The concept of unreliable failure detector was introduced by Chandra and Toueg as a mechanism that provides information about process failures. This mechanism has been used to solve different problems in asynchronous systems, in particular the Consensus problem. In this paper, we present a new class of unreliable failure detectors, which we call Eventually Consistent and denote by ♦C. This class combines the failure detection capabilities of class ♦S with the eventual leader election capability of class . This capability allows all correct processes to eventually choose the same correct process as leader. We study the relationship between ♦C and other classes of failure detectors. We also propose an efficient algorithm to transform ♦C into ♦P in models of partial synchrony. Finally, to show the power of this new class of failure detectors, we present a Consensus algorithm based on ♦C. This algorithm successfully exploits both the leader election and the failure detection ...