Optimal scheduling in meta-computing environments still is an open research question. Various resource management (RM) architectures have been proposed in the literature (e.g. [2][13][12]). In the present paper we explore, through simulation, various multi-level scheduling strategies for compound computing environments comprising several clusters of workstations. We study global and local RM and their interaction. The local RM comprises both the cluster management and operating system schedulers. Each level refines the scheduling decisions of the layer above it, taking into account the latest resource information. Our experiments explore conventional strategies like First Come, First Served (FCFS) and Shortest Job First (SJF) at the global RM level. At all levels, the schedulers strive to maintain a good load balance. The unit of load balancing at the global level is the job consisting of one or more parallel tasks; at the local level it is the task. The results of our simulations indicate that, especially at high system loads, the use of a global RM can result in a significant performance gain.