Nanosized powders of Fe3O4 and MgFe2O4 are synthesized by microwave-hydrothermal (MH) method. The ferrite powders thus obtained are characterized by powder X-ray diffraction, Mossbauer spectroscopy, scanning and transmission electron microscopies, vibrating sample magnetometer and AC magnetic susceptibility studies. Stoichiometric, nanosized (similar to 34 nm) Fe3O4 particles, having cubic symmetry with a(0) approximate to 8.39 angstrom, are obtained when molar ratio of Fe/NaOH used for the synthesis is 0.133. On the other hand, non-stoichiometric Fe3O4 is obtained when Fe/NaOH molar ratio is increased to 0.4. Though the powder XRD patterns of both stoichiometric and non-stoichiometric Fe3O4 are identical, Mossbauer spectroscopic studies showed different features in terms of asymmetry, intensity, isomer shift, etc. Saturation magnetization, M-s = 70 emu/g and coercivity, H-c = 178 Oe, at room temperature, are obtained for stoichiometric Fe3O4 powders. In the case of MgFe2O4, spherical, nanosized (similar to 3 nm) powders with cubic symmetry (a(0) approximate to 8.30 angstrom) and having very narrow size distribution are obtained under the MH conditions. The temperature and field dependent magnetic measurements on MgFe2O4 powders confirmed the existence of superparamagnetic state in this material with a superparamagnetic blocking temperature of 38 K below which typical magnetic hysteresis behaviour is observed.