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Iron gallate nanoparticles are very prospective material which can find applications in medicine and electronics due to its specific magnetic and magneto-optical features. The combustion method was used to prepare a precursor powder of iron-gallium oxide compound which further was heat treated in order to obtain the Fe1+xGa2-xO4 nanoparticles. The Mössbauer spectroscopy revealed only ferric Fe3+ ions in the smallest 1.8 nm particles implying a Fe3+ 1-x Ga3+ 1+x O3 composition. The cation distribution in the pure FeGa2O4 compound obtained from the Mössbauer data at room temperature can be given as (Fe2+ 0.76Ga3+ 0.24) tet [Fe2+ 0.24Ga3+ 1.76] oct O4. Magnetic measurements reveal hysteresis loops in M(H) only at lowest temperature of 5 K. The maximum in the ZFC magnetization curves appears in all samples at temperatures of about 20−30 K which are only slightly dependent on the particle size. At high temperatures (T >> Tsg) the 1/M(T) dependence for the 1.8 and 28.0 nm particles follows the Curie-Weiss law, and the estimated ΘC values are rather high and positive, which indicate the ferromagnetic interaction. Because of a large value of ΘC and small value of Tsg, the magnetic frustration parameter f is rather high (up to 7), which supports spin-glass type of magnetic ordering. The low temperature Mössbauer data (Fig. 1) reveal magnetic ordering of Fe ions in all samples with the magnetic transition temperatures from 20 to 26 K depending on the nanoparticle size. At low temperatures the <Hhf>(T) dependence is well approximated by a linear law which is a characteristic of collective magnetic excitation which is a specific of the spin-glass properties rather than the superparamagnetic relaxation. Support by the Russian Scientific Foundation (Project #14-12-00848) is acknowledged.