Abstract: The messages are broadcast successively and at regular intervals to mobile stations on a particular radio channel of the TDMA network. They comprise service messages and schedule messages respectively associated with successive schedule periods, each schedule message including information about the distribution of the service messages which will be broadcast during the associated schedule period. For each service message which will be broadcast during a schedule period, the associated schedule message includes a cue indicating whether this service message has been broadcast during the preceding schedule period. The schedule message furthermore indicates, as the case may be, the broadcasts of service messages which are repetitions of service messages already broadcast during the period. Use in particular in cellular radio telephone networks.