Abstract: The system for transmitting messages is used in a mobile radio telephone network (1) having a number of terminals (4, 9). The terminals may be either permanently allocated to a specific user or allocated to a specific user by means of a chip card insertable in the terminal. At least two terminals can enter into voice or data communication with one another in the mobile radio telephone network. The mobile radio telephone network comprises at least one center (8) for controlling the message transmission, each message being a data communication in which data telegrams containing a standardized data header are exchanged. For processing special services according to a special procedure accessible only to a certain authorized subscribers, the data telegram comprises an identification code in addition to the standardized data header. A central unit (10) associated with the center and at least some of the terminals have units for generating data telegrams provided with the identification code.