A power-assist system for a bicycle by which the bicycle can be operated in various modes. There is a pedal-alone mode, a power-assist mode, a combined pedaling and power-assist mode, and a coasting mode. An overriding clutch is positioned between the pedal section and the sprocket, and a second overriding clutch is positioned between a speed reducing gear section, driven by a motor, and a power-assist shaft located in the crank housing.