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This paper extends the two-level hierarchical scheme in (Deng et al., 1997) for scheduling independently developed real-time applications with non-real-time applications in an open environment. The environment allows the schedulability of each real-time application to be validated independently of other applications in the system. The extended scheme removes the following two restrictions of the scheme: real-time applications that are scheduled preemptively must consist solely of periodic tasks; and applications must not share global resources (i.e., resources used by more than one application). Consequently, the extended scheme can accommodate a much broader spectrum of real-time applications.