Abstract: A hydraulic shock absorber for motor vehicles produces additional damping, starting at a certain immersion depth of the piston rod. This takes place by an auxiliary cylinder positioned axially inside the cylinder which, when the piston rod is immersed, is closed by an auxiliary piston that moves at the same time. The associated pressure increase inside the hydraulic shock absorber causes a correspondingly designed valve to open inside the auxiliary cylinder. The fluid exchange that causes damping takes place between two working chambers of the cylinder through a connection of the two working chambers that runs through the auxiliary piston and reduces their opening cross section to the working chamber associated with the auxiliary piston by pushing the auxiliary piston into the auxiliary cylinder.