Theoretical results on the electromagnetic properties of such a structure as a negative-permittivity layer placed on a reflecting grating are discussed. Effect of this structure resonant absorption of the excitation electromagnetic energy is studied in a wide range of problem parameters. The sufficient conditions of the effect appearance are determined by solving the dielectric-layer eigenoscillation problem. A comparative analysis of the absorption by the negative- and the positive-permittivity structures is made to reveal the characteristic features of the effect. Phenomenon of the absorption resonance splitting is shown in the case of plane wave oblique incidence on the structure. The E-polarized plane wave diffraction is considered to find out essential difference of the resonant absorption in the E and H cases.