We summarize some of our computational studies (involving an ab initio self-consistent-field molecular orbital procedure) of the reactive properties of halogenated hydrocarbon epoxides. Two of the factors that are believed to determine the carcinogenicities of halogenated olefins and their metabolically produced epoxides are discussed in detail. These are the epoxide's tendency toward oxygen protonation, and its subsequent reactivity. The first of these provides a means for identifying suspect carcinogens, on the basis of our earlier observation that epoxide carcinogenicities are associated with relatively strong negative electrostatic potentials near the oxygens (the protonation sites). With regard to the epoxide's reactivity, optimum carcinogenicity appears to require that this be at an intermediate level. We have investigated the feasibility of using calculated C-O bond orders as measures of reactivity, with encouraging initial results, which suggest that this reactivity requirement may provide a means for ranking the activities of carcinogens.