An hydraulic damping mount has an outer sleeve, an inner sleeve for securing thereto a piston of a spring strut (activatable in at least one direction), an elastomeric body and two chambers. The two chambers are interconnected via a gap. The inner sleeve comprises a radially projecting boss separating the two chambers from each other. The connection between the two chambers is configured in accordance with the invention as a gap between the boss and the outer sleeve so that when activated, the fluid flow through the gap is in the direction opposite to the movement of the boss, resulting in a reduction in the stiffness. This simplifies assembly whilst enhancing the stiffness response of the mount. The invention relates furthermore to a mount for supporting a spring strut in making use of such a mount.