Flux-explicit transport laws based on Newman's concentrated-solution theory are developed for application to phases with domains of imbalanced charge. General procedures are provided to create flux laws and a current-voltage relation that describe diffusion and migration in isothermal, isobaric, non-neutral multicomponent electrolytes. To retain thermodynamic consistency within the non-neutral concentrated-solution theory, driving forces for diffusion are based on the chemical potentials of neutral combinations of species, and an excess current density is used as a driving force for migration. Procedures are developed for identifying the solution conductivity and Hittorf transference numbers in non-neutral electrolytes comprising three or more species. Flux laws for non-neutral binary electrolytic solutions involving the thermodynamic diffusion coefficient, cation transference number, and ionic conductivity are presented. When local electroneutrality is assumed, the new transport equations reduce to the familiar flux laws for binary electrolytes. (C) 2013 Elsevier Ltd. All rights reserved.