The invention relates to a hydraulic drive system used for the covers of vehicle openings, in particular for vehicle roofs with a construction that can be opened. In said system, the actuator that is designed to displace the cover is supplied with a bulk current, whose target value is determined in accordance with the control path of the actuator, which is in correlation with the controlled displacement of the cover and whose actual value is detected when supplied to the actuator by means of a bulk current sensor. The bulk current is adjusted to compensate for differences between the actual and target values.