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Modern reconfigurable devices such as FPGAs can be reconfigured at run time. Some of them can be dynamically partially reconfigured, which means part of the FPGA is changed without interrupting other parts. This feature adds tremendous flexibility to the Reconfigurable Computing (RC) Field but also introduces challenges. Reconfigurable Operating Systems tend to ease applications development and most importantly applications verifications and maintenance. In this paper we propose novel scheduling algorithms for reconfigurable computing that can handle both hardware and software tasks. The algorithms proposed reuse hardware tasks to reduce reconfiguration overhead, migrate tasks between software/hardware, and give priority to hardware tasks. Results obtained indicate that adding a software processor element not only adds flexibility, but also increases system performance. Two on-line schedulers were designed and implemented. RCSched-I is a simple based implementation that nominates the first available free Partial Reconfigurable Region (PRR) for new tasks. RCSched-II on the other hand nominates any free PRR. Both schedulers check the nominated PRR(s) against the ready task for a match, then decide if there is a need for reconfiguration or not. RCSched-II reconfigures the least recently configured PRR, which increases hardware tasks reuse and decreases total processing time.