A motor vehicle has at least one adjustable air-guiding device on the underbody. The air-guiding device has a cross-sectionally U-shaped duct and is adjustable between a closed position and an open position. The motor vehicle also has a radiator device with a radiator and a radiator shutter with adjustable flaps for controlling the air flow through the radiator. A control device actuates the air-guiding device depending on the position of the radiator shutter so that, irrespective of the position of the flaps of the radiator shutter, an at least approximately identical pitching moment is obtained at the motor vehicle and at the same time the aerodynamic drag is reduced.