The invention relates to a damping device, particularly for damping or avoiding pressure surges such as pulses, in hydraulic supply circuits, preferably in the form of a silencer, comprising a damping housing which surrounds a damping chamber (19) and has at least one fluid inlet (11) and at least one fluid outlet (13) and a fluid receiving chamber (19) which extends between said fluid inlet (11) and fluid outlet (13), wherein, during operation of the device, a fluid flow crosses the damping chamber (19) in a through-flow direction (15), coming from the fluid inlet (11) in the direction of the fluid outlet (13), and wherein at least parts of the fluid receiving chamber (19) extend in at least one extension direction transversely with respect to the through-flow direction (15). The invention is characterised in that the fluid receiving chamber (19) immediately adjoins the fluid inlet (11) and the fluid outlet (13) and is delimited by at least one yielding wall part (4).