Abstract. The mutual exclusion protocol presented ensures that whatever perturbation the network undergo, it regains consistency in nite time: one and only one privilege token is present. Many such protocols are know for rings, ours is the rst one for anonymous network with any topology in the shared memory communication model. It carries out the token random walk scheme presented by Israeli and Jalfon in PODC '90 and extends a ring protocol presented by Beauquier and Delaet in PODC '94. It uses O(lnn) states per register and the expected transient time is polynomial. Key-words. Self-stabilization, Mutual exclusion, Random walks.