A device for the longitudinal guidance of a motor vehicle, having a sensor device for the location of objects in the nearfield of the vehicle, a controller which generates a reference variable for a motion variable of the vehicle for the regulation of the vehicle's speed, as a function of the location data of the sensor device, and an actuator which has an effect on the motion variable as a function of the reference variable, wherein a mathematical model of the actuator is stored in a memory, which describes the dynamic behavior of the actuator, that is, it produces a relationship between an input variable supplied to the actuator and an output variable of the actuator; and a compensating element is provided to convert the reference variable, by way of the model, into the input variable in such a way that the dynamic behavior of the actuator is compensated for.