Abstract. This paper describes a hybrid grouping genetic algorithm for a multiprocessor scheduling problem, where a list of tasks has to be scheduled on identical parallel processors. Each task in the list is defined by a release date, a due date and a processing time. The objective is to minimize the number of processors used while respecting the constraints imposed by release dates and due dates. We have compared our hybrid approach with two heuristic methods reported in the literature. Computational results show the superiority of our hybrid approach over these two approaches. Our hybrid approach obtained better quality solutions in shorter time.