKOF PERIOD AND I WAS NOT AWARE INITIALLY OF YYY'S PRESENCE OR HIS RELATIVE POS TO MY AIRPLANE. YYY PASSED ME! THERE IS LITTLE ARGUMENT THAT IT IS RATHER DIFFICULT TO MAINTAIN VISUAL SEPARATION ON ANOTHER AIRPLANE WHEN YOU MOVE OUT FRONT AND TAKE THE LEAD. THE CHAIN OF EVENTS THAT LEADS TO AN ACCIDENT WAS; IN MY ESTIMATION; IN THE PROCESS OF FORMATION. I CALLED BACK LATER AND TALKED TO THE TWR SUPVR. HE HAD TALKED TO THE CTLR INVOLVED. THE CTLR SAW NO PROB; HE THOUGHT THIS WAS GOOD CTLING. NOW THAT WORRIES ME. THE TWR GENERATED A PROB BUT DOESN'T RECOGNIZE IT! OUR COCKPIT OBSERVER TOLD ME THAT OUR AIRPLANE AND YYY ROTATED SIMULTANEOUSLY (APPROX 800 FT LATERAL SEPARATION).