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 article, we present a new algorithm, the Sporadic Server algorithm, which 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 previously published aperiodic service algorithms.