This paper deals with Heidegger's existential analysis of there-being (Dasein) and the phenomena of angst, fear, care (Sorge) and Nothingness as they are discussed in the following works: Prolegomena to the History of the Concept of Time (1925.), Being and Time (1927.), and the lecture "What is metaphysics?" published in The End of Philosophy and the Task ofThinking (1929.). The phenomena of fear and angst as seen from the perspective of Heidegger's existential analysis are devoid of their anthropological and psychological dimension. The central problem of his philosophical thought is the question of Being (Sein), and not that of human existence, although his philosophy contains elements of existential ontology. Seeking to find a more genuine basis for the crucial ontological problem of Being, he formulates his fundamental ontology, where the problem of Being is founded on the analysis of human existence (Dasein). Considering that the analysis of the phenomena of fear and angst demands a prior analysis of Dasein, this paper deals with the existential structure of Dasein before analysing those ontic phenomena. In contrast with the modern philosophy of subjectivity, Heidegger’s ‘’human’’ is not a subject, the mind or the body. The unity of a person demands a different structure from the things of ordinary existence. Dasein is, as a pure expression of Being, organised ontologically, and to understand it, we use existentials instead of categories. The phenomena of angst and fear should be considered from the context of analysis of the fundamental structure of Dasein. The core existentials of the constitution of Dasein are attunement (Befindlichkeit), understanding (Verstehen) and discourse (Rede). Taking ontic phenomena, which reveal an ontological structure when analysed phenomenologically, in account, the phenomenon of fear illustrates the existential of attunement concretely, as well as the existentially and ontologically important, fundamental attunement of Dasein – angst. When discussing these phenomena, we start with the ontic phenomena of fear and flight to get to the fundamental attunement of angst.