A motor-vehicle shock absorber has a tube at least partially filled with damping liquid and extending, a piston rod axially shiftable inside the damper tube, and a piston connected to the piston rod and subdividing the damper tube into a piston rod-side working chamber and an opposite working chamber. An on-off control valve is axially movable inside the piston between a closed and an open position. A first soft-characteristic damping valve inside the piston through which the damping liquid may flow in both flow directions is connectable to a flow path of the damping liquid from one into the other working chamber through the control valve. A second hard-characteristic damping valve through which the damping liquid may flow in both flow directions is also provided in the piston.