A general class of two-step alternating-direction semi-implicit methods is proposed for the approximate solution of the semi-discrete form of the space-dependent reactor kinetics equations. An exponential transformation of the semidiscrete equations is described which has been found to significantly reduce the truncation error when several alternating-direction semi-implicit methods are applied to the transformed equations. A subset of this class is shown to be a consistent approximation to the differential equations and to be numerically stable. Specific members of this subset are compared by considering two-dimensional numerical experiments. An “optimum” method, termed the nonsymmetric alternating-direction explicit method, is extended to three-dimensional geometries. Subsequent three-dimensional numerical experiments confirm the truncation error, accuracy, and stability properties of this method.