Results on oxygen permeation through dense ceramics of La2-xSrxNi1-y-zFeyCuzO4+delta (x =0-0.10; y= 0.02-0.10; z = 0-0.10), LaPrNi0.9Fe0.1O4+delta, La2Cu1-xCoxO4+delta (x = 0.02-0.30) and Ln(2)CuO(4+delta) (Ln = Pr, Nd) at 973-1223 K suggest two significant contributions to the ionic conductivity of the oxygen-hyperstoichiometric phases with K2NiF4-type structure. The relative role of the first of them, oxygen interstitial migration in the rock-salt-type layers of the K2NiF4-Iike lattice, increases with increasing temperature; the role of oxygen vacancy diffusion in the perovskite layers increases when temperature decreases. This behavior was attributed to the lower activation energy for ionic conduction via the vacancy diffusion mechanism. The oxygen permeability of the title materials was found to be limited by both bulk ionic conductivity and surface exchange rates and may thus be enhanced by catalytically active layers, including Pt, Ag and praseodymium oxide, deposited on the membrane surface. Oxygen permeability of K2NiF4-type phases exhibiting maximum ionic transport, such as La2Ni0.98Fe0.02O4+delta, La2Ni0.88Fe0.02Cu0.10O4+delta and La2Cu0.09Co0.10O4+delta is about one order of magnitude lower than that of most permeable perovskite-type materials. Decreasing radii of the rare-earth cations in the A-sublattice of cuprates and nickelates leads to a dramatic decrease in ionic transport, similar to perovskite oxides. Thermal expansion coefficients of the title materials vary in the range (10.1-13.4) X 10(-6) K-1.