Nanosized powders of conductive complex fluorites based on δ-Bi2O3 and perovskites based on LnMnO3, SrFeO3, LnGaO3 have been obtained by mechanochemical synthesis. Complex doping was used for kinetic stabilization of the metastable phases, which provides dense ceramics prepared by the standard sintering procedure. Some perovskites and especially fluorites with a large cell parameter are rhombohedrally distorted during sintering, and their conductivity decreases. Complex fluorites with sintering temperatures optimal for composite membranes and with ion conductivity as high as that of the known conductor Ce0.8Gd0.2O2-δ have been obtained. There are chemically compatible systems that can give composites with mixed conductivity — potential materials for catalytic membrane reactors — prepared from nanopowders. Criteria for selecting oxide conductors for composites are formulated: appropriate sintering temperature, chemical compatibility, and high conductivity.