B727 ACFT ENCOUNTERED TURB ENRTE WHILE DEVIATING AROUND WX RESULTING IN ALTDEVS.

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WE WERE FLYING N ON A300 AT FL350 AND RECEIVED A MESSAGE VIA NEW YORK FROM DISPATCH OF SOME WX UP ALONG OUR RTE OF FLT. SINCE THERE WAS ALSO WX RPTED TO OUR W; WE DECIDED TO CONTINUE ON COURSE. ABOUT 150 MI S OF CHAMP WE BEGAN TO SEE THE WX ON THE RADAR. ABOUT 100 MI S OF CHAMP; WE REQUESTED AND SOON RECEIVED A CLRNC TO DEVIATE 25 MI W OF COURSE FOR WX AVOIDANCE. WE SOON BEGAN TO TURN W OF COURSE AS THE LINE OF WX APPEARED TO END 20 MI W OF A300 AND WAS RPTED TO BE MOVING NE. I INFORMED THE PAX THAT THERE WAS A CHANCE THAT WE MIGHT ENCOUNTER SOME ROUGH AIR; PUT ON THE SEAT BELT SIGN AND HAD THEM BUCKLE UP. I BRIEFED THE #1 FLT ATTENDANT; AND THEY STOWED ALL THE FOOD CARTS; CLEANED UP THE CABIN; MADE ONE FINAL SWEEP THROUGH THE CABIN TO ENSURE THAT ALL THE PAX WERE BUCKLED IN. THEY THEN STRAPPED THEMSELVES IN AT THEIR ASSIGNED JUMP SEATS. WE MANAGED TO FIND OUR WAY AROUND MOST OF THE BAD WX; PICKING UP A FEW BUMPS ALONG THE WAY. ABOUT 22 MI W OF COURSE WE SAW AN OPENING ON THE RADAR BACK TO THE N. WE COMMENCED A TURN TO THE N AND WERE HEADING BACK TOWARDS CHAMP WHEN WE ENCOUNTERED THE TURB. THE ACFT DEVIATED UP TO 500 FT ABOVE AND 900 FT BELOW FL350; AND THE AIRSPD VARIED FROM MACH .75 TO MACH .84 DURING THE CLBS AND DSCNTS. WE JUST TRIED TO MAINTAIN MACH .80 AND SMOOTH OUT THE ALTDEVS. IT WAS OVER IN ABOUT 30 SECONDS; AND WE WERE IMMEDIATELY OUT IN CLR SKY. DESPITE THE FACT THAT WE NEVER SAW WHAT CAUSED ALL OF THIS WE WERE VERY WELL PREPARED AND THERE WERE NO INJURIES OR DAMAGE TO THE ACFT. WE NOTIFIED ATC AND DISPATCH OF THE WX.