A redundantly operated industrial communication system includes communication devices that are redundantly linked to an industrial communication network and includes network infrastructure devices associated with the industrial communication network, wherein message transmission occurs wirelessly at least in sections. The industrial communication network contains a plurality of buffer memory units for message elements that are received at a network node by wire and message elements that are to be sent by the network node wirelessly. When a maximum buffer size is exceeded, an oldest message element situated in a respective buffer memory unit is erased. Until the maximum buffer size is exceeded, the oldest message element is selected as the next message element to be sent wirelessly.