In the wireless telegram communication (28) from data-generating, unidirectionally communicating terminal devices (12) by way of primary radio sections (10) and by way of subsequent bidirectionally operating data collectors (13) of a radio network (11) to a data-documenting master data collector (14), a memory and selection expenditure governed by redundancy as a consequence of multiple connections by way of the primary radio sections (10) is avoided and nonetheless very reliable telegram communication (18) is achieved with simplified data collectors (13) if distribution criteria such as for example reception field strength-dependent quality information (22) is currently detected and stored in data collectors (13) for primary radio sections (10) from terminal devices (12). In dependence on the instantaneous distribution criteria for each terminal device (12) the master data collector (14) implements a quasi-stationary association with one and only one of the data collectors (13) for the subsequent telegram communications (18), until for example periodically or in an event-controlled manner a new association of a terminal device (12) is again implemented with one and only one, possibly a different one of the data collectors (13). The data collectors (13) also operate with each other as relay stations (25) for forwarding the data telegrams (18) to the master data collector (14) and are equipped, to prevent telegram doublets occurring on different routes, with a barrier against the same data telegram (18) being read out a plurality of times.