For operation of a data bus to which multiple bus participants each with a respective serial number are connected, a new bus participant is connected. A request bus message is generated by the new bus participant containing a preliminary participant identification number. The request bus message is arbitrated in the data bus by means of the identification number. A final participant identification number is assigned for the new bus participant having fewer digits than the serial number of the new participant. The final participant identification number is used for further bus messages by the new bus participant. During an initialization bus messages are used with an identifier in which a complete serial number is entered as the identifier. After the initialization a different type of bus message is used that has a shorter identifier.