AN ACR MD80 CLBED IN RESPONSE TO A TCASII RA. THE ACFT WAS ON THE ILS RWY 25L AT LAX. THE INTRUDER WAS UNDER TRACON CTL; PASSING UNDER THE RPTRS FOR THE ILS RWY 25R. ALTDEV. NON ADHERENCE TO TRACON INSTRUCTIONS; BUT THEY FOLLOWED TCASII.

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INBOUND TO LAX; WE WERE VECTORED ON AND OFF CIVET ARR TWICE FOR SPACING. AFTER CLRED FOR ILS RWY 25L AT LAX; WE WERE ADVISED OF TFC WHICH WOULD CROSS UNDER US IN ORDER TO LAND RWY 25R AT LAX. WE NEVER DID ACQUIRE THE TFC VISUALLY. INSIDE THE HUNDA FIX ON THE RWY 25L ILS AND DSNDING OUT OF APPROX 3300 FT MSL; WE RECEIVED A TCASII RA CALLING 'CLB; XING CLB;' WITH A VSI COMMANDING INITIALLY 2000 FPM CLB. WE TOLD APCH THAT WE WERE RESPONDING TO A TCASII RA; AND HE SEEMED SURPRISED; AND TOLD US IT WAS THE TFC HE HAD CALLED EARLIER. HE THEN GAVE US A L TURN TO 070 DEGS AND MAINTAIN 4000 FT MSL. WE COMPLIED WITH THIS AFTER TCASII CALLED CLR OF CONFLICT. THE VECTOR THAT APCH GAVE US TOOK US OUT OF THE CLASS B AIRSPACE WHICH IS NOT SAFE IN THE LA BASIN. WE RETURNED FOR AN UNEVENTFUL LNDG ON RWY 25L. SUPPLEMENTAL INFO FROM ACN 345884: AT APPROX 3300 FT AND 8 DME; WE RECEIVED A 'CLB; XING CLB;' RA ON THE TCASII AND SAW A TARGET JUST UNDER US ON THE TCASII SCREEN AT 700 FT BELOW AND AN UP ARROW. THE TFC HAD STATED THAT HE SAW US VISUALLY AT OUR POS SOME 18 MI OUT ON FINAL.