Nonequilibrium plasma states involving nonsmall current densities and/or enhanced electron temperatures are studied by taking 13 moments of the Boltzmann equation and using a new approach. New and nonlinear collisional terms are found for the basic equations. The electrical conductivity is calculated for the fully ionized case under no applied magnetic field: It first decreases slowly from the Spitzer‐Ha¨rm value, then turns sharply around and finally increases as a cubic power in the current density. The sharp turn‐around is located roughly at theelectron sonic point. Regarding the supersonic states it is observed that they can be reached and maintained as steady states if the local electric field is properly reduced below the critical runaway field∈cand is limited to the steady‐state value. Some associated instabilities and ways of stabilization are discussed. It is also observed that unsteady “run‐away” will occur when∈cis exceeded, as emphasized by Dreicer. The possibility of an insurmountable “electron sonic barrier” is indicated. Experimental studies are urged.