This paper presents real-time scheduling techniques for reducing the response time of aperiodic tasks scheduled with real-time periodic tasks on multiprocessor systems. Two problems are addressed in this paper: (i) the scheduling of aperiodic tasks that can be dispatched to any processors when they arrive, and (ii) the scheduling of aperiodic tasks that must be executed on particular processors on which they arrive. In order to improve the responsiveness to both types of aperiodic tasks, efficient dispatching and migration algorithms are designed based on the Earliest Deadline First (EDF) algorithm and the Total Bandwidth Server (TBS) algorithm. The effectiveness of the designed algorithms is evaluated through simulation studies. Keywords Real-Time Scheduling, Response Time, Earliest Deadline First, Total Bandwidth Server, Multiprocessors.