A coupling device for coupling rotatable bodies together includes first and second rotatable bodies, a plurality of coupling members for selectively coupling the first and second rotatable bodies together to transfer drive between the rotatable bodies, and an electro-magnetic actuator for controlling engagement of the coupling members. The coupling device can be incorporated into a transmission system, which includes first and second drive shafts, first and second gear sets mounted on the shafts for transferring drive between the shafts, a selector for selectively transferring drive between the first shaft and either the first or second gear set, and an electro magnetic actuator for controlling engagement of the engagement members and the drive formations.