As task preemption/relocation with acceptably low overheads become a reality in today's reconfigurable FPGAs, they are starting to show bright prospects as platforms for executing performance critical task sets while allowing high resource utilization. Many performance sensitive real-time systems including those in automotive and avionics systems, chemical reactors, etc., often execute a set of persistent periodic safety critical control tasks along with dynamic event driven aperiodic tasks. This work presents a co-scheduling framework for the combined execution of such periodic and aperiodic real-time tasks on fully and run-time partially reconfigurable platforms. Specifically, we present an admission control strategy and preemptive scheduling methodology for dynamic aperiodic tasks in the presence of a set of persistent periodic tasks such that aperiodic task rejections may be minimized, thus resulting in high resource utilization. We used the 2D slotted area model where the floor of the FPGA is assumed to be statically equipartitioned into a set of tiles in which any arbitrary task may be feasibly mapped. The experimental results reveal that the proposed scheduling strategies are able to achieve high resource utilization with low task rejection rates over various simulation scenarios. © 2015 IEEE.