A RA390 LOST ALL HYDRAULIC PRESSURE. THE CREW DECLARED AN EMERGENCY AND DIVERTED. A HYDRAULIC SYSTEM FILTER 'O' RING FAILED.

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WHILE FLYING AT FL400 ENRTE TO ZZZ1; THE L AND R HYD LOW ANNUNCIATORS ILLUMINATED; AS WELL AS ALL 3 SPOILER SYS FAIL ANNUNCIATORS. HYD PRESSURE DECREASED TO 500-1000 PSI FOR ABOUT 10 MINS; THEN WENT TO ZERO. DURING THIS TIME; MY FELLOW CO-CAPT AND I STARTED TO LOOK AT SUITABLE LNDG SITES. WE WERE E OF ZZZ APPROX 50 NM WHEN THE EVENT OCCURRED -- SO WE LOOKED AT THE WX IN THE ZZZ AREA. ZZZ SHOWED OVCST SKIES APPROX 1700 FT WITH GOOD VISIBILITY. I CALLED THE TWR ON #2 RADIO AND THEY CONFIRMED RWY WAS IN GOOD CONDITION -- NO PRECIP. AFTER CALCULATING THE LNDG DISTANCE NEEDED WITH EMER BRAKES ONLY -- WE DECLARED AN EMER WITH CTR. WE WERE RADAR VECTORED FOR THE ILS RWY 35R. THE MANUAL GEAR EXTENSION TOOK AWHILE; SO WE REQUESTED A GAR FOR MORE TIME. AFTER EXTENDING THE LNDG GEAR A LNDG WAS MADE SUCCESSFULLY -- HOWEVER; WITHOUT ANTI-SKID THE EMER BRAKES 'BLEW' THE MAIN TIRES. THE ACFT AND CREW WERE FINE -- NO DAMAGE. WE ARRANGED FOR THE ACFT TO BE JACKED AND PUT ON 'DOLLIES.' IT WAS TOWED TO A HANGAR AND FIXED. THE CULPRIT WAS A BROKEN 'O-RING' ON A HYD FILTER BULB -- WHICH ALLOWED FLUID TO LEAK OUT DURING THE COURSE OF FLT.