A brake-system damping device includes a first chamber, to which hydraulic pressure is to be applied, a second chamber, in which there is a compressible medium, and a first separating element for separating the first chamber from the second chamber. The brake-system damping device includes a third chamber, in which there is a compressible medium, and a second separating element for separating the second chamber from the third chamber. The second chamber is connected, for medium conduction, to the third chamber by means of a passage formed in the second separating element. A closure element is to be moved with the first separating element, by means of which closure element the passage is to be closed as soon as the hydraulic pressure has reached predefined pressure value in the first chamber.