There is provided a connectivity scheme for heterogeneously coupling computer systems of dissimilar architectures, such as a client/server system to a mainframe system, using a high speed, low overhead protocol. The connection uses a channel-to-channel protocol, such as a Bus and Tag connection or ESC on connection. The scheme allows mainframe systems, particularly non-IBM and non-IBM plug compatible mainframes, to communicate with each other and with IBM and IBM plug compatible mainframes over the same high speed interfaces using large block sizes. Thus, the scheme provides non-IBM and non-IBM plug compatible mainframes to appear as peers in a channel-to-channel network.