The current density equation of hopping ions (and localized electrons) is evaluated for high driving forces originating both from high internal electric fields and high gradients in the particle concentrations. Both high concentration of the ions and the dilute limit are discussed. Interaction between the mobile ions is included. Attention is paid to details of the derivation. It requires the discussion of local thermal equilibrium, as opposed to chemical equilibrium, of local exchange current, hopping probability, and conductivity. A comparison with other equations aimed at coping with higher driving forces is given. In particular, the results are compared with those of irreversible thermodynamics and the substitution of activity instead of concentration in a chemical kinetic rate equation. The latter is shown to be inaccurate, yet to recover the correct dependence on the difference in the electrochemical potential of the ions. Additional topics that come up during the evaluation and are discussed are the interaction potential between the ions, the activity of building elements and of structure elements, and the effect of frequency on the hopping probability.