The dielectric constants (epsilon) of the simple point charge (SPC) and extended simple point charge (SPC/E) models of liquid water have been determined at 277 and 300 K using a reaction field (epsilon(RF)) treatment for the long-range electrostatic interaction. Consistent dielectric constants are obtained by using statistical mechanical perturbation theory, such that the properties of the system correspond to epsilon(RF)=epsilon, and are therefore representative of a true infinite system. The dielectric constants of SPC were determined to be 55.8 and 54.0 at 277 and 300 K, respectively, while the dielectric constants of SPC/E were 68.5 and 62.3 at 277 and 300 K, respectively.