We consider an asymmetric electrolyte between two cylindrical concentric electrodes that are uncharged in the absence of an applied voltage difference. We calculate the dielectric response of this capacitor to an alternating voltage difference. The problem is solved using both classical boundary conditions and the new boundary conditions using excess densities to describe the charge build-up near the condensator plates as given in a previous article (C. Chassagne, D. Bedeaux and G.J.M. Koper, Colloid Surf. A 210 (2002) 137.). We verify that both boundary conditions give the same results. The advantage of the new boundary conditions lies in the possibility to extend in the future the analysis to real electrodes including reactions and specific ion adsorption. A comparison of the model predictions, involving no adjustable parameters with experimental dielectric spectroscopy data, is performed and excellent agreement is found.