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Layered perovskites of K2NiF4-type consist of single octahedral sheets alternating with NaCl-type layers, containing a substantial interstitial space. Based on the parent LaSrInO4+δ oxide, the series of title compounds have been prepared and investigated as possible solid electrolytes for solid-oxide fuel cells (SOFC). A charge misbalance is created by departure from the La/Sr = 1 : 1 ratio, favoring the insertion of extra oxygen atoms. The oxygen diffusion is further favored by introducing large Ba2+ ions, expanding the unit-cell size. Surprisingly, the presence of basic Ba ions drives the spontaneous insertion of water molecules in the interstitial space, as unveiled by a neutron powder diffraction (NPD) study at RT. Moreover, H2O molecules are split within the structure with protons bonded to the axial oxygens of the InO6 octahedra, and with OH units occupying the interstitial space. Electrical Conductivity measurements were made. The dc conductivity was measured under different oxygen partial pressures for both Ba-doped compounds at 600 °C and 800 °C showing mixed ionic and p-type electronic behavior at different oxygen partial pressures but with conductivities of the order of ≈10−4 (S cm−1), far below the conductivities values of the oxide electrodes used in SOFCs. To analyze the nature of the majority charge carrier, ac impedance spectroscopy (IS) was applied. In the temperature range 500-900 °C, La1.2Sr0.6Ba0.2InO4+δ oxide exhibits a conductivity improvement with respect to La1.2Sr0.8InO4+δ. Temperature-dependent NPD data show at 600 °C and 800 °C the presence of oxygen vacancies at the axial octahedral positions as well as interstitial oxygen, favoring a mixed conduction mechanism for oxide ions, which may account for the enhancement of the transport properties. The present result endorses the validity of this design procedure and supports K2NiF4-related compounds as promising candidates for solid-oxide electrolytes.