Sensors based on high-temperature-stable semiconducting gallium oxide thin films may be used to monitor the composition of hot exhaust gases from internal combustion engines or furnace installations. The electrial d.c. conductance of these low-cost devices, operable in the temperature range 700-1000-degrees-C, represents the sensor signal. Investigations have been performed in the laboratory, using a special gas-mixing system that supplies a mixture of the main components of real exhaust gas (N2, O2, CH4, CO, NO, water vapour) to produce a synthetic exhaust gas with very precisely defined composition. Additional investigations have been performed in real exhaust gas on an engine bench test-bed. In the temperature range 1000-900-degrees-C the gallium oxide sensors respond to the oxygen partial pressure of the mixture's thermodynamic equilibrium. With knowledge of the fuel composition (carbon-hydrogen ratio), this yields a simple k measurement for lambda=1.2-0.85 with a resistance jump of about three decades at the stoichiometric point. The main mechanism in this temperature regime is a setting of the bulk defect equilibrium. At lower temperatures, the influence of surface-located mechanisms becomes more important: between 800 and 700-degrees-C the jump at the stoichiometric points becomes smaller and broader, but there is still a monotonic lambda dependency. At 600-degrees-C or below, the monotonic A dependency is lost.