An air-guiding device for cooling the brakes has adjustable air-guiding flaps and an electronic control unit for controlling the air-guiding flaps as a function of the vehicle speed and of the pilot control pressure, triggered by the activation of the brake pedal, in the brake system. A first mode and a second mode for opening the air-guiding flaps are provided in the control unit by a corresponding program module. The first mode is directed to a strong deceleration demand at a relatively high vehicle speed, in particular on freeways and country roads. The second mode is directed to an acceleration prevention demand at a relatively low vehicle speed, in particular when travelling downhill on roads through mountain passes.