System for the evaluation of the driving environment of a vehicle and for influencing the speed of the vehicle in its own lane, with an electronic control unit that is connected to a signal generator generating a signal characteristic of the desired speed of the vehicle, to a signal generator generating a signal characteristic of the turning rate of the vehicle about its vertical axis, to a signal generator that generates for objects located in the space in front of the vehicle and in the direction of travel of the vehicle a characteristic signal with respect to their distance and orientation relative to the vehicle, said signal being the speed relative to the speed of the driver's vehicle and/or the distance relative to the driver's vehicle and/or the angular displacement or the lateral deviation relative to the longitudinal axis of the driver's vehicle, and to a signal generator that generates a signal characteristic of the speed of at least one wheel of the vehicle, and that is connected to at least one control device having an influence on the driving behaviour of the vehicle, in order to feed to said control device output signals that are derived from the driving behaviour of the vehicle located in front of the driver's vehicle, in which in order to define the mid line of the driver's lane in the space detected in front of the driver's vehicle the radius of curvature R of the path curve of the centre of gravity of the driver's vehicle is modified in the electronic control unit on the basis of the change of angular bearing of the objects driving in front, and/or on the absolute position of the objects driving in front relative to an instantaneously predicted lane.