Thin films of the non-stoichiometric perovskite SrFeO2.5 + x have been grown by the pulsed excimer laser deposition technique onto sapphire substrates. The electrical conductance properties of the thin films have been determined in a series of experiments done both isothermally and with programmed temperature changes from ambient to 490 degrees C and under O-2/N-2 atmospheres with oxygen concentrations in the range from 100 ppm to 100%. Over these ranges of temperature and oxygen partial pressure a wide range of oxygen stoichiometry in SrFeO2.5 + x occurs (approximately 0 < x < 0.5), which includes all four known phases in the SrFeO2.5 + x + O-2 system. The experimentally measured values for the activation energy of conduction, epsilon(A), for SrFeO2.5 + x films at temperatures 100 < T < 200 degrees C are in the range 0.30 < epsilon(A) < 0.47eV under oxygen at partial pressures 0.001 < P-(O2 < 0.05 atm and 0.18 < epsilon(A) < 0.28 eV for 0.2 < P-(O2) < 1 atm. These values for epsilon(A) are typical for compositions of SrFeO2 + x with stoichiometries in the range 0.25 < x < 0.45. For T < 300 degrees C and for P-(O2) < 0.001 atm the films were essentially insulators. For T > 250 degrees C and P-(O2) > 0.001 atm, the oxygen stoichiometries of the films change during the programmed temperature ramps. For these conditions, the values delta epsilon(A)/delta T exhibit minima/maxima in the temperature range 250 < T < 320 degrees C which are interpreted as being due to the onset of the order-disorder phase transition from the cubic to the tetragonal and orthorhombic ordered phases of SrFeO2.5 + x with oxygen stoichiometry in the range 0.08 < x < 0.38. The SrFeO2.5 + x thin films have application as oxygen sensing materials, and a relationship between conductance and oxygen sensitivity, S-ox, has been derived. The values of S-ox for SrFeO2.5 + x thin films increases by more than an order of magnitude for compositions close to the lower stoichiometric limit where the principal phase conversion is between the cubic perovskite and the brownmillerite forms.