The invention relates to a composite material storing hydrogen. Said composite material can alternate, in an essentially reversible manner, between a storage state and a non-storage state and optionally at least on intermediate state. In the storage state thereof, the system comprises the following constituents: (a) at least one first hydride constituent and (b) at least one second constituent that is at least one hydrogen-free constituent and/or one other hydride constituent. The at least one first hydride constituent and the at least one second constituent are in a first solid multiphase system, and during the changeover to the non-storage state of the system, the at least one first hydride constituent reacts with the at least one second constituent, forming H2, in such a way that, in the non-storage state, at least one other hydrogen-free compound and/or alloy is formed and another solid multiphase system is created.