A damping device for damping a relative movement of device parts of a device for pivoting and/or displacing a furniture part guided movably on a furniture body is proposed, the damping device comprising a damper housing with an inner volume and an inner part accommodated in the inner volume, the damper housing and the inner part executing a relative movement during a damping action, so that, during the relative movement, wall portions delimiting the inner volume and an at least essentially cylindrical portion of the inner part can be moved past and opposite one another. According to the invention, the wall portions have an essentially hollow-cylindrical basic shape, guide means portions projecting in regions into the hollow-cylindrical basic shape, which guide means portions are in bearing contact against the cylindrical portion of the inner part during the relative movement.