The oxygen atoms of cubic ZrO2 form a primitive cubic (pc) lattice. Two positions of the pc lattice are occupied by metal atoms in the perovskite-related structures (PER group) of superconducting oxides. Many ZrO2-related structures with ordered oxygen defects square like Zr(3)Sc(4)square(2)O(12) or Cu2O square(3) and most superconducting oxides can be characterized by the ordering of the defects and oxygen atoms. The structures are analyzed by the self-coordination numbers T-i of the oxygen atoms with other oxygen atoms in the i=1-3 coordination shell and the T-1, T-2 values plotted in structure maps. The T-i values can be correlated with attractive or repulsive interactions and the mobility of oxygen atoms. The different structures can be classified in about 20 structure families like the Ruddlesden-Popper phases. The characterization by sequences of structural units or sequences of coordination numbers allows the search for new compounds with high oxygen mobility. (C) 2000 Elsevier Science B.V. All rights reserved.