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This paper presents adaptive algorithms for mutual exclusion using only read and write operations; the performance of the algorithms depends only on the point contention, i.e., the number of processes that are concurrently active durhag the algorithm execution (and not on n, the total number of processes). Our algorithm has O(k) remote step complexity and O(log k) system response time. where k is the point contention. The remote step complexity is the maximal number of steps performed by a process where a wait is counted as one step. The system response time is the time interval between subsequent entries to the critical section, where one time unit is the minimal interval in which every active process performs at least one step. The space complexity of this algorithm is O(Nlog n), where N is the range of processes' names. We show how to make the space complexity of our algorithm depend solely on n, while preserving the other performance measures of the algorithm.