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High quality stoichiometric brownmillerite-type oxide single crystals have been successfully grown by the floating zone method using a mirror furnace. We report here on the growth conditions and structural characterization of two model compounds: Ca2Fe2O5 and Sr2ScGaO5. Both show oxygen deficiency with respect to the average perovskite structure, and are promising candidates for oxygen ion conductivity at moderate temperatures. While Sr2ScGaO5 single crystals were obtained in the cubic oxygen-deficient perovskite structure, Ca2Fe2O5 crystallizes in the brownmillerite framework. Having no cubic parent high temperature counterpart, Ca2Fe2O5 crystals were found to be not twinned. We report on structural characterization of the as-grown single crystals by neutron and X-ray diffraction, as well as scanning electron microscopy (SEM) coupled with EDX (Energy Dispersive X-Ray Spectroscopy) analysis and isotope exchange experiments.