Samples in the system BaCe1-xInxO3-alpha were prepared in a concentration range 0.05 mole less than or equal to x less than or equal to 0.25 mole InO1.5 and the physical-chemical properties determined. The maximum doping level is 0.20 mole InO1.5 in BaCeO3 for which almost single phase products were obtained. The doped barium cerates correspond with the structure of BaCeO3 with a small amount of CeO2. The compounds are stable in reducing and oxidizing atmospheres and have a high solubility of oxygen. The In-doped BaCeO3 shows a point defect behaviour in the oxygen pressure range from 1 bar to 10(-6) bar. The highest total electrical conductivity was observed for a content of 0.20 mole InO1.5 in BaCeO3. It is influenced by the water vapour partial pressure in reducing and inert gases in the temperature range from 700 degrees C to 1000 degrees C. The electrical conductivity of In-doped BaCeO3 does not exceed the conductivity of yttria-stabilized zirconia and not even that of the brownmillerite-structure oxides Ba2In2-xCexO5. The mean ionic transport number is (t) over bar(ion) = 1 in hydrogen between 630 degrees C and about 800 degrees C whereas above 800 degrees C a deviation from 1 is detected. In argon larger deviations from 1 are observed in the whole temperature range.