A G4 AT FL320 FOLLOWING A B777 BY NINE MILES EXPERIENCED WAKE VORTEX UPSET WITH A 45 DEG ROLL AND 200-300 FT ALT LOSS.

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WE WERE LEVEL AT CRUISE FL320 APPROX 40 MINUTES AFTER BLOCKING OUT FROM ZZZ. WX WAS NOT A FACTOR. WE SUDDENLY EXPERIENCED AN ABRUPT ROLL TO THE R TO APPROX 45 DEGS AND THEN AN ABRUPT TURN TO THE L; AUTOPILOT DISENGAGED AND WE AGAIN ROLLED BACK TO THE R WHERE I WAS THEN ABLE TO CTL THE ACFT. I DID NOT TAKE SPECIFIC NOTE OF THE EXACT ALTITUDE LOSS SINCE I WAS MORE CONCERNED WITH GETTING THE ACFT UPRIGHT BUT IT WAS NOT SIGNIFICANT; APPROX 200-300 FT. I RPTED IT TO CENTER AND WAS TOLD THEY DSNDED A B777 9 MILES IN FRONT OF US. WINDS WERE 230/50 (45 KT DIRECT HEADWIND). WE WERE EVENTUALLY SWITCHED TO THE NEXT SECTOR (STILL CENTER) AND DSNDED TO FL280 (NOT SURE EXACT ALTITUDE) WHEN ABOUT 15-20 MINUTES AFTER THE FIRST ENCOUNTER WE AGAIN EXPERIENCED THE SECOND EPISODE OF WAKE TURBULENCE. THIS TIME I TOOK CTL OF THE ACFT AND PROCEEDED ON AN OFFSET TO THE R OF COURSE. I INFORMED CENTER AND WAS CLEARED FOR A 5 MILE OFFSET. THE WINDS THIS TIME WERE 31 KTS DIRECT HEADWIND. I SPOKE WITH THE CENTER CHIEF. I DID RECEIVE A CALL FROM THE CENTER SAFETY OFFICE AND SPOKE WITH HIM AT GREAT LENGTH ABOUT THE INCIDENT. THEY INFORMED ME THEY ALSO HAD ANOTHER INCIDENT WITH A GIV AND B747 WITHIN A FEW DAYS OF OUR ENCOUNTER. I SUSPECT MANY OF THESE ENCOUNTERS ARE NOT BEING RPTED. WE WERE FORTUNATE NO ONE WAS INJURED ON OUR ACFT; BUT UNDER DIFFERENT CIRCUMSTANCES THEY COULD HAVE BEEN.