The problem of jointly scheduling both hard deadline periodic tasks and soft aperiodic tasks has been the subject of considerable research in real-time systems. The main goal of such a system is to minimize the response time of soft aperiodic tasks, without jeopardizing the hard deadlines of periodic tasks. Although, several approaches have been developed to schedule critical workloads on multiprocessors and to manage aperiodic tasks on monoprocessors, the proposed problem has not been fully solved for multiprocessors and integrated solutions are still required.This paper addresses the problem of scheduling an aperiodic workload on a multiprocessor system, where every processor has been previously allocated a critical periodic workload. Such pre-allocated workload is the result of executing a partitioning algorithm in order to ensure the timeliness of the critical workload. Two different approaches are used in order to minimize the response time of the aperiodic workload: aperiodic on-line assignment and global aperiodic scheduling. On highly loaded systems, the results show the global aperiodic scheduling obtains aperiodic average response times between 20% and 50% lower than those obtained by the on-line assignment approach.