An arrangement and a method with which wireless terminal devices which can usually be reached via a call number of one individual network computer can also be reached when they are located in the wireless communication area of a base station that is connected to another network computer. To this end, connection information is retrieved via a mobility server, and a connection setup to a corresponding network computer in whose radio area the wireless terminal device is located is controlled via that mobility server. The wireless terminal device delivers information, which is transmitted to the mobility server and from which, together with additional information from the network computer or the base station, this server is able to derive the information for the connection setup to the wireless terminal device. In order to limit the utilized network computers to only a switching function, performance features of the wireless terminal device are realized via a performance feature server, which controls the corresponding network computer via a CTI interface. The mobility servers are likewise connected to the respective network computers via a CTI interface. In this way, it is possible to realize private wireless communication networks with DECT functionality and with a large coverage, in which networks it is possible to reach wireless terminal devices at will, though they are dialed simply via the call number of a single network computer allocated to them.