Damping movement device of pieces of furniture which are movable relative to stationary parts. The device has a cylinder with a piston movable in a longitudinal direction, forming a modifiable working chamber filled with liquid medium. The liquid medium is transferred in a throttled manner. A piston rod is sealingly guided and connected to one side of the piston. The movement of the parts of furniture which is to be damped is transmitted to the piston via the outer end of the piston rod facing away from the piston. A volume compensating mechanism is provided. The piston rod is coupled to the piston with overflow ports. The non-return disk with overflow port is moved into sealing contact with the facing piston face. A spring biasing the facing faces of the non-return disk and the piston into the spaced-apart position is arranged between the non-return disk and the piston.