For a group of nine hydrocarbon and halogenated hydrocarbon expoxide, there is shown to be a good correlation between their abilities to inhibit epoxide hydrase and the quantity V (sub min), E (sub s) where V (sub min) is the most negative value of the molecule's electrostatic potential in the neighborhood of the epoxide oxygen and E (sub s ) is a factor that take account of steric effects. It is also demonstrated that carcinogenicity, for thirteen epoxides, appears to be associated with V (sub min) having a relatively large negative value. On this basis, several other epoxides are predicted to be carcinogenic. The electrostatic potentials used in developing these relationships have been computed by an ab initio self-consistent-field molecular orbital procedure, using optimized molecular geometries.