An auxiliary power drive system is incorporated into a bicycle either as a retrofit or in initial construction. The power for the drive system is derived either from an electric motor or an internal combustion engine. The power developed by said motor or engine is delivered to the rear wheel of the bicycle by a flexible drive shaft which either drives a friction wheel operating on the tire of the rear wheel or to worm gear affixed to the rear wheel. The flexible drive shaft includes a friction clutch which discontinues the power of the drive shaft from driving the rear wheel when normal pedaling is resumed. The flexible drive shaft also includes a telescoping coupling to compensate any change in lengths of the drive shaft due to impacts on the rear wheel caused by the terrain the bicycle is riding on.