The tensioner contains a tension adjusting spring for pressure engagement of the eccentric ring for its swivel in one direction, and a hydraulic damper with a cylinder, contg. a pressure and a storage chamber. A pressure accepting part engages the eccentric ring for damping its rotary motion when the belt tension rises. A non-return valve is located between the pressure and storage chambers. The hydraulic damper is fitted within the outer periphery of the tensioning belt pulley. Pref. the pressure accepting part is axially movable in the damping cylinder.