PLT OF A C172 MAKES AN UNAUTH R TURN OFF OF RWY 25R AT LGB; CA. HE SUFFERS AN NMAC WITH A DEP S80 OFF RWY 30. TWR HAD ISSUED A TFC ALERT AFTER CREW SAW TFC. TCASII THEN ISSUED AN EVASIVE RA. S80 PASSED OVER THE C172 AT 200 FT.

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AM31Z; FREQ: 120.5; ALT: 800 FT. ATC FAC: LGB TWR. LOCATION: RWY 30 DEP END. I WAS MAKING THE TKOF AT LGB. AFTER RAISING GEAR; THE CAPT SPOTTED A CESSNA AHEAD AND SLIGHTLY TO OUR L IN A CLBING R TURN. I VISUALLY ACQUIRED THE TARGET AND DETERMINED THAT WE COULD CLR OVER THE TOP OF THE CESSNA BY MAINTAINING OUR PRESENT SPD (APPROX V2) AND CLB ATTITUDE OF APPROX 20 DEGS. ABOUT THAT TIME; TWR ISSUED A COLLISION ALERT. AS THE CESSNA DISAPPEARED UNDER THE NOSE; THE TCASII GAVE US AN RA OF 'MAINTAIN VERT SPD' FOLLOWED BY 'CLB; CLB.' OUR RATE OF CLB WAS APPROX 3000 FPM AND THE CLOSEST WE CAME WAS APPROX 200 FT BASED ON THE TCASII DISPLAY. WE CONTINUED CLBING UNTIL THE RA ENDED AT ABOUT 1800 FT AT WHICH POINT WE COMMENDED OUR TURN OUT OF TFC (NORMALLY 1500 FT) AND ACCOMPLISHED THE REST OF THE CLEANUP. WE THEN ADVISED TWR WE WERE FILING A NEAR MISS RPT. WX WAS VFR; IFR FLT PLAN; ALTIMETER 29.94. OUR HDG WAS 301 DEGS; CESSNA IN A CLBING R TURN HDG APPROX 030 DEGS. WE SPOTTED THE CESSNA ABOUT 1/2 TO 1 MI AHEAD AS WE WERE RAISING GEAR; AND STARTED EVASIVE ACTION; MAINTAINING V2 AND TKOF PWR WITH WINGS LEVEL ABOUT 5 SECONDS AFTER SIGHTING CESSNA. WE FOLLOWED THE TCASII RA AND AVOIDED THE CESSNA BY 200 FT VERT; 0 FT HORIZ. LGB TWR REQUESTED A COPY OF THIS AS WELL AS LAX CHIEF PLT. SUPPLEMENTAL INFO FROM ACN 378546: SAW A CESSNA TO OUR L FRONT. REALIZED THAT IT WAS IN A R TURN AND WAS GOING TO CROSS OUR PATH. POINTED OUT TO FO WHO WAS AT CTLS AND HE MAINTAINED V2 SPD AND FLAPS 11 DEGS MAX PWR AS WE CLBED UP THROUGH 800 FT. TCASII SHOWED TARGET 200 FT ABOVE AND XING AT 12 O'CLOCK IN CLBING R TURN. TWR ISSUED AN ALERT AS WE WERE LOSING SIGHT OF CESSNA. EWE CROSSED OVER CESSNA AT ESTIMATED 200 FT. ACKNOWLEDGED TWR AND SAID WE COULD NOT TURN AT 1500 FT.