Impedance spectroscopy measurements of the LiI-4AgI samples, in the frequency range 20 Hz{1 MHz, and in the temperature range between 353 K and 378 K were made. Both pure and lithium-doped silver iodide showed blocking phenomena in the electrodes and the grain boundary. The blocking phenomena allowed a change in the transport properties of the pure compound in respect to the doped compound as the temperature varied. The curves of electrical modulus in the LiI-4AgI system show asymmetric peaks corresponding with a weak correlation between mobile ions in the diusion process. The electrical conductivity in the AgI-LiI system can be described using a stretched relaxation function of the Kohlrausch-Williams-Watts (KWW) type. We speculat e that the phase of lithium dissolved in the silver iodide favors the formation of islands that disperses the conductivity due to the modication of the relationship among the microscopic energies: microscopic energy and migration energy.