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We analyze theoretically the effect of dynamical nuclear spin polarization on the electronic transport through a double quantum dot in the spin blockade (SB) regime in the presence of hyperfine interaction. The electron and nuclei hyperfine interaction produces electron spin flip which partially removes SB. Induced nuclei spin polarization produces a finite magnetic field which acts on the electrons generating an additional Zeeman splitting of the electronic spin up and down levels in each quantum dot. This additional Zeeman splitting changes dynamically with the electronic level occupation. Then, strong feedback between the induced nuclear polarization within each quantum dot and the electronic charge distribution occurs and it produces strong non-linearities in the current as a function of both, external magnetic field and dc voltage. We analyze as well electron spin resonance in a double quantum dot driven by crossed dc and ac magnetic fields. The time dependent magnetic field produces coherent electron spin rotations within each quantum dot. In this configuration, spatial Rabi oscillations due to inter-dot tunnel compete with Rabi oscillations between spin up and down states induced by the time dependent magnetic field, giving rise to a complicated time dependent behavior of the tunneling current.