Abstract: The invention relates to a network system for data transmission between two data processing units, e.g. a peripheral unit (PE) and a Token Ring network with a cable concentrator. Full duplex transmission is effected over each transmission channel between the two data processing units. For this purpose, the transmission channel comprises a two lead connection (KOAX) with an adapter (APE, AMAU) on either side. One of the adapters is coupled to a peripheral unit and the other to the media access unit (MAU). Each adapter has a transmitting file (TS, TS') for receiving data which is to be transmitted on the two lead connection to the other adapter, a receiving file (TM, TM') for transmitting data to its coupled unit after being sent over the two lead connection from the other unit, and a sorting coupling (TB, Rb, 2; TB', Rb', 4) which sorts out the data on the two lead connection which the adapter has not sent out thereon itself, and feeds this data to the receiving file (TM, TM').