MgH₂ is one of the most promising materials for hydrogen storage. However, its rather slow hydrogen absorption and desorption kinetics and high dissociation temperature essentially limit its application in this field. Nevertheless mixing Mg or MgH₂ with small amount of transition metals or their oxides remarkably accelerates the hydrogen kinetics. Recently a series of new hydrides Mg₇TiH_x, Mg_6.5NbH_x and Mg₆VH_x of Ca₇Ge type structure has been synthesized. The hydrogen desorption properties have been found to be better than for pure MgH₂. Here, we report on the results of our theoretical study of the electronic structure of these new hydrides carried out within the framework of the full-potential, self-consistent linearized augmented plane-wave method. We use these results, along with calculations of the heat of formation and relative stability, to discuss the bonding of these materials and their hydrogen-storage properties.