The travelling waves of the front type that are initiated in a system in which there is an ionic autocatalytic reaction, with a quadratic rate law, are considered when a constant current I is applied, These waves are seen to depend on both the current and the parameter delta(B), the ratio of diffusion coefficients of autocatalyst and substrate. For delta(B) > 1 there is a transition from kinetic front waves to Kohlrausch electrophoretic fronts as I is varied. For delta(B) < 1, both kinetic waves and Kohlrausch fronts an seen as well as an additional type of wave where a much enhanced reaction takes place.