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The design of a distributed computer system for coordinated-motion control of two industrial robots is discussed. The control mechanism for the coordinated-motion control has a hierarchical nature. For hierarchically related computational tasks, a tree-structured multicomputer system is selected as the architecture of the distributed computer system (DCS). The emphasis of the work is on the design of a distributed operating system (DOS) called REKCOR, which stands for REal-time Kernel for Coordinating Robots. It provides transparent operations to the users, and maintains the flexibility and modularity of the system. The successful design of REKCOR is verified by a practical experiment, in which the distributed computer system controls two industrial robots to successfully execute a coordinated-motion.