A process for the reversible storage of hydrogen, comprising bringing into contact a material that consists of magnesium elements and nitrogen elements with gaseous hydrogen leading to the formation of an amide or corresponding hydrides, comprises the use of a balanced system corresponding to the formula: Mg.sub.3N.sub.2Mg(NH.sub.2).sub.2+2MgH.sub.n where n is the number of hydrogen atoms corresponding to the stoichiometry of the hydride or hydrides formed. The material can also comprise, in a minor proportion, at least one transition metal of groups 3 to 12 of the periodic table that is selected from among Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn and Pd.