Oxygen permeability of Ln(1-x)M(x)CoO(3-delta) (Ln = La, Pr, Nd; M = Sr, Ca, Bi, Pb; x = 0-0.9) and SrCo(1-x)Me(x)O(3-delta) (Me = Cr, Mn, Fe, Ni, Cu; x = 0-0.5) perovskite-like oxide ceramics, which are promising materials for high-temperature electrochemical oxygen membranes where matter is transferred owing to conjugate transport of oxide ions O2- and electrons through a gas-tight ceramic material, has been investigated. Dependencies of the density of the molecular oxygen flow passing through the membrane on the chemical potential gradient of O-2 in the gas phase and temperature have been analyzed. Physicochemical models of such dependencies are proposed. It is shown that complex oxides SrCo1-xFexO3-delta (x = 0.2-0.35) and La1-xSrxCoO3-delta (x = 0.65-0.75) having the highest oxide ionic conductivity can be used as materials for electrochemical oxygen membranes.