A device for damping the movement of a movably mounted component includes a first, mechanically acting braking device with at least one friction pair, wherein, in order to generate a braking force, a driven friction surface can be rotated about an axis of the first braking device relative to a secured friction surface resting thereon, and a second braking device which is coupled to the first braking device, wherein the friction surfaces of the friction pair, or of at least one of the friction pairs, are pressed against each other in response to a braking force exerted by the second braking device. The second braking device has at least one driven damper surface that can be rotated about an axis of the second braking device and cooperates with at least one secured damper surface to enclose at least one gap in which a viscous damping medium is present that causes a braking force of the second braking device when the at least one driven damper surface is rotated with respect to the at least one secured damper surface.