Abstract: A chainless bicycle includes a drive system having a speed change arrangement is provided. In a first mode of speed change a forward pulling of a forward cable clockwise pivots a front pivotal member to move the forward sleeve rearward so that a first toothed portion of the forward sleeve clears a second gearwheel to move into a first gearwheel to mesh with a toothed portion of the first gearwheel whereby rotating a shaft will rotate a drive gear, the first gearwheel, the second gearwheel, the forward sleeve, a drive shaft, a rear sleeve, a fourth gearwheel, second inner engaging members, second outer engaging members, a third gearwheel, and a rear axle co-rotating with a rear wheel.