The present invention relates to a hydrogen-storing composite material which is convertible essentially reversibly between a storing state and a non-storing state, wherein the reaction enthalpy in this conversion reaction can be set in a targeted manner to a value between 15 and 80 kJ/mol of H2, preferably 25 to 40 kJ/mol of H2. Hydrogen-storing composite materials are characterized in that, in the storing state, they comprise at least one complex metal halide of alkali metal or alkaline earth metal and an element of main group three of the Periodic Table of the Elements and also at least one complex metal hydride of alkali metal or alkaline earth metal and an element of main group three of the Periodic Table of the Elements, or in the storing state at least one metal halohydride of alkali metal or alkaline earth metal and an element of main group three of the Periodic Table of the Elements, and in the non-storing state, at least one alkali metal halide or alkaline earth metal halide and a metal of main group three of the Periodic Table of the Elements.