A brake system damping device includes a first space, a second space, a third space, a first separating element, a second separating element, a closure element, and a plug-type element. The first space is configured to have hydraulic pressure applied thereto. A compressible medium is situated in the second space and the third space. The first separating element separates the first space from the second space, and the second separating element separates the second space from the third space. The second space is connected in medium-conducting fashion to the third space by a passage formed in the second separating element. The closure element is configured to be moved with the first separating element so as to close the passage in a movement direction as soon as the hydraulic pressure has reached a predefined pressure value in the first space. The plug-type element is arranged in the passage.