An adequate philosophical investigation of the mind and, extensively, of human subjectivity requires a strong notion of continuity, which is the only element that allows us to account for the identity and permanence of the individual in time. In this article, the author examines the relation between this concept and that of substance, which has been understood in many ways throughout the history of philosophy and, as it turns out, only in some of them sufficiently enough to tackle this problem, which appears when the temporal dimension of human beings is brought into account.