Abstract: A multiple speed bicycle of the coaster brake type has a single drive sprocket and a drive chain in longitudinal alignment with one another. A sun gear is keyed to the main drive axle of the bicycle and rotates with the main drive axle. The sun gear engages a drive gear mounted on a planet gear axle and a planet gear is mounted on the same planet gear axle. Driving and driven satellite gears are mounted on satellite gear axles that are pivotally mounted on a nonrotatable ring concentric with the main drive axle. The satellite gears have differing diameters and differing numbers of teeth, one for each GEAR of the bicycle, and are positioned radially outwardly of the planet gear, in circumferentially spaced relation to one another. The planet gear orbits the main drive axle in incremental degrees of angular rotation when the bicycle operator manipulates a remote control member on the handlebar of the bicycle to change from one preselected gear to another preselected gear.