Abstract: A device for monitoring air pressure in the tires of a vehicle includes devices for determining the wheel speed or other characteristic variables for the speed of the tires of the vehicle, a device for calculating differential variables on the basis of the wheel speed variables, a device for evaluating the differential variables with respect to a setpoint value deviation and for generating a warning signal if the setpoint value deviation exceeds a threshold value, and a device for directly measuring the air pressure in the tire of a wheel and for transferring an air pressure characteristic variable to the evaluation device. A warning signal is generated if the deviation of the air pressure characteristic variable with respect to a setpoint value exceeds a corresponding threshold value. A method of monitoring tire pressures is also provided.