FLC OF B767-200 IS GIVEN CLRNC TO DSND. AS THEY START DSCNT; THE TCASII SHOWS AN ACFT IN FRONT OF THEM. A TCASII TA IS GIVEN AND CTR ISSUES A TURN AND CLB BACK TO PREVIOUS ALT.

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WE WERE CRUISING WBOUND ENRTE TO LAX ON J4 ABOUT 75 MI E OF TNP VOR. WE WERE LEVEL AT FL390 AND WERE EXPERIENCING LIGHT TURB. WE REQUESTED A LOWER ALT FROM ZLA AND WERE GIVEN A CLRNC TO FL370. AFTER ABOUT 1 MIN WE NOTICED AN ACFT IN FRONT OF US ON OUR TCASII SCREEN INDICATING FL370. A FEW SECONDS LATER; WE RECEIVED A TA FROM THE TCASII SYS AND SIMULTANEOUS INSTRUCTIONS FROM ZLA TO 'TURN L 40 DEGS AND CLB TO FL390.' WE RESPONDED IMMEDIATELY AND WERE LEVEL AT FL390 WHEN THE OTHER ACFT PASSED ABEAM OUR R SIDE AT 3-5 MI DISTANCE. OUR LOWEST ALT REACHED WAS FL380. OUR ATC CTLR WAS IMMEDIATELY REPLACED BY ANOTHER AND RADIO TFC WAS HVY AT THE TIME. I DO NOT CONSIDER THIS EVENT TO BE A NEAR MISS SINCE WE ALWAYS HAD SOME LATERAL SEPARATION AS WELL AS 1000 FT MINIMUM VERT SEPARATION. HOWEVER; THIS IS OBVIOUSLY A RARE OCCURRENCE IN THE ENRTE POSITIVE CTL ENVIRONMENT AND MAY HAVE ENCROACHED ON THE MINIMUM ENRTE SEPARATION STANDARDS USED BY ATC. CONTRIBUTING FACTORS TO THIS EVENT WERE OBVIOUSLY A HVY CTLR WORKLOAD; A SATURATED RADIO FREQ; AND HIGH VOLUME TFC ARRIVING AND DEPARTING THE LOS ANGELES AREA. SUPPLEMENTAL INFO FROM ACN 386387: I WOULD LIKE TO KNOW WHY CTLRS ASSIGN WRONG WAY ALTS (370 WBOUND) IN BUSY AIRSPACE LIKE ZOA. ALSO; I AM GLAD THAT WE NOW HAVE TCASII. IT GAVE US INSTANT SITUATIONAL AWARENESS IN A VERY CONFUSING SIT; AND MAY HAVE SAVED A NEAR MISS OR COLLISION.