A method is provided for assessing the attentiveness of the driver of motor vehicle traveling in a lane including, but not limited to detecting the position of the motor vehicle on the lane transverse to the direction of travel, determining the extent of fluctuations of the position, and assessing the attentiveness as insufficient if within an observation period at least one first significant period is detected in which the extent of fluctuations of the position falls below a first low limiting value and a second significant period is detected in which the extent of the fluctuations exceeds a second high limiting value.