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This paper considers the fault-tolerant quorum-based mutual exclusion problem in a message-passing asynchronous system and determines a failure detector to solve the problem. This failure detector, which we call the modal failure detector star, and which we denote by M驴, is strictly weaker than the perfect failure detector P but strictly stronger than the eventually perfect failure detector 驴P. The paper shows that at any environment, the problem is solvable with M驴. In addition, we make an analysis of our algorithm performance in terms of the number of messages and synchronization delay.