ACR X NON ADHERENCE TO ATC CLRNC TCASII TA RA HAD LTSS FROM Y. EVASIVE ACTION DSND.

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ACFT X FERRY TO LAX AND CLRNC RECEIVED WAS FOR A DEP OFF RWY 26R; 255 DEG HDG TO V363 TO INTERCEPT LAX RWY 25L LOC; MAINTAIN 4000 FT. DEP VECTOR WAS 230 DEG HDG TO INTERCEPT THE LOC. CTLR THEN INFORMED US THAT LAX FLOW CTL COULD NOT ACCEPT US AT THIS TIME SO MAKE A L 360 DEG TURN AND SLOW TO 210 KTS. I INITIATED THE TURN WHILE THE FO TUNED AND IDENTED HIS RADIO TO RWY 25L LOC FREQ. HE DID NOT HEAR THE COMPLETE XMISSION; SO I REPEATED INSTRUCTIONS TO HIM. AFTER HE READ BACK ATC INSTRUCTIONS; THE CTLR THEN CHANGES CLRNC TO NOW ANTICIPATE A 360 DEG TURN BUT MAINTAIN 210 KTS. AFTER APPROX 45 DEG HDG CHANGE WE RECEIVED A TA FOLLOWED BY AN IMMEDIATE RA COMMANDING A DSCNT. SIMULTANEOUSLY; WE RECEIVED A NEW CLRNC TO TURN 20 DEGS R AND INTERCEPT RWY 24R LOC AT LAX ON FREQ 108.5. THE TFC Y CONFLICT INDICATED A TARGET AT 11:30 O'CLOCK POS AND 300 FT ABOVE OUR ALT AND DSNDING. I CONTINUED TURNING L AND DSNDED UNTIL TFC WAS CLR AND THEN CLBED BACK TO 4000 FT FROM 3300 FT. WE ADVISED ATC THAT WE RESPONDED TO AN RA AND THEN THEY POINTED OUT ADDITIONAL TFC AT 1 O'CLOCK AND 4500 FT. WE TURNED R AND INTERCEPTED THE RWY 24R LOC AND WERE EVENTUALLY CLRED FOR AN ILS APCH. TOTAL FLT TIME WAS 11 MINS. OUR RELEASE FROM FLOW CTL CHANGED TWICE WHILE ON THE GND AT ONT AND 1 SHORT- LIVED CHANGE AIRBORNE. COORD AND COM BTWN FLOW CTL AND DEP CTL MAY HAVE DISTRACTED THE CTLR FROM HER RADAR SCREEN AND RELEVANT POS AT OUR ACFT. OUR APCH CLRNC CHANGED ALSO. INSTEAD OF AN APCH TO RWY 25R; WE WERE SWITCHED TO RWY 24R. TOO MANY FLOW CTL AND APCH CTL CHANGES IN SUCH A SHORT FLT. SUPPLEMENTAL INFO FROM ACN 295902: WHILE I WAS TUNING IN RADIOS; I MISSED THE NEXT XMISSION WHICH THE CAPT (FLYING) HAD HEARD AS 'MAKE A L 360 DEG TURN AND SLOW TO 210 KTS.' (HE PROCEEDED INTO A L TURN.) UPON READING THIS BACK; THE CTLR SAID 'ANTICIPATE A 360 DEG TURN; SLOW TO 210 KTS.' AT THAT POINT WE WERE APPROX 45 DEG INTO OUR 360 DEG L TURN. AT THAT POINT; WE GOT AN RA AND A CTLR COMMAND TO 'TURN 20 DEGS R AND INTERCEPT THE RWY 24R LOC; 108.5.' THE RA COMMANDED A 1500 FPM RATE OF DSCNT; WHICH WE DID; DSNDING APPROX 500 FT; AND WE STARTED OUR TURN BACK TO THE R. THE CTLR HAD NOT REALIZED WE HAD INITIATED THE L 360 DEG TURN AS THE 20 DEG R TURN INSTRUCTION WAS AT LEAST 20-25 DEGS L OF A PARALLEL HDG FOR THE RWY 24R LOC. THE CTLR THEN CALLED OUT TFC PASSING OFF OUR R (NOT THE RA ACFT). WE INFORMED THEM OF OUR RA AND DSCNT. THE CTLR RESPONSE WAS 'SAY YOUR ALT.' WE RESPONDED 'CLBING BACK TO 4000 FT.' (WE WERE THEN ABOUT 200 FT LOW.)