A device (1) for the hydraulic lash adjustment for several identically acting gas-exchange valves per cylinder of a valve train of an internal combustion engine is provided, the device (1)including a common housing (2) with directly adjacent pressure pistons (3) provided corresponding to the number of identically acting gas-exchange valves. Each pressure piston (3) moves relative to the housing in an axial direction in a separate guide (4) in the housing (2), and also has a support (6) for an at least indirect contact with the corresponding gas-exchange valve on a distal end (5) away from the housing, and a non-return valve (8) in the region of a housing bottom (7) wherein a separate high-pressure chamber (9) is associated with each pressure piston (3) in which the non-return valve (8) opens. The high-pressure chamber (9) extends axially between the bottom (7) of the pressure piston (3) and a base (10) of the housing (2), and the pressure pistons (3) arranged in the common housing (2) have a common reservoir.