The invention relates to a damping arrangement for dissipating oscillation energy of an element in a system, more particularly in a microlithographic projection exposure apparatus, comprising an absorber mass, which is mounted via a stable mounting with respect to the element, wherein the absorber mass is arranged in a cavity present within the element and is at least partly surrounded by a fluid situated in the cavity, wherein a mass-spring system is formed by the absorber mass, the system damping a translational movement component of an oscillation of the element that exists at the linking point of the absorber mass, and wherein the stable mounting is formed by a rheological fluid that is electrically controllable or controllable via electric or magnetic fields.