A transmission intended to be mounted on a rear wheel axle of a bicycle between a sprocket carrier and a wheel hub has a transmission housing, which is provided with connecting means for the connection of the sprocket carrier to the transmission housing, as well as coupling means for coupling the transmission to the hub. The transmission further has a planetary gear set which is present in the transmission housing and is provided with three rotational members, of which a first rotation body is connected to the transmission housing, a second rotation body is connected to the coupling means, and a third rotation body can be coupled with the wheel axle. The first rotation body is connected via a first clutch to the second rotation body and the third rotation body is connected to a second clutch via which the third rotation body can be connected to the wheel shaft.