Similar to the coldest terrestrial periglacial regions like Yakutia (Siberia), the planet Mars exhibits wide outflow channels. This analogy and the presence of permanent ground ice suggest that thermal erosion have existed during Martian fluvial outbursts 3000 m.y. ago. Thermal erosion here is considered to be the result of ground thawing produced by heat transfer between the water flow and the frozen ground, followed by a transport of unfrozen sediments. This paper proposes a qualitative explanation of thermal erosion with the help of some physical models. From the quantitative point of view, two thermal mathematical models are proposed and discussed. The zones undergoing the most efficient erosion are river banks. The first model studied here describes extreme thermomechanical actions: a constant thermal flux on the ground surface produces ground thaw, and the unfrozen sediments are immediately removed by water flow. It is an ablation model. It allows a theoretical evaluation of the fiver bank recession. Validity of theoretical estimations is acquired by comparing the calculations to the observed backwearing of the banks of some Siberian rivers which can reach 25 m yr -• . Thermal erosion acting upon the bottom of wide rivers (on Mars or in Siberia as well) is a very complex mechanism. Indeed, the mathematical modeling requires the study of interaction between thermal processes and transport of sediments laws. These laws are not yet well defined and are very difficult to establish. Thus another model presented in this paper concerns only onedimensional thermal actions of water flow upon the bottom of wide rivers. It considers fluvial flow at positive Celsius temperature producing a thermal flux from the bottom to the initially frozen semi-infinite ground. This model considers a constant convective heat transfer coefficient and allows an estimation of the thickness of the thawed ground beneath the river (talik). Calculated thickness of the melted ground is given in the paper for different periods of time. 1983; Battistini, 1985; Rossbacher and Judson, 1981; Squyres et al., 1992]. According to Boyce [1980] and Kuzmin [1980], the crater size seems to be an indicator of the depth to which an impact event must excavate the regolith to reach Paper number 94JE00073. 0148-0227/94/94JE-00073505.00 the ground ice table. Due to sublimation processes, the ground ice table is covered with a dry porous layer. A minimum thickness of desiccated zone of 30 m is predicted for Acidalia Planitia and Utopia Planitia [Costard, 1989b], while a mean value of 300 m is predicted for the equatorial zone, the intensity of sublimation increasing when the temperature rises [Aguirre-Puente and Sukhwal, 1984; Sakly et al., 1987]. The presence of runoff and outflow channels [Baker, 1982] suggests that liquid water has existed in the regolith throughout most of Martian history [Mazursky et al., 1977; Carr, 1986]. Examination of the Martian conditions leads to the idea that analogies may be considered between the Martian and terrestrial periglac...