A viscous damper for driving accessories by a crankshaft though a viscous coupler of the viscous damper. The rotational driving force of the crankshaft is transmitted to the viscous damper hub through the meshing of a large diameter gear and a driven gear, the viscous damper forming a unit with the driven gear. The rotational driving force is further transmitted to a viscous damper housing through the hub and the viscous coupling means, i.e., the viscous coupling means comprising a number of plates which are movable relative to each other in a space filled with silicon oil. The rotational driving force, which is transmitted to the housing and is dampened in torque changes by the function of the coupling means, is transmitted to a rotor shaft of an alternator to smoothly rotate the alternator rotor. A smooth performance in driving the accessories is ensured by the viscous damper having the viscous coupling.