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The paper concentrates on the deadlock-avoidance problem for a class of resource allocation systems modeling manufacturing systems. In these systems, a set of production orders have to be executed in a concurrent way. To be executed, each step of each production order needs a set of reusable system resources. The competition for the use of these resources can lead to deadlock problems. Many solutions, from different perspectives, can be found in the literature for deadlock-related problems when the production orders have a sequential nature [sequential resource allocation systems (S-RAS)]. However, in the case in which the involved processes have a nonsequential nature [nonsequential resource allocation systems (NS-RAS)], the problem becomes more complex. In this paper, we propose a deadlock avoidance algorithm for this last class of systems. We also show the usefulness of the proposed solution by means of its application to a real system.