Abstract: A fifteen speed bicycle transmissiion wholly located on the rear driving wheel except for a manual control mounted elsewhere, e.g. on the handle bar, and including two closely arranged circular co-axial plates on the hub, one plate being a drive plate with radial slots and the other plate being a cam plate with curved slots, and sprocket elements each located in a combined curved and straight slot for radial adjustment upon rotary motion between plates, and locking member including notches and pawls on the plates at the peripheries thereof and actuated to unlock the plates by the control.