Damping devices of this kind are state of the art. Such hydraulic dampers, which are also referred to as sound dampers or silencers, serve to reduce oscillations. The oscillations are generated by pressure pulsations, to which a corresponding hydraulic system is repeatedly subjected, in particular due to the operation of hydraulic pumps. As is disclosed in the document DE 102 17 080 C1, the known damping devices of this kind have a damping housing in the form of a circular cylinder, which is rounded in a spherical manner at both axial end regions. The fluid inlet and the fluid outlet are located coaxial to the cylinder axis on a respective end region. As the damping chamber, which the fluid flow crosses from the fluid inlet to the fluid outlet, a damping tube is provided in such damping devices, which tube extends coaxially between the fluid inlet and the fluid outlet. The tube wall has openings to the fluid chamber surrounding the tube. According to the cylinder diameter, the fluid chamber is radially expanded relative to the axial throughflow direction defined by the damping tube.