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The use of LAN-based clusters of computers for computational purposes has been in use for several years with significant success and acceptability. The introduction of the Internet infrastructure as the interconnection medium of the cluster allows for additional flexibility and transparency of such systems. PLEIADES is an Internet-based parallel/distributed system whose purpose is to allow users to use distant computational resources in order to form virtual clusters. In addition, PLEIADES can be used as a computational infrastructure service provider for applications in need of computational resources. PLEIADES uses a tiered architecture with particular emphasis on the existence of a middle tier, whose task is to assist in the communication between the interface and the resource management tiers. The existence of the middle tier allows for the creation of an open system that is able to easily integrate with new resource management platforms and tools. Since the use of a mature resource management system for parallel/distributed computing was a prerequisite of the PLEIADES architecture, the Condor resource management environment was used. The design and implementation characteristics of PLEIADES together with some experimental uses of the system are also presented.