Real-time scheduling algorithms that provide responsive aperiodic service in the presence of hard real-time periodic tasks require the creation of a high-priority periodic server task for servicing aperiodic requests. The authors describe the extended priority exchange algorithm, which can provide better aperiodic response than previous aperiodic service algorithms, particularly for cases where the worst-case periodic load is high and little or no utilization is left for a server task. The extended-priority-exchange (EPE) algorithm attains better aperiodic responsiveness by exploiting unused time allocated to periodic tasks for aperiodic service. The average aperiodic response times for the EPE algorithm and four other aperiodic service algorithms (background, polling, deferrable server, and priority exchange) are compared for a range of periodic and aperiodic loads. Simulation results show that for a difference between the average and worst-case periodic load of only 12.5%, the EPE algorithm provides significantly better response times for aperiodic tasks.