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fuel problems, gone off maybe needs a carb clean as ....well, plenty of write ups about ethanol.
ZZR6's Ive had needed to change filter in fuel cut off valves on each carb comes with new orings to...

any zzr 600 pre 2000 will probably need carb diaphragms as well, Ive worked on 3 and all the same ,also the small filters in the carbs get blocked.
my youngest had his eye on a budget bikes item,...