An asynchronous transfer mode (ATM) network includes a plurality of data links interconnecting a plurality of data exchange nodes, and a plurality of data terminals connected by data links associated therewith to the data exchange nodes in the ATM network. In the ATM network, a virtual circuit is selectively established over which a series of data packets including one or a plurality of coded cells is routed from a source terminal toward a destination terminal. Each of these cells includes an information field and a header section. The terminals are assigned with identification parameters respectively, which parameters are uniform in value within the network. When a cell is transferred from the source terminal to the destination terminal along a presently determined route including selected links associated with certain data exchange node or nodes, a specific identification parameter being assigned to the destination terminal is written into the header section of the cell. This cell is then transferred toward the destination terminal on the basis of the specific identification parameter without causing this parameter to be written or converted at the certain data exchange node or nodes in the presently determined route.