We investigate the electrical conductivity of the dilute nitride alloy GaAs(1-x)N(x), focusing on the range of concentrations of N over which this material system behaves as a good conductor. We report a large increase of the resistivity for x>0.2% and a strong reduction of the electron mobility, μ, at x∼0.1%. In the ultra-dilute regime (x∼0.1%) and at low electric fields (<1 kV cm(-1)), the electrical conductivity retains the characteristic features of electron transport through extended states, albeit with relatively low mobility (μ∼0.1 m(2) V(-1) s(-1) at T = 293 K) due to scattering of electrons by N atoms. In contrast, at large electric fields (>1 kV cm(-1)), the conduction electrons gain sufficient energy to approach the energy of the resonant N level, where they become spatially localized. This resonant electron localization in an electric field (RELIEF) leads to negative differential velocity. The RELIEF effect could be observed in other III-N-V compounds, such as InAs(1-x)N(x) and InP(1-x)N(x), and has potential for applications in terahertz electronics.