Lamellar gratings illuminated in conical (off-plane) mounting can achieve with suitable optogeometrical parameters (grating profile, angle of incidence and wavelength) a total absorption of light for any polarization provided there is only the zeroth propagating order. A detailed analysis shows that electromagnetic resonances are involved and their nature strongly depends on the polarization. When the incident electric field is parallel to the cross-section of the grating, the resonance is provoked by the excitation of surface plasmons. For the orthogonal polarization, total absorption occurs for deep gratings only, when the grooves behave like resonant optical cavities. It is possible to reduce the optimal grating height by filling the grooves with a high refractive index material.