WDB ACFT HAS TCASII RA ON ILS APCH WITH MIL ACFT WHICH PROBABLY DID NOT HAVE TCASII.

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APCHING BOOKE INTXN; ZHN CLRED US TO TURN AND INTERCEPT THE HNL 08L LOC AND MAINTAIN 8000 FT. LISTENING; I HAD ALSO HEARD THEM WORKING SOME HAWAII AIR NATIONAL GUARD FGT'S. I ALSO NOTED THAT THERE WAS A FAIRLY LARGE AMOUNT OF OTHER TFC IN THE AREA. WE WERE TURNED OVER TO APCH CTL A LITTLE BIT LATE; AND WE WERE ON THE LOC AT 8000 FT; ABOUT 28 MI OUT. APCH CTL CLRED US TO DSND TO 3000 FT; AND WE DSNDED SLIGHTLY FASTER THAN NORMAL; SINCE WE WERE ABOVE THE GS. INITIALLY; WE WERE ASKED TO MAINTAIN 250 KIAS TO 10 MI; BUT I REFUSED THAT CLRNC FOR SAFETY REASONS; AND WE WERE SUBSEQUENTLY TOLD TO MAINTAIN 170 KIAS. WHEN WE REACHED THE GS AT ABOUT 4400 FT; WE DECIDED TO DSND ON THE GS TO 3000 FT IN ANTICIPATION OF A FORTHCOMING APCH CLRNC. JUST AFTER PASSING THE SHORELINE; OUR TCASII ANNOUNCED 'TFC.' CHKING; I NOTED AN AMBER DOT AT OUR 7 O'CLOCK POS; JUST INSIDE THE 2 MI CIRCLE. AS I LOOKED; CONSIDERING THE SPD; I THOUGHT IT MIGHT BE AN FGT ENTERING THE PATTERN FOR A 360 DEG OVERHEAD AT HNL AT AROUND 2000 FT. BEFORE I HAD TIME TO CONFIRM THIS; THE RA SOUNDED; INSTRUCTING; 'CLB' AND ASKING FOR A 1500-2000 FPM RATE OF CLB. I INSTRUCTED THE COPLT; WHO WAS FLYING THE ACFT; TO FOLLOW THE RA; AND HE ADDED PWR AND SMOOTHLY TRANSITIONED FROM THE DSCNT TO A CLB. WE CONTINUED THE CLB TO ABOUT 5400 FT; WHEN THE TCASII ANNOUNCED; 'CLR OF CONFLICT.' AS WE TRANSITIONED TO THE CLB; I SPOTTED AN FGT AT OUR 9:30 POS; SLIGHTLY (400 FT?) ABOVE US AND ABOUT 3000-4000 FT AWAY. AS WE CLBED; IT WAS PASSING US ON THE L; AND IT WAS ALSO CLBING; STAYING AT OR ABOVE OUR ALT. IT WAS IN A TURN; AND; ALTHOUGH I SUSPECTED THAT IT WAS A L TURN; I COULD NOT BE SURE. THE VISIBILITY AT ALT WAS POOR IN HAZE; AND ALL I COULD MAKE OUT WAS A SILHOUETTE. SINCE IT DID NOT SEEM TO BE TURNING AWAY AS FAST AS I THOUGHT IT MIGHT; AND SINCE ITS BEING IN A R TURN WOULD PUT US IN A DANGEROUS CONFLICT; I INSTRUCTED THE COPLT TO CONTINUE THE CLB AT THE BEST RATE. I LOST SIGHT OF THE FGT AT ABOUT OUR 11 O'CLOCK POS. AT THE TIME; THE FLT ATTENDANTS WERE IN THE AISLES; AND CHKING THE PAX FOR LNDG. I LATER RECEIVED A NUMBER OF COMMENTS ABOUT THE MANEUVER AND HOW DIFFICULT IT WAS FOR THEM TO HANG ON. FORTUNATELY; THE TRANSITION TO THE CLB WAS SUFFICIENTLY SMOOTH AND THE FLT ATTENDANT'S REACTIONS WERE GOOD ENOUGH THAT NO ONE WAS INJURED. I FEEL THAT WE WERE QUITE LUCKY IN THIS REGARD. WE STARTED THE MANEUVER AT ABOUT 3800 FT. AT THE TIME; I RPTED TO APCH CTL THAT WE WERE CLBING IN RESPONSE TO A TCASII RA. AT ABOUT 5400 FT; WHEN THE TCASII SAID 'CLR...;' I RPTED THIS TO APCH CTL. THEY THEN CLRED US FOR AN APCH. HOWEVER; I FELT THAT WE WERE TOO HIGH AND TOO CLOSE IN TO SAFELY EXECUTE AN APCH. AFTER I RPTED THIS TO APCH CTL; THEY GAVE US A VECTOR TO 170 DEGS FOR A MOMENT; THEN A TURN BACK TO 030 DEGS TO INTERCEPT THE LOC. TO ASSIST US; WE DROPPED THE GEAR AT ABOUT 5500 FT AND; CLRING THE CLOUDS AND INTERCEPTING THE LOC AT AROUND 3000 FT; I RPTED THE FIELD AND ACCEPTED A VISUAL APCH. UNFORTUNATELY; AS WE ENTERED BRIGHT SUNLIGHT AGAIN; THE COPLT LOST SIGHT OF THE RWY. IT WAS DIFFICULT; BUT; DUE TO MY GREATER FAMILIARITY WITH THE FIELD; I COULD MAKE OUT THE LNDG AREA. I INSTRUCTED THE COPLT TO FLY THE ILS UNTIL I HAD A BETTER VIEW OF THE RWY. AT ABOUT 1000 FT WE WERE FAIRLY WELL ESTABLISHED ON LOC AND GS; AND THE REST OF THE LNDG WAS UNEVENTFUL.