FLC OF A B737-200 HAD TO DECLARE AN EMER FOR MINIMUM FUEL IN ORDER TO OBTAIN PRIORITY HANDLING FROM APCH CTLR AFTER THEIR FUEL BECAME LOW DUE TO HOLDING AND MAKING 1 MISSED APCH. IN ADDITION; THAT THEY WOULD BE #2 FOR THE NEXT APCH.

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ON A ROUTINE FLT FROM LIH-HNL; THE FLT WAS VECTORED FOR AN LDA APCH RWY 26L AT HNL ARPT. WE WERE #4 ON THE APCH. THE WX WAS BETTER THAN MINIMUMS. IN FACT; AS WE WERE VECTORED FOR THE APCH; WE COULD SEE THE RWY IN USE. THE WX DETERIORATED RAPIDLY. A DC10 MISSED IN FRONT OF US. WE CONTINUED ON THE APCH; MISSED AND WAS TOLD ON THE MISS TO CLB TO 4000 FT DIRECT TO ALANA; HOLD L TURNS; 2 MIN LEGS. WE ENTERED HOLDING WITH 8000 LBS OF FUEL. WE THEN HELD AS OTHER ACFT MISSED AND JOINED IN THE STACK. WE WERE THEN TOLD WX HAD IMPROVED AND WE WOULD BE VECTORED FOR ANOTHER LDA. WE HAD 6000 LBS AS WE WERE NOW #2 FOR THE APCH AND THE CTLR RPTED VISIBILITY IMPROVING. 1 ACFT GOT IN ANOTHER MISSED. NOTING THAT THE WIND WAS STARTING TO SWING TO A XWIND QUARTERING TAILWIND; I ASKED FOR AN ILS. WE WERE AT 5000 LBS FUEL AT THIS TIME. THE SUPVR THEN CAME ON AND ASKED IF I WOULD TAKE AN ILS RWY 8L. WE REPLIED IN THE AFFIRMATIVE. WE WERE THEN TOLD WE WERE #2. I ASKED FOR #1. THERE WAS HESITATION. I THEN DECLARED AN EMER; TO FORCE ATC TO ACCEPT ME AS #1 FOR AN ILS AND REQUESTED RWY 4L ILS TO EXPEDITE LNDG. WX FOR THE ILS RWY 8L AND RWY 4R WAS ABOVE MINIMUMS; WIND BEING THE FACTOR FOR NOT USING THESE APCHS. WE LANDED WITHOUT EVENT; WITH 3700-4000 LBS OF FUEL. ALL OTHER ACFT MADE IT IN AT THIS POINT. THE LDA WAS NOT USED AFTER THIS TIME.