In a computer network a communication session established between a user node such as a data terminal (31) and an application program (13) in a host processor (1) node defines the communication rules to be used and can be shared by a third user node (32, 175) without a new session establishment operation. Session identifier information (138, 158) is stored in the host processor (1) and in a communication controller (2) when a session is established and this stored information is compared with session sharable fields in information units sent from the session sharing third user node (32, 175) to the application program (13a) in the host processor (1). When the session is established between a primary port (161-163) of the communication controller (2) and an application program (13) in the host, it can be shared on transaction basis by a plurality of data terminals (31-33) in a group (3) of terminals operating as secondary ports (171-173) in the network.