A generalization of the second-order coupled-wave theory of diffractions on planar dielectric gratings are presented. The theoretical analysis is rigorously based on the static Maxwell s equations. Therefore, it is easy, in principle, to obtain accurate results by following the computational method given by the present paper. The planar dielectric gratings studied in this paper are only required to hava planar isoplanes and plane surfaces. As the direction of the illuminating wave with respect to the grating is not restricted, the incident plane may be not parallel to the grating vector plane. Furthermore, the incident wave may be arbitrarily polarized and a series of Jone'g matrices are adopted to characterize the grating. This means that gratings are also considered as elements which change the state of polarizatioa of light waves.