In recent years a number of writers have defended and attacked various features of structural, or neo-realist theories of international politics. Few, however, have quarrelled with one of the most foundational features of neorealist theory: its assumptions about the nature of science and scientific theories. In this essay I assess the views of science underlying much neorealist theory, especially as they are articulated in the work of Kenneth Waltz. I argue not only that neorealist theories rest on assumptions about science and theory that have been questioned by postpositivist philosophers and historians of science, but also that the failure to consider the work of these writers yields theories of international politics that are deficient in several respects: they are "weak" theories in the sense that they cannot illuminate crucial features of international politics, they presuppose and sustain a narrow view of power and power relations, they reify practices and relations in the international arena and they offer little promise of producing the sort of "Copernican Revolution" for which Waltz called (or, more modestly, even a minimally satisfactory theory of international politics). In light of these shortcomings, I sketch an alternative approach to the study of international affairs, one that has been termed "prototype studies." I contend that such an approach provides scholars with a rigorous way of studying international politics, without being a theoretical science.