This paper investigates diffractions by gratings made of a dispersive material in an epsilon-near-zero (ENZ) regime and having one-side corrugations, and those by two-component dielectric-ENZ gratings with the inner corrugations and flat outer interfaces. The goal is to achieve wideband and simultaneously wide-angle −1st order blazing (deflection) that may enable wideband spatial filtering and demultiplexing in reflection mode. Several typical scenarios are discussed, which differ in the maximum magnitude of the blazed wave and size of the blazing area observed on the frequency-incidence angle plane, as well as the contribution of the ranges of positive and negative permittivity in the vicinity of zero. The high capability of ENZ and dielectric-ENZ gratings in asymmetric reflection is demonstrated for three different levels of losses for the dispersive material.