This paper describes a hierarchical scheme for scheduling periodic messages of distributed real-time applications in a cluster of PCs connected by a Myrinet. The scheme allows the developer of each real-time application to validate the schedulability of the application as if it were running alone on slower dedicated processors and network. A simple acceptance test is provided. According to the test, the operating system can determine whether to admit a new real-time system application into a system without having to perform detailed global schedulability analysis. Simulation results show that the hierarchical scheduling scheme outperforms the corresponding one-level heuristic algorithms. An open system prototype on a Myrinet cluster PCs running Windows NT uses this hierarchical scheme.