A device is indicated for controlling at least one gas exchange valve for an combustion cylinder of an internal combustion engine, having an hydraulic actuator for valve actuation and having a high-pressure pump that supplies the actuator with a pressure medium. In order to reduce the production costs, the high-pressure pump is formed as a control-sleeve pump having a stroke-driven pump plunger that limits a pump chamber, and having a spool valve surrounding this plunger. In the pump plunger and spool valve, on the one hand a control groove that runs obliquely to the stroke direction is provided, and on the other hand a spill opening that cooperates therewith is provided, which together bring about a relief of pressure of the pump chamber when they overlap. For the controlling of the phase position and duration of the valve actuation, the pump plunger and the spool valve are able to be rotated relative to one another, and the spool valve is able to be displaced relative to the pump plunger.