Magnetic metal-oxide compounds with high magnetoresistance (MR) values have attracted an extraordinary interest of researchers and engineers due to their possible spintronic applications. Among these materials, the strontium ferromolybdate Sr2FeMoO6–δ (SFMO) has been relatively less known compared to cobaltites and manganites despite its 100% spin polarization of the conduction electrons and a high Curie temperature. In the present chapter, a stable fabrication technology and a systematic analysis of nanocomposites consisting of SFMO grains with SrMoO4 (SMO) dielectric shells are presented. SFMO-SMO nanocomposites were fabricated as follows: synthesis of the SFMO single-phase nanopowders by a modified citrate-gel technique; compaction under high pressure; thermal treatment for the formation of dielectric shells on the grain surface. The nanocomposite exhibits a transitional behavior of the conductivity type from metallic, which is characteristic of the SFMO, to semiconducting in the temperature range from 4 to 300Â K in applied magnetic fields up to 10Â T. A negative MR is observed due to the tunneling of spin-polarized charge carriers through dielectric interlayers. The MR value reaches 43% in a field of 8Â Т at 10Â K. The dielectric shell thickness was determined to be about 10Â nm from the electrical breakdown voltage on the current-voltage characteristics. The observed electrical breakdown is found to be a reversible process determined by the impact ionization of atoms in the dielectric in strong electric fields depending on the electrons knocked-out from SrMoO4. It was found that the MR changes the sign from negative to positive in the electrical breakdown region, revealing giant MR properties.