A multiple sprocket assembly includes a number of sprockets attached to a hub of a bicycle frame, and a rear chain transfer device having a carrier slidably attached to the bicycle frame and movable relative to an image plane formed by addendum of the teeth of the sprockets for engaging with a chain and for carrying and moving the chain onto the teeth of the sprockets, the rear chain transfer device includes a support attached to the bicycle frame, and a sliding member slidably attached to the support, and the carrier is attached to the sliding member for engaging with the chain and for carrying and moving the chain onto the teeth of the sprockets, an actuating device moves the sliding member relative to the support.