The structure and ionic conductivity of fluorite-related Bi20Ca7NbO39.5, Bi10.75Ca4.375GaO22 and the high temperature form of Bi9ReO17, formed by quenching from 800 C, were studied by neutron powder diffraction, X-ray powder diffraction and impedance spectroscopy. All materials formed distorted delta-Bi2O3-related monoclinic superstructures of a fluorite-related hexagonal subcell. The supercell, with P2(1)/m symmetry, is derived from the cubic fluorite subcell axes (a(f), b(f), c(f)) using the transformation matrix: (graphics). Both Bi20Ca7NbO39.5 and Bi10.75Ca4.375GaO22 are shown to display good oxide ion conductivity (2.52 x 10(-5) Omega(-1) cm(-1) and 1.02 x 10(-5) Omega(-1) cm(-1) at 673 K with activation energies of 1.12 eV and 1.25 eV, respectively): quenched Bi9ReO17 has enhanced oxide ion conductivity (1.44 x 10(-3) Omega(-1) cm(-1) at 673 K) with a lower activation energy of 0.76 eV. (C) 2010 Elsevier B.V. All rights reserved.