A damping device, in particular for damping or preventing pressure surges, such as pulsations, in hydraulic supply circuits, preferably in the form of a silencer, has a damping housing (2) encompassing a damping chamber (10). The damping housing (2) has at least one fluid inlet (6) and at least one fluid outlet (8), as well as a fluid receiving chamber extending between the fluid inlet (6) and the fluid outlet (8). During operation of the device, a fluid flow coming from the fluid inlet (6) passes through the damping chamber (10) towards the fluid outlet (8). A wall part of the fluid receiving chamber extends as a guide element (16) in at least one direction of extension transverse to the direction of the fluid flow. In the damping chamber (10), several guide elements (16) are provided, against which guide elements the fluid can flow to alter the flow velocity in certain areas.