This paper addresses the problem of jointly scheduling tasks with both hard and soft real-time constraints. We present a new on-line aperiodic admission algorithm to be used with on optimal dynamic priority preemptive scheduler, such as the Earliest Deadline First (EDF) or the Least Laxity First (LLF). The admission algorithm transforms a soft aperiodic task into a hard one by assigning a deadline. The proposed algorithm is shown to be optimal in terms of providing the shortest response time for soft aperiodic tasks among fixed and dynamic priority schedulers (assuming aperiodic tasks are severed in a FCFS order), without endangering the execution of any periodic task. The paper also shows how the main results and ideas developed for the fixed priority theory can be adapted and extended for dynamic priority schedulers. The algorithm has also been extended to work with firm deadline aperiodic tasks.