This paper considers the problem of electing an eventual leader in an asynchronous shared memory system. While this problem has received a lot of attention in messagepassing systems, very few solutions have been proposed for shared memory systems. As an eventual leader cannot be elected in a pure asynchronous system prone to process crashes, the paper first proposes to enrich the asynchronous system model with an additional assumption. That assumption, denoted Ï , requires that after some time (1) there is a process whose write accesses to some shared variables are timely, and (2) the timers of the other processes are asymptotically well-behaved. The asymptotically well-behaved timer notion is a new notion that generalizes and weakens the traditional notion of timers whose durations are required to monotonically increase when the values they are set to increase. Then, the paper presents two Ï -based algorithms that elect an eventual leader. Both algorithms are independent of the va...