In order to help satisfy an apparent need for tools for monitoring the activities of a computer network, a system of special hardware and software, called a Computer Network Monitoring System (CNMS) is being implemented in the University of Waterloo Computer Communications Networks Group (CCNG). The paper discusses the motivation and derivation of the CNMS, then provides functional descriptions of most of the major hardware and software components, illustrates use of the CNMS, and lists experiments and applications. The CNMS consists of: 1) a set of hybrid monitors, each of which is controlled by a locally or remotely located computer; 2) monitor control and data analysis software; 3) a network traffic generator; 4) measurement software in each computer monitored. Each computer to be monitored is attached to a monitor. Telephone lines, possibly different from those of the network, connect the monitors to the controlling computer.