Both Popper and Lakatos are strong advocates of the idea of scientific method, although they differ in several crucial respects as to what this might be. They also give different metamethodological arguments on behalf of their differing conceptions of scientific method. In this chapter we shall focus on their conception of method and their attempts at a metamethodological justification of it. Much has been written on other aspects of their views, especially on Popper's anti-inductivism, his non-inductivist account of corroboration, his account of verisimilitude, and the like. These will enter into our discussion only in so far as it is necessary to develop Popper's rule-based conception of method and its justification. Popper's basic stance is that of a hypotheticodeductivist, but with several distinctive variations. Arising from this is a proposal for a criterion for the demarcation of science. This is itself a central rule of method that is intended to realize certain aims, and that needs to be accompanied by several other methodological rules if it is to be effectively applied. Taken together these rules and values constitute the principles of Popper's theory of scientific method, oft en called critical rationalism; they govern what he calls “the game of science”, the many particular moves in theory change made by scientists in the many episodes within the history of science. There are a number of ways to evaluate Popper’s rules for science, some of which will arise in §10.1.2. Popper himself gives two varieties of metamethodological justifi cation employing his h-d stance as a metamethod; these are explored in §10.1.3.