A process for the reversible storage of hydrogen, comprising bringing into contact an alloy of magnesium and palladium with the gaseous hydrogen leading to the formation of hydride or corresponding hydrides, comprises the use of a balanced system corresponding to the formula: Mg.sub.xPdMg.sub.xPdH.sub.n in which atomic ratio x takes on a value of 3 to 6, and n is the number of hydrogen atoms corresponding to the stoichiometry of the hydride or hydrides formed or to the formula: Mg.sub.xPdMg.sub.2PdH.sub.4+Mg.sub.x-2H.sub.n in which the atomic ratio x takes on a value of 7 to 9, and n is the number of hydrogen atoms corresponding to the stoichiometry of the hydride or hydrides formed.