Abstract: A transmission for bicycles, which substitutes the conventional chain transmission, and which comprises a rimcarrier plate connected to the pedal shaft of the bicycle. A plurality of concentric rings or rims engage with respective pinions mounted with freedom of rotation on a tubular transmission shaft. Within the transmission shaft is positioned a sliding element provided with a diametrical arm, which allows one of the pinions to be blocked at will with respect to the transmission shaft. One guiding rims-pinions group is complemented by a second similar guided rims-pinions group, at the other end of the shaft. The other group of rims and pinions may be selected by an identical arrangement in which a second guided rimcarrier plate transmits the movement through a multiplying planet assembly and ratchet pawls to the shaft of an outlet planetary pinion which is engaged with an engaging track provided on the inner side of the rim of the rear wheel.