Abstract: A variable valve timing system in an engine having a rotating cam-shaft includes a timing pulley driven by the engine and a damper case rotatably fixed to the crank-shaft. A piston is movable in a space defined by the timing pulley and the damper case and has helical gears engaging helical gears of the timing pulley and damper case such that the angular position between the timing pulley and the damper case varies as the piston is moved. Movement of the piston is induced by hydraulic pressure in a pressure chamber selectively connected to hydraulic pressure by an electronically controlled solenoid valve. Engaging labyrinth grooves on the timing pulley and damper case damp rotational vibrations which would otherwise be induced by variations in the torque applied to the damper case, and so prevent undesirable movement of the piston.