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Dynamically reconfigurable system-on-a-chip (RSoC) technology features embedded microprocessors that are dispersed on the same die with significant amounts of programmable logic fabric. In this paper, we present a strategy to solve the recently emerging problem of how to utilize the flexible but still limited RSoC resources in an effective manner for a multi-task application. The major contribution of this paper is the development of a dynamic task scheduling algorithm that can be implemented in fixed or reconfigurable hardware that will perform the online scheduling of task systems onto the RSoC type architecture. The results from extensive simulations demonstrate the benefits of the proposed dynamic scheduling approach as compared with that of other static scheduling techniques taken from the technical literature.