β-BaAlF5 is monoclinic (space group P21 n): a = 5.1517(1), Å, b = 19.5666(4), Å, c = 7.5567(2), Å, β = 92.426(1)°, Z = 8. γ-BaAlF5 is monoclinic (space group P21): a = 5.2584(1), Å, b = 9.7298(2), Å, c = 7.3701(2), Å, β = 90.875(1)°, Z = 4. Both structures are determined ab initio from X-ray powder data; final results are given from neutron powder data refinements (RI = 0.038, RP = 0.072, and RWP = 0.087 and RI = 0.048, RP = 0.083, and RWP = 0.101 for the β and γ phases, respectively). Like α-BaAlF5, the β and γ phases are built up from isolated infinite (AlF5)2 n-n chains with AlF6 octahedra sharing corners in a cis-position. Close structural relationships are shown to exist between the BaAl cationic subnetwork of: α-BaAlF5 and the CrB-type structure; β-BaAlF5 and the SrAg-type; γ-BaAlF5 and the FeB-type. The polymorphic transitions are proposed to be topotactic and a displacive mechanism is suggested. © 1990.