In a motor vehicle having a plurality of display devices, a gaze direction of a driver of the motor vehicle is detected and used to check whether the driver has directed his gaze to a display region of the display devices for at least a predefined gazing duration. If the gaze has been directed to one of the display regions of one of the display devices for at least the predefined gazing duration, an interaction mode of an operating device for controlling the relevant display device is activated. An extended gazing duration which is longer than the predefined gazing duration is predefined for at least one of the display devices and for this display device, the interaction mode is activated only if it has been detected that the gaze of the driver has been directed to the display region of this display device for at least the extended gazing duration.