A wireless apparatus includes a cellular radio interface that is adapted to perform a data exchange by way of a wireless data network, a user identity module containing information for authorization of a user for use of wireless networks, and a control unit which controls establishment and implementation of the data exchange. A second control unit is included and adapted to limit, in respect of the duration of its effect, a rejection of the user identity module expressed by the locally available wireless data networks in logging on to the wireless data network by suitable control of the first control unit in the further course of the log-on process by bypassing communicated information about the rejection.