Method for transmitting data telegrams (13a, 13b) from a transmitter to at least one receiver, in which - a priority level is allocated to the data telegrams (13a, 13b) to be transmitted, which level specifies a priority to be taken into consideration in the transmission of the respective data telegram (13a, 13b) in such a manner that data telegrams (13a, 13b) having a higher priority level compared with those having a lower priority are transmitted preferably by the transmitter, via a physical communication medium connected both to the transmitter and to the receiver, to the receiver, wherein - in the transmitter, an intermediate storage area (17a, 17b) is allocated to each priority level; - the data telegrams (13a, 13b) are transmitted via the physical communication medium via different logical data links (15a, 15b), the number of logical data links (15a, 15b) corresponding to the number of priority levels; - data telegrams present in an intermediate storage area allocated to a lower priority level are transmitted via the logical data link allocated to this priority level for such a time until at least one data telegram is present in an intermediate storage area allocated to a higher priority level; and - the data telegram present in the intermediate storage area allocated to the higher priority level is transmitted via the logical data link allocated to the higher priority level, characterized in that - for the start-up of a system of at least one transmitter and at least one receiver, at least one of the devices (11a, 11b) sends a broadcast message to a destination address defined throughout the system, this destination address defined throughout the system being allocated to a particular priority level; and - a device receiving this broadcast message takes a sender address, specifying the sender of the broadcast message, from the broadcast message and uses this sender address from then on as destination address for this priority level, allocated to the sender. - a priority level is allocated to the data telegrams (13a, 13b) to be transmitted, which level specifies a priority to be taken into consideration in the transmission of the respective data telegram (13a, 13b) in such a manner that data telegrams (13a, 13b) having a higher priority level compared with those having a lower priority are transmitted preferably by the transmitter, via a physical communication medium connected both to the transmitter and to the receiver, to the receiver, wherein - in the transmitter, an intermediate storage area (17a, 17b) is allocated to each priority level; - the data telegrams (13a, 13b) are transmitted via the physical communication medium via different logical data links (15a, 15b), the number of logical data links (15a, 15b) corresponding to the number of priority levels; - data telegrams present in an intermediate storage area allocated to a lower priority level are transmitted via the logical data link allocated to this priority level for such a time until at least one data telegram is present in an intermediate storage area allocated to a higher priority level; and - the data telegram present in the intermediate storage area allocated to the higher priority level is transmitted via the logical data link allocated to the higher priority level, characterized in that - for the start-up of a system of at least one transmitter and at least one receiver, at least one of the devices (11a, 11b) sends a broadcast message to a destination address defined throughout the system, this destination address defined throughout the system being allocated to a particular priority level; and - a device receiving this broadcast message takes a sender address, specifying the sender of the broadcast message, from the broadcast message and uses this sender address from then on as destination address for this priority level, allocated to the sender.