Discussions of crime and conflict have been characterized by imprecision in defining and relating the two concepts. This has contributed to confusion about the subject matter and research aims of criminology, to a tendency to introduce new theoretical formulations before older alternatives have been adequately explored, and to an investment of resources in piecemeal instead of cumulative research. Since formalization is an aid to the clearer statement and more thorough exploration of theoretical alternatives, an effort is made to develop a system of formal propositions as a basis for research. This paper includes (1) a summary of conceptualizations found in the literature, (2) discussions and suggested resolutions of the basic conceptual issues, and (3) a presentation of the theoretical scheme as it has so far been developed, i.e., of a set of propositions stating conditions under which the probability of conflict between legal authorities and subjects varies and, given a conflict, conditions under which the probability of criminalization of subjects varies. It is concluded that further elaboration of propositions requires additional exploratory and descriptive research, and that rigorous formalization would be premature until the various hypothesized relationships have been more thoroughly examined in empirical research.