This paper describes a bilateral robot control system that uses a real-time network and a prioritization scheme for data transmission via a network. The bilateral robot system is controlled by a new controller that improves impedance matching performance. The network system is implemented by a device named responsive processor which is was newly developed to enable real-time networking. Because the network capacity is limited, it is necessary to determine the priority order for the robot control data. The authors analyzed a control system with a time delay and assigned the priority order on the basis of robustness against time delay. To evaluate the priority assignment, experiments on a network-based bilateral robot were conducted. The experiment results confirmed the appropriateness of both the prioritization scheme and the order of the priority assignment.