This paper analyses the leader election problem in terms of the failure detectors in asynchronous distributed systems. A Leader is a Coordinator that supports a set of processes to cooperate a given task. This concept is used in several domains such as distributed systems, parallelism and cooperative support for cooperative work (CSCW). We first discuss the relationship between the Election problem and the Consensus problem in asynchronous distributed systems with unreliable failure detectors. Chandra and Toueg have stated that Consensus is solvable in asynchronous systems with unreliable failure detectors. But, in contrast to the Consensus problem, the Election problem is impossible to solve with unreliable failure detectors even with a single crash failure. More precisely, the weakest failure detector that is needed to solve this problem is a Perfect Failure Detector, which is strictly stronger than the weakest failure detector that is needed to solve Consensus.
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