A tyre air-pressure abnormality alarm device for informing decrease in air-pressure of tyres attached to a four-wheeled vehicle, characterised in that the device prohibits start of initialising operations for updating stored values for physical amounts related to tyres or wheels in the case where air-pressures of the tyres are judged to be normal, if air-pressure abnormality of a tyre is being alarmed. Initialisation is accepted only after the internal pressure has become normal, whereby erroneous initialisation with any tyre being in a decompressed condition can be prevented. Thus, normal operations for detecting decompression of a tyre can be maintained.