Device and method for monitoring the air pressure in the tires of a motor vehicle

A device for monitoring an air pressure in vehicle tires, comprising:

• determining units configured to determine wheel speed variables characterizing wheel speeds of a motor vehicle;
• a calculating unit operatively connected to said determining units and configured to calculate differential variables from the wheel speed variables;
• an evaluation unit configured to evaluate the differential variables with respect to a setpoint value deviation, said evaluation unit generating a warning signal if the setpoint value deviation exceeds a first threshold value;
• a measuring unit operatively connected to said evaluation unit, said measuring unit being configured to directly measure an air pressure in a tire of a wheel and configured to transmit a pressure variable characterizing the air pressure to said evaluation unit;
• and
• said evaluation unit further generating a warning signal if a deviation of the pressure variable from a pressure setpoint value exceeds a second threshold value, said evaluation unit using a first tolerance range for a permitted setpoint value deviation of the differential variables, the first tolerance range representing a first pressure difference range, said evaluation unit further using a second tolerance range for a permitted setpoint value deviation of the pressure variable, the second tolerance range representing a second pressure difference range, the first pressure difference range being smaller than the second pressure difference range.