A damping pulley assembly is disclosed including a pulley with an outer flange and a fixed pulley plate. A floating pulley clutch plate is located within and engaged with the outer flange. Circumferentially spaced apart leaf springs are connected to a pulley hub. Second ends of the leaf springs are connected to a driven hub that includes a fixed hub plate. Floating clutch plates are located between the fixed pulley plate and the fixed hub plate, which are biased toward the fixed pulley plate by the leaf springs so that the clutch plates contact one another and/or the fixed hub or pulley plates.