Herein, for the first time, a model is developed for the description of magnetoresistance in nanosized, granular Sr 2 FeMoO 6-δ -SrMoO 4 core-shell structures, which is based on the fluctuation-induced tunneling model. Parameters of the fluctuation-induced tunneling model of granular materials are calculated. The magnetic field is considered to affect the tunneling barrier height. The linear and quadratic coefficients of this effect are estimated.