ACFT DIVERTS TO LAND AT ALT FIELD BECAUSE OF HYD FAILURE IN 1 OF ITS SYSTEMS.

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EXPERIENCED A GREEN HYD SYS FAILURE. WAS ENRTE CVG-ORY. DIVERTED INTO JFK. DECLARED AN EMER. ABNORMAL PROCS WORKED FINE. NO PROBLEMS WITH ATC. REQUESTED RWY 31L AT JFK BECAUSE IT'S THE LONGEST RWY 31L WAS NOT AVAILABLE DUE TO EQUIP ON RWY 31R WAS NEXT LONGEST RWY AND APCH SAID IT WAS AVAILABLE. AS WE INTERRUPTED THE LOC FOR RWY 31R. TWR ASKED IF WE WERE RECEIVING THE GS. WE WEREN'T TWR SAID TECHNICIANS WERE TRYING TO GET THE GS WORKING. THE GS NEVER WORKED AND NO VASI ON RWY 31R. I WOULD HAVE PREFERRED A RWY WITH VERT GUIDANCE AS IT WAS NIGHT AND WE WERE MAKING AN OVERWT LAND. OTHER THAN THAT; NO PROBS. SUPPLEMENTAL INFO FROM ACN 277508: ACFT HAD A HISTORY OF A VERY SLOW HYD LEAK (MAIN GREEN SYS) FOR ABOUT A WK (WOULD HAVE TO ADD FLUID AFTER 2-3 INTL LEGS. MAINT HAD JUST CHANGED THE GREEN AND YELLOW SYS FLUID SHUT-OFF VALVES JUST PRIOR TO OUR FLT. TURNED GREEN PUMPS OFF BUT FLUID LEVEL CONTINUED TO DECREASE AND EVENTUALLY WENT TO ZERO (TOOK ANOTHER 20 MINS). ACCOMPLISHED LOSS OF GREEN SYS ABNORMAL CHKLISTS; MANUALLY EXTENDED THE GEAR; WE DECLARED AN EMER; GOT ATC VECTORS TO JFK AND MADE A OVER GRASS LNDG ON RWY 31R (SMOOTH TOUCHDOWN 293000 LBS.