Anxiety poses serious problems in regards to the phenomenological conception of perceptual awareness: what is the particular mode of “givenness” proper to the experience in anxiety? Is the existentialist tradition right to understand anxiety in relation to or in opposition with fear (i.e., as a sort of object-less fear)? The work of Lacan in his Anxiety Seminar (1962-1963) challenges the notion that anxiety can be understood in relation to fear, and it offers a novel way of addressing the troublesome phenomenological problem of anxiety’s object-relation. The formula that he puts forward, and which we explore in this essay, is that “anxiety is not without an object”. As a point of reference, the essay explores the properties of a curious topological object that greatly interests Lacan – viz. the Möbius strip – in order to shed light on a very peculiar class of phenomena, viz. uncanny phenomena. The overall aim is to show how the category of uncanny phenomena comprises a field of experience that forces us to revise the basic eidetic categories of Husserlian and existentialist phenomenology.