We use an sp³s^* tight-binding Hamiltonian to investigate the band-anti-crossing (BAC) model for dilute GaN_xAs_1−x alloys. The BAC model describes the strong band-gap bowing at low N composition x in terms of an interaction between the conduction band edge (E₋) and a higher-lying band of localized nitrogen resonant states (E₊). We demonstrate that the E₋ level can be described very accurately by the BAC model, in which we treat the nitrogen levels explicitly using a linear combination of isolated nitrogen resonant states (LCINS). We also use the LCINS results to identify E₊ in the full tight-binding calculations, showing that at low N composition E₊ forms a sharp resonance in the conduction band Γ-related density of states, which broadens rapidly at higher N composition when the E₊ level rises in energy to become degenerate with the larger L-related density of states. We then turn to the conduction band dispersion, showing that the two-level BAC model must be modified to give a quantitative understanding of the dispersion. We demonstrate that the unexpectedly large electron effective mass values observed in some GaNAs samples are due to hybridization between the conduction band edge and nitrogen states close to the band edge. Finally we show that there is a fundamental connection between the strong composition-dependence of the conduction-band-edge energy and the n-type carrier scattering cross-section in Ga(In)N_xAs_1−x alloys, imposing general limits on the carrier mobility, comparable to the highest measured mobility in such alloys.