In this paper we present algorithms for jointly scheduling periodic tasks and hard aperiodic tasks with precedence relations in a distributed systems under the earliest deadline first algorithm. The periodic distributed processes are assumed to be guaranteed off-line and decomposed into a set of independent tasks by means of release time and deadline modifications. This paper proposes a similar on-line decomposition of aperiodic tasks using a guarantee algorithm based on dynamically-calculated response times. An extension of a dynamic slack stealing algorithm is proposed that allows to obtain minimal response times for aperiodic task with release time constraints. Based on such extension, an on-line algorithm splits every aperiodic distributed process into a set of independent tasks, determining the end-to-end response time and, therefore, allowing the use of hard aperiodic distributed processes.