Hydraulic vibration damper, comprising: a tank, an inner pipe which is arranged in the tank, a piston which is arranged axially movably in the inner pipe and divides the interior space of the latter into a first working chamber and a second working chamber, a seal element, via which the piston bears against the inner pipe, in order to seal the first and second working chamber (6, 7) with respect to one another, and a bottom valve which is arranged on an axial end section of the inner pipe, in order to connect the second working chamber to a compensation space which is formed between the tank and the inner pipe, the bottom valve protruding axially with a section into the second working chamber, and the piston having an operating position, in which it radially surrounds that section of the bottom valve which protrudes into the second working chamber, the seal element lying at the level of the bottom valve in this operating position, characterized in that the piston has a cover (17, 17') on its end side which points towards the bottom valve, and the seal element is arranged on the cover (17, 17'), the hydraulic vibration damper has an electrically actuable valve for connecting the first and second operating chamber (6, 7), which valve is arranged on the piston, and the piston has a valve unit with the electrically actuable valve, and the valve unit is fastened by means of the cover to a piston rod, or the piston comprises a valve housing which receives the electrically actuable valve, and the cover is fastened to the valve housing, the electrically actuable valve being fixed by means of the cover in the valve housing. a tank, an inner pipe which is arranged in the tank, a piston which is arranged axially movably in the inner pipe and divides the interior space of the latter into a first working chamber and a second working chamber, a seal element, via which the piston bears against the inner pipe, in order to seal the first and second working chamber (6, 7) with respect to one another, and a bottom valve which is arranged on an axial end section of the inner pipe, in order to connect the second working chamber to a compensation space which is formed between the tank and the inner pipe, the bottom valve protruding axially with a section into the second working chamber, and the piston having an operating position, in which it radially surrounds that section of the bottom valve which protrudes into the second working chamber, the seal element lying at the level of the bottom valve in this operating position, characterized in that the piston has a cover (17, 17') on its end side which points towards the bottom valve, and the seal element is arranged on the cover (17, 17'), the hydraulic vibration damper has an electrically actuable valve for connecting the first and second operating chamber (6, 7), which valve is arranged on the piston, and the piston has a valve unit with the electrically actuable valve, and the valve unit is fastened by means of the cover to a piston rod, or the piston comprises a valve housing which receives the electrically actuable valve, and the cover is fastened to the valve housing, the electrically actuable valve being fixed by means of the cover in the valve housing.