An outstanding result of the Viking mission has been the detection of water vapor in the martian environment. The only possible reservoir for the water, where no evidence of surface frost has been detected, is the soil. Comparative morphologic analyses of periglacial terrestrial and martian terrains suggested that permafrost can paly an important role in forming many surficial structures as the Valles Marineris landslides or the collapse structures in the volcanic region of Tharsis. In this paper a study of the thermodynamics which regulate the processes of thawing and freezing of the layers of permafrost on Mars has been carried out. The equation of the heat propagation has been solved under martian conditions both in the case of periodic variations of the surface temperature and in the case of an anomalous heating of the ground. Seasonal temperature variations do not allow survival of CO2 or clathrate permafrost down to a depth of 15 m. We have demonstrated the existence of a secular 'active layer' of about 100-m depth.