We report the electric-field-dependent conductivity above a finite threshold field (ET) in the spin-density wave (SDW) state of the organic conductors (TMTSF)2X, X=NO3, PF6. ET is temperature independent below half of the transition temperature (TC) and varies close to TC. For most pristine PF6 samples ET increases substantially towards TC, while for irradiated samples this rise becomes much smaller. The value of ET increases linearly with defect concentration and the magnetude of field-dependent conductivity strongly decreases. We discuss our results in the framework of the Maki's theory for the sliding SDW becoming depinned above a finite electric field and being responsible for the electric-field-dependent response.