In this paper, I address the relationship between the scientific claim of phenomenology and the limit-phenomena. Not only that the limit-phenomena pose some problems to the phenomenological approach, in the sense that they refuse the possibility of being grasped by the transcendental consciousness, so that some researchers (e.g., De Palma 2019) argue that they lay outside the field of phenomenology. But they can also pose problems to the very scientific claim of phenomenology. One such phenomenon is death. Both Husserl and Heidegger have addressed this limit-phenomenon but in different ways. While Husserl’s approach to death preserves the scientific character of phenomenology, Heidegger’s ontological approach poses some significant problems to its scientific character, even though his aims in Being and Time are also scientific. This issue has not been addressed in the literature, i.e., the relationship between the scientific character of phenomenology and the limit-phenomena, and Husserl’s and Heidegger’s different approaches to it. The paper has the following structure: First, I give an account of the problems the limit-phenomena pose to the scientific character of phenomenology, then I present Husserl’s way of dealing with this issue, and last, I show a contradiction inherent in Heidegger’s approach from Being and Time.