An apparatus for processing ground surfaces comprises a moving device, a working device, especially a milling device for milling the ground surface, and a drive device for driving the moving device and the working device, wherein the working device is movable between a working position, in which it is in operative engagement with the ground surface, and a maneuvering position, in which it is not in operative engagement with the ground surface, wherein a sensor device is provided which detects the maneuvering position and/or at least one working parameter of the working device, namely its power consumption, working speed, rotational speed or its inclination, and/or at least one load parameter of the moving device, and a control device which reduces the frictional connection between the drive device and the working device and/or the drive power transmitted by the drive device to the working device in the maneuvering position and/or in case of the detection of a deviation of the at least one detected working parameter or load parameter from a set parameter value.