The invention relates to a local area network operating in the asynchronous transfer mode, with a first transceiver (1 to 8, 54 to 57) which includes a radio device (33, 60) for transmitting cells to a plurality of other transceivers (1 to 21, 54 to 57). For a data exchange between the first and the other transceivers (1 to 21, 54 to 57) without cells being blocked, a radio device (49, 60) includes a first buffer memory (73) assigned to a respective other transceiver (1 to 21, 54 to 57). A first buffer memory (73) is used for storing a cell whose destination is another transceiver (1 to 21, 54 to 57) which is assigned to the respective first buffer memory (73).