We evaluate the relaxation times for an electrolytic cell subject to a step-like external voltage, in the case in which the mobility of negative ions is different from that of positive ions. The electrodes of the cell, in the shape of a slab, are supposed to be perfectly blocking. The theoretical analysis is performed by assuming that the applied voltage is so small that the fundamental equations of the problem can be linearized. In this framework, the eigenvalues equations defining all relaxation times of the problem are deduced. In the numerical analysis, we solve the complete set of equations describing the time evolution of the system under the action of the external voltage. Two relaxation processes, connected with the ambipolar and free diffusion phenomena, are sufficient to describe the dynamics of the system, when the diffusion coefficients are of the same order of magnitude.