Considering an asynchronous system made up of n processes and where up to t of them can crash, finding the weakest assumptions that such a system has to satisfy for a common leader to be eventually elected is one of the holy grail quests of fault-tolerant asynchronous computing. This paper is a step in such a quest. It has two main contributions. First, it proposes an asynchronous system model, in which an eventual leader can be elected, that is weaker and more general than previous models. This model is captured by the notion of intermittent rotating t-star. An x-star is a set of x + 1 processes: a process p (the center of the star) plus a set of x processes (the points of the star). Intuitively, assuming logical times rn (round numbers), the intermittent rotating t-star assumption means that there are a process p, a subset of the round numbers rn, and associated sets Q(rn) such that each set {p}∪Q(rn) is a t-star centered at p, and each process of Q(rn) receives from p a message t...