Two ionic relaxation processes reveal in the conductivity spectra recorded for the electrolyte solutions of water + NH4NO3. In the kilohertz range of the frequency of electric stimulus one observes the relaxation related to the double layers formation at the blocking electrodes/ electrolyte interface and in the megahertz range - the relaxation due to the ions inertia. The low frequency process exhibits a large distribution of the relaxation times and can be well described with an empirical Cole-Cole - type equation while the high frequency process is exactly of the Debye-type, as predicted by the theory of Chandra and Bagchi. It was found an inverse dynamic behavior of these two processes in relation to the conductivity level: the higher conductivity the faster double layers relaxation and the slower relaxation related to the ions inertia. (C) 2015 Published by Elsevier Ltd.