A communication system has cordless system units (1, 2, 3, 4) connected to a communication network (7). The cordless system units respectively has at least one cordless base station (11-13, 21-23, 31, 32, 41). The identification of a respective cordless terminal equipment (8) is stored in a cordless system unit (1, 2, 3, 4) allocated thereto as a home system unit. The possibility or, respectively, allowability of a connection setup from the respective cordless system unit (1, 2, 3, 4) to a cordless terminal equipment (8) can be checked by a check apparatus (15, 25, 35, 45) respectively allocated to the cordless system units (1, 2, 3, 4). The cordless system units (1, 2, 3, 4) are connected to a network (6, 61) offering a connectionless service in order to exchange information with one another dependent on check results of the check apparatus (15, 25, 35, 45).