Abstract: A hydraulically damping elastomer bearing comprises an outer bearing sleeve as well as an elastomer element arranged therein and a bearing core which is held by the elastomer element. Between the bearing core and the bearing sleeve chambers are formed and filled with fluid, which chambers are interconnected via at least one channel. In order to achieve progressive damping characteristics in the impact region, between the bearing core and the inside wall of the bearing sleeve there is arranged in at least one of the chambers an inflexible, hydraulically supported displacement element. In the unloaded state, this displacement element is at a predetermined distance from a reference surface. Between the displacement element and a component bearing the latter there is formed a displacement chamber of small height between the displacement surfaces, the displacement chamber being in communication with one of the further chambers via at least one throttling orifice.