The crystal structures of the fast ionic conductors Li6MgBr8 and Li2MgBr4 oC 14 and cF 56 were determined by single crystal X -ray diffraction and neutron powder studies, respectively. At ambient temperature, Li6MBr8 (M = Mg, Mn) crystallize in a Suzuki-type structure (space group Fm3̄̄̄ m , Z = 4, Li6MgBr8: a = 1098.0(1) pm, 114 unique reflections, R = 0.037). Li2MgBr4 oC 14 crystallizes in a SnMn2S4-type structure (space group Cmmm , Z = 2, a = 777.94(2), b = 1104.25(4), and c = 386.55(1) pm , RI, = 0.073, 318 K), the high-temperature polymorph (HTM I) in the Li2MnBr4 cF 56 type (space group Fd 3 m , Z = 8, a = 1124.55(4) pm , RI , = 0.052, 673 K). These structure types are more or less ordered NaCl superstructures. The thermal ellipsoids of the lithium ions are discussed in terms of the conduction pathways and the order-disorder phase transitions observed.