ACR X HAD NMAC. TCASII TA RA WITH C-172. EVASIVE ACTION CLB. RECEIVED ANOTHER TCASII RA FROM ACFT ABOVE. SEE AND AVOID CONCEPT.

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I WAS CHK AIRMAN FOR A NEW CAPT ON INITIAL OPERATING EXPERIENCE CHKOUT. I WAS PNF IN COPLT SEAT. HE WAS FLYING. APCHING LAX FROM SAN WE WERE LEVEL AT 7000 FT DIRECT SLI ABOUT 10 MI S. ATC HAD ISSUED TA FOR A CESSNA 172 AT 1 O'CLOCK; 10 MI; OPPOSITE DIRECTION; 1500 FT LOW; EARLIER AND REISSUED WHAT I ASSUME WAS ADVISORY ON SAME TARGET; NOW AT 500 FT BELOW US. TCASII SHOWED TARGET NOT AT MINUS 500 FT ABOUT 3 MI AT 12 O'CLOCK OPPOSITE DIRECTION. TFC RPTED US IN SIGHT AND LEVEL. SOCAL APCH NOW SWITCHED US TO LAX FINAL APCH CTLR. AS I LOOKED UP FROM CHANGING THE FREQ; I NOTICED THE TARGET'S RELATIVE ALT CHANGE FROM MINUS 500 FT TO MINUS 400 FT THEN TO MINUS 300 FT. BEFORE I COULD TAKE ACFT; TCASII ISSUED A 'CLB; CLB' RA; WHICH STUDENT INITIATED. AS I VISUALLY ACQUIRED THE TARGET; STUDENT SAID; 'TCASII SHOWS ANOTHER TARGET AT PLUS 500 FT. TCASII THEN ISSUED A 'MONITOR VERT SPD' AND STUDENT TURNED TO THE R OF THE INITIAL HDG AS BOTH TARGETS PASSED BEHIND US. USE OF TKOF/GAR PWR BY THE STUDENT FOR THE INITIAL CLB PUT US INTO AN OVERSPD WARNING (FLAPS WERE AT 2 DEGS IN ANTICIPATION OF A 'SLAM- DUNK'). THE OVERSPD BELL WAS LOUD TO THE POINT OF ALMOST DROWNING OUT THE TCASII COMMANDS AND MY OWN VERBAL INSTRUCTIONS TO THE STUDENT. AFTER DSNDING BACK TO 7000 FT AND TURNING BACK TOWARD SLI; WE RPTED THE DEV TWICE TO APCH CTL AND RECEIVED NO ACKNOWLEDGMENT. THE FREQ WAS TOO BUSY TO PURSUE IT FURTHER UNTIL AFTER LNDG.