Method for monitoring tyre pressure values on vehicle tyres (6, 7) of a vehicle, comprising at least the following steps, a) providing vehicle tyres (6, 7) with tyre modules, the tyre module having at least a temperature sensor and a tyre pressure sensor, b) carrying out a multiplicity of temperature measurements, the measured temperature values being continuously buffer-stored at a defined time interval in a data memory on the tyre module, characterized in that b1) carrying out a multiplicity of tyre pressure measurements, the measured tyre pressure values being continuously buffer-stored at a defined time interval in a data memory on the tyre module, c) carrying out a comparison of values in which the measured temperature values and the tyre pressure values are compared at a defined time interval with the last temperature values and tyre pressure values measured at the time in question, d) determining a stable temperature value, the stable temperature value being obtained when the last temperature value at the time in question deviates by less than about 2 degrees Celsius from all of the buffer-stored temperature values, e) determining a stable tyre pressure value, the stable tyre pressure value being obtained when the last tyre pressure value at the time in question deviates by less than about 0.1 bar from all of the buffer-stored tyre pressure values, f) storing the stable temperature value and stable tyre pressure value at the respective time in question in the memory of the tyre module, the stable temperature value at the time in question and the stable tyre pressure value at the time in question being obtained when both values have been recorded within a time difference of less than one minute, g) transmitting the stable temperature value at the time in question and the stable tyre pressure value at the time in question to a base station outside the vehicle, h) evaluating the received data by means of the base station, i) initiating a warning message to a final customer if the received stable temperature values and stable tyre pressure values deviate significantly from the prescribed values for the vehicle tyre. a) providing vehicle tyres (6, 7) with tyre modules, the tyre module having at least a temperature sensor and a tyre pressure sensor, b) carrying out a multiplicity of temperature measurements, the measured temperature values being continuously buffer-stored at a defined time interval in a data memory on the tyre module, characterized in that b1) carrying out a multiplicity of tyre pressure measurements, the measured tyre pressure values being continuously buffer-stored at a defined time interval in a data memory on the tyre module, c) carrying out a comparison of values in which the measured temperature values and the tyre pressure values are compared at a defined time interval with the last temperature values and tyre pressure values measured at the time in question, d) determining a stable temperature value, the stable temperature value being obtained when the last temperature value at the time in question deviates by less than about 2 degrees Celsius from all of the buffer-stored temperature values, e) determining a stable tyre pressure value, the stable tyre pressure value being obtained when the last tyre pressure value at the time in question deviates by less than about 0.1 bar from all of the buffer-stored tyre pressure values, f) storing the stable temperature value and stable tyre pressure value at the respective time in question in the memory of the tyre module, the stable temperature value at the time in question and the stable tyre pressure value at the time in question being obtained when both values have been recorded within a time difference of less than one minute, g) transmitting the stable temperature value at the time in question and the stable tyre pressure value at the time in question to a base station outside the vehicle, h) evaluating the received data by means of the base station, i) initiating a warning message to a final customer if the received stable temperature values and stable tyre pressure values deviate significantly from the prescribed values for the vehicle tyre.