Two types of narrow-band Dielectric Frequency-Selective Surfaces (DFSSs) have been designed at microwave frequencies. Firstly, a DFSS showing total reflection has been analyzed under guided-mode resonance conditions, based on a single dielectric grating which is illuminated by a TM polarized two-dimensional plane wave at Brewsterangle incidence, presenting extremely low-reflectance sidebands adjacent to the resonance peak. Secondly, a DFSS exhibiting total transmission at normal TE incidence has been designed, by superimposing the resonance condition of a dielectric grating on the classical high-reflectance response of a periodic (band-gap based) structure formed by alternating homogeneous dielectric layers. Finally, the oblique incidence and polarization effects on the spectral response of the designed DFSSs have been also studied. Additionally, dielectric ohmic losses and the problem of the finite size of the periodic structures have been accounted for in both structures. The obtained results have been successfully validated with the commercial software tool HFSS.