In a method for allocating addresses in a CAN network having at least one master bus user and at least one slave bus user, the master bus user initiates the address allocation via a query message that is arranged for all bus users. Slave bus users which have already been assigned an address respond to this query message by transmitting a message at their assigned address. Slave bus users which have not yet been assigned an address take measures in response to this query message to be able to transmit on the bus without collisions, and transmit their serial number to the master bus user using these measures. At least the slave bus users which have not yet been assigned an address are assigned a suitable address by the master after receipt of the serial number, and use this address for further communication on the bus.