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Complex perovskite-related cobaltates with Co3+ fit perfectly to the majority of the requirements for cathode materials for IT-SOFC listed above. However, they possess high TEC due to thermally activated transition between low (LS) and high-spin (HS) state of Co3+. Influence of this transition on high-temperature thermal expansion properties of perovskite-related oxides is discussed using an example of layered (Pr,Sr)2(Ni,Co)O4 oxides [2]. One of the ways to decrease TEC of cobaltates is to stabilize HS Co3+ in ground state. Such compounds can be found among cobaltates with the brownmillerite-type structure. We have recently discovered the presence of HS Co3+ in ground state in CoO6 octahedra of Sr2Co1.2Ga0.8O5 with the brownmillerite structure [3]. This cobaltate is found to possess as low TEC as 13.1 ppm K-1 (298-1073K). Cuprates R2CuO4, R – rare-earth cation with layered crystal structures contain perovskite slab alternating with rock-salt slab (R=La, so called Т-phase) and fluorite slab (R=Nd-Gd, so called T’-phase) are considered as prospective cathode materials for IT-SOFC due to their low TEC (~12 ppm K-1) and moderate high-temperature conductivity (>100 S/cm for Pr2CuO4). Correlation between the presence of the particular structural slab in the crystal structure of layered cuprates and their high-temperature oxide-ion conductivity is discussed.