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A novel vectorial modal method is presented for studying guidance and scattering of frequency-selective structures based on lossy all-dielectric multilayered waveguide gratings for both TE and TM polarizations. The wave equation for the transverse magnetic field is written in terms of a linear differential operator satisfying an eigenvalue equation. The definition of an auxiliary problem whose eigenvectors satisfy an orthogonality relationship allows for a matrix representation of the eigenvalue equation. Our proposed technique has been applied to the study of lossy all-dielectric periodic guiding media with periodicity in one dimension. This method yields the propagation constants and field distributions in such media. The reflection and transmission coefficients of a single layer under a plane-wave excitation can be obtained by imposing the boundary conditions. Study of the scattering parameters of the whole multilayered structure is accomplished by the cascade connection of components as characterized by their scattering parameters. Results obtained with this method for the propagation characteristics of a one-dimensional periodic dielectric medium are compared with those presented by other authors, and results for the scattering of several dielectric frequency-selective surfaces (DFSS) are compared with both theoretical and experimental results presented in the literature, finding a very good agreement. A symmetrical band-stop filter with a single waveguide grating is also demonstrated theoretically.