The article discusses the possibility of understanding continuity in the ontological context and the paradoxical nature of continuity as an existential ‘background’ for thinking about the being. The analysis focuses on a number of phenomena characterizing spiritual and moral, political and cognitive aspects of a modern person’s existence and requiring philosophical thematization of continuity. The research has involved the principal strategies used for understanding of the continuity paradox in the contemporary philosophy. The paradoxical strategy applied to understanding of continuity in a discrete act of the subject’s self-refl ection is seen as the most consistent with the nature of the given problem.