Mg-rich region of phase diagram of the Mg-Li-Al ternary system was investigated by means XRD, SEM/WDS and EPMA methods. The Mg-based solid solution extend up to Mg76Li12Al12 composition. The Mg76Li12Al12Hx hydrides were prepared by different methods, such as gas phase hydrogenation and thermal synthesis. Two hydride phases forms at the interaction of Mg76Li12Al12 alloy with hydrogen. In the first stage, the insertion of hydrogen in to the structure of the initial hexagonal phase up to the maximum content of hydrogen equal 3.2  wt. % was observed. This Mg76Li12Al12Hx (0   <  x   <  74) reversible hydride has a hexagonal crystal structure (P-6m2, a   =  3.1485(1), c   =  5.1111(2) angstrom) in which the hydrogen atoms inserts to octahedral voids. During the next stage of hydrogenation a new Mg76Al12Li12Hx (74   <  x   <  200) hydride phase with higher hydrogen content up to 8.2  wt.% H-2 is formed. This hydride has a orthorhombic structure (Cmmm, a   =  6.8198(3), b   =  6.8543(3), c   =  3.3609(1) angstrom) in which the hydrogen atoms has coplanar triangle coordination. This orthorhombic hydride has also higher hydrogen content in compare to binary MgH2 hydride (7.6  wt,% H-2).