A damped vibration system includes a plurality of rotationally inert bodies arranged on a common axis of rotation facing each other with a small gap therebetween. Spring elements are provided between the facing bodies that are displaceable circumferentially with respect to the axis of rotation. Damping elements, preferably in the form of steel balls disposed in radial or circular grooves having sufficient clearance to permit relative angular movement between the facing inert bodies, are provided between the facing bodies. The apparatus is directly connectable to the crank-shaft of the internal combustion engine and also engageable with the drive train of a vehicle. The damped vibration system has a resonant angular frequency preselected to be a certain value below the angular frequency of ignition of the internal combustion engine.