Strontium magnesium tetrahydride (SrMgH4) and its deuteride (SrMgD4) were prepared from SrMg alloy at 765 K under a hydrogen (deuterium) pressure of 95 bar and characterized by X-ray and neutron powder diffraction. The compound crystallizes with the BaZnF4 structure type, with the space group Cmc21 and with the following lattice parameters at 295 K: , , (deuteride) and Z=4. It contains four symmetry-independent deuterium sites having tetrahedral (D(1), D(2) [3Sr, Mgl, D(4) [2Sr, 2Mg]) and T-shaped (D(3) [Sr, 2Mg]) metal coordinations. The metal-deuterium bond distances range from 1.87 to 2.06 Å (Mg-D) and from 2.43 to 2.82 Å (Sr-D).