An automatically driven motor vehicle automatically runs on a running path having path markers while detecting the path markers with a marker sensor. A present position of the motor vehicle on the running path is recognized, and a speed plan which governs a position and a speed of the motor vehicle on the running path is generated. A planned position to be reached by the motor vehicle after a predetermined time and a planned speed of the motor vehicle at the planned position are determined from the present position of the motor vehicle based on the speed plan. A predicted position to be reached by the motor vehicle after the predetermined time and a predicted speed of the motor vehicle at the planned position are determined from the present position, speed, and acceleration of the motor vehicle. A distance deviation between the predicted position and the predicted position and a speed deviation between the planned speed and the predicted speed are determined. Acceleration/deceleration correcting data for the motor vehicle are determined based on the distance deviation and the speed deviation. Acceleration/deceleration of the motor vehicle are controlled based on the acceleration/deceleration correcting data.