DC10 CREW HAD TCASII RA ON DEP IN HNL CLASS B.

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THE FO CONTACTED HNL DEP 118.3 AT APPROX 1500 FT AGL; WHILE WE WERE IN A R TURN TO A 155 DEG HDG. DEP CTL INSTRUCTED US TO TURN L TO A 140 DEG HDG FOR TFC AND CLB MAINTAIN FL280. DEP CTL THEN ASKED US IF WE HAD THE TFC IN SIGHT AT 10-12 O'CLOCK POS AT 5000 FT. WE CONFIRMED THE TFC VISUALLY AND ON TCASII AT 1200 FT ABOVE DSNDING. DEP CTL REPLIED OUR ALT WAS 3800 FT CLBING; 'MAINTAIN VISUAL SEPARATION.' WHEN THE DC9 APCHED IT WAS STILL DSNDING TOWARD OUR ALT THE TCASII REPLIED 'TFC TFC.' ALMOST IMMEDIATELY THE TCASII RA ISSUED A 'CLB; CLB; CLB' WARNING AND THE RED ARC ON THE VSI WAS FROM 0-1000 FT UP. I PITCHED UP TO 1200-1500 FT ON THE VSI. THE RA WAS A SOLID RED SQUARE AND 300 FT DSNDING. SHORTLY AFTER PASSING 4000-4200 FT; THE TCASII REPLIED 'CLR OF CONFLICT.' AFTER PASSING 10000 FT; THE FO TOOK CTL OF THE ACFT AND THE CAPT RETURNED TO THE DP CTL FREQ AND TOLD THE CTLR THAT THE TFC HAD BEEN VERY CLOSE; AND QUESTIONED WHETHER HE OR THE DC9 HAD INDICATED A TFC CONFLICT. HE REPLIED 'NEGATIVE.' I THEN HEARD THE DC9 QUESTION THE CTLR AS TO WHAT ALT HE HAD BEEN CLRED TO AND THE CTLR RESPONDED '3000 FT'. THE REST OF THE FLT WAS NORMAL; AS WAS THE APCH AND LNDG. POSTFLT INSPECTION BY THE FE AND ONBOARD FLT MECH; REVEALED NOTHING UNUSUAL. THE ACFT THEN FLEW WFFN-YSSY (DIFFERENT CREW). ELEVATOR DAMAGE -- NOTED ON POSTFLT INSPECTION IN YSSY.