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We propose a distributed prioritized h-out of-k mutual exclusion algorithm for a mobile ad hoc network (MANET) with real-time or prioritized applications. The h-out of-k mutual exclusion problem is a generalization of the k-mutual exclusion problem and the mutual exclusion problem. The proposed algorithm is sensitive to link forming and link breaking and thus is suitable for a MANET. If we do not consider the link breaking and forming, the proposed algorithm can also be applied to distributed systems consisting of stationary nodes that communicate with each other by exchanging messages over wired links. For nonreal-time applications, we may associate the priority with the number of requested resources to achieve the maximum degree of concurrency.