In a method for addressing messages in a computer network in which two different types of address are used, wherein at least one first network element (4, 5, 6, 7, 8) uses exclusively a first type of address, at least one second network element (14, 15, 16, 17, 18) uses exclusively a second type of address and at least one third network element (9, 10, 11, 12, 13, 14) uses both types of address, at least one third network element (9) is a communication terminal which, besides its function as a communication terminal, also performs a function as an address converter for messages for which said communication terminal is neither the original sender nor an ultimate recipient.