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A transmission of a bicycle includes a driving and a driven gears connected by a chain, at that, the driving gear is mounted on the axis assembled in the supports of bushing of the bicycle frame carrying the pedal cranks rigidly connected with the axis, and driven gear has a ratchet and it is mounted on the rear wheel of bicycle. Driving gear is mounted with possibility of free running relative to axis and has a mechanism for guaranteeing the mechanical connection of wheel with the axis containing two back-to-back enveloping coupling, and disk and gears rigidly connected with the axis. In thiscase the disk is mounted with possibility of interaction directly with enveloping coupling, and the gear - through auxiliary gears.
Bicycle with one front wheel and two rear wheels has rear wheels mounted connecting shaft-free, whereby driven rear wheel has rear wheel pinion which via chain drive engages with external pinion of transmission shaft