A complex oxide Ba5In1.9Y0.1Al2ZrO13 with hexagonal perovskite structure (a = 5.971(4) angstrom, c = 24.012(1) angstrom) is prepared for the first time. The phase is found to dissociative-absorb water from gas phase, the degree of hydration being as high as 0.39 mol H2O. It was found by using IR-spectroscopy that protons are present therein as energetically nonequivalent OH--groups involved in hydrogen bonds of diverse strength. Isovalent yttrium-doping of the Ba5In2Al2ZrO13 phase is shown not to lead to any valuable change in the oxygen-ion-conductivity as compared with the Ba5In2.1Al2Zr0.9O12.95 acceptor doping that allows increasing the oxygen-ion-conductivity by a factor of 1.3. Both types of doping lead to increase in the proton conductivity and, as a corollary to this, an increase in the proton concentration. For these phases the degree of hydration depends on the cell parameters, hence, is determined by space availability for OH--groups in the barium coordination. Proton transport dominates in the Ba5In2Al2ZrO13, Ba5In2.1Al2Zr0.9O12.95, and Ba5In1.9Y0.1Al2ZrO13 phases below 600(o)C in humid atmosphere (pH(2)O = 1.92 x 10(-2) atm).