Kenneth Waltz's seminal work Theory of international politics (1979) conceptualizes international relations as a complex system in which the structure of the system and the interacting units (sovereign states) that comprise it are mutually affecting. Nevertheless, Waltz seeks to develop a nomothetic theory in which the structure of the international political system is isolated as an independent variable, state behaviour being the dependent variable. Waltz's explanatory strategy is therefore characterized by a deep tension: he treats structure as an independent variable whilst also arguing that structure and units are mutually affecting. Consequently, his systemic theory only generates partial explanations: it indicates how structure affects behaviour, but not how structure interacts with other variables to produce specific behavioural outcomes. This thesis draws on Waltz's theoretical writings, on Waltz's applications of his theory to empirical subjects in international relations (superpower relations during the Cold War, Soviet socialization into international society, and NATO's role after the Cold War), and on a wide range of theoretical literature. It explores the implications of the tension in Waltz's approach for explanatory theory in International Relations. It shows that Waltz's theory cannot ground many of his substantive arguments, that realists who attempt to improve Waltz's theory misunderstand the problems Waltz encounters, and that constructivists are unable to offer causal generalizations about complex systems. It concludes that explanatory theory in International Relations is currently poorly equipped to address complex systems in which structure and units are mutually affecting.