A real-time system consists of both aperiodic and periodic tasks. Periodic tasks have regular arrival times and hard deadlines. Aperiodic tasks have irregular arrival times and either soft or hard deadlines. In this paper, we present a new algorithm, the Sporadic Server algorithm, that greatly improves response times for soft-deadline aperiodic tasks and can guarantee hard deadlines for both periodic and aperiodic tasks. The operation of the Sporadic Server algorithm, its performance, and schedulability analysis are discussed and compared with previous, published aperiodic service algorithms. Real-time systems are used to control physical processes that range in complexity from automobile ignition systems to controllers for flight systems and nuclear power plants. In these systems, the correctness of system functions depends upon not only the results of computation but also the times at which results are produced.