The frequency dependence of the thallium sulfide (TlS) crystal impedance is analyzed in wide frequency and temperature range for the hopping and superionic conduction mechanisms. It has been established that in weak alternating electric fields, there is a hopping mechanism of charge transfer. The use of impedance spectroscopy methods in TlS crystals, at temperatures of 300, 350 and 400 K in the frequency range of 2*106 Hz and subjected to γ-irradiation doses 0, 0.25 and 0.75 MGy charge transfer processes, has been investigated. Hodographs constructed from the data of experimental measurements of 400 K, in the low-frequency region (>103 Hz) and regardless of the absorbed gamma quanta, indicating additional contributions to the conductivity, presumably corresponds to the fact that in the frequency range of the applied signal, carrier diffusion does not reach the diffuse layer. This type of hodographs at low frequencies is characteristic of the Warburg impedance.