A waste gate actuator for an exhaust gas turbocharger, including an actuator housing and an actuator cover, an element for actuating the waste gate valve and electronic components for controlling the element to actuate the waste gate valve being arranged in the waste gate actuator. Provided is a simple and inexpensive revolution counting system on the turbocharger which allows the number of revolutions of the rotating parts (turbine wheel, compressor wheel, turboshaft) to be detected without substantial constructional alterations to the design of existing turbochargers. A sensor for detecting the variations in a magnetic field that are produced by the rotation of the rotating parts is arranged in or on the actuator housing or in or on the actuator cover.