The capability of sorbing hydrogen was studied for the magnesium alloys and related composites. The microstructures of the Mg-Ni binary eutectic alloys and Mg-La-Ni and Mg-Mm-Ni ternary eutectic alloys were studied. Both the initial alloys and alloys modified by the method of equal channel angular pressing were used as objects of the study. Features of interaction of the alloys with hydrogen were revealed. Sorption of hydrogen by the metal hydride composites based on alloys and “pseudoalloys,” viz., alloys obtained by sintering of mechanochemically treated highly dispersed powders formed by the hydride dispersion of metallic phases, was studied. Metal—carbon composites based on highly dispersed magnesium alloys or pseudoalloys and carbon nanostructures were formed, and the absorption of hydrogen by these composites was examined.