A wheel nut or axle nut for vehicles, having a nut body, having a central threaded hole, having a peripheral wall, having an abutment face at a lower side of the nut and having a plurality of wrench faces on the peripheral wall of the nut body for tightening or releasing the nut by means of a tool which cooperates with the wrench faces, characterised by at least one recess, in which a sensor element is arranged, wherein the sensor element is connected to a wireless interface which is configured to transmit a sensor signal of the sensor element wirelessly to an external reception unit.