In a tire air pressure monitoring device and/or in a method for performing tire air pressure monitoring by a device, each monitored pneumatic tire is provided with a wheel module, which generates radiotelegrams provided with air pressure data and sends them telemetrically to a control device in the vehicle. In addition, by an acceleration sensor serving as selection signal, a proportionate wheel position signal is generated in the wheel module and entered and stored in a data memory device on the wheel module. The control device generates a selecting demand signal that queries the presence or absence of the selection signal, which requires only the wheel modules that have or do not have the storage selection signal to send a radiotelegram within a stipulated time window or time frame. Thereupon, within the stipulated time window or time frame, only the radiotelegrams originating from the selected wheel module or the selected wheel modules are sent.