Gullies are among the most intriguing structures identified on the surface of Mars. Most common are gullies located on the slopes of craters which are probably formed by liquid water transported by shallow aquifers (Heldmann, J.L., Carlsson, E., Johansson, H., Mellon, M.T., Toon, O.B. [2007]. Icarus 188, 324–344). Two particular types of gullies are found on slopes of isolated hills and dunes. The hill-slope gullies are located mostly at 50°S, which is at the high end of latitudes of bulk of the gullies found so far. The dune gullies are found in several locations up to 65°S (Reiss, D., Jaumann, R., Kereszturi, A., Sik, A., Neukum, G. [2007]. Lunar Planet. Sci. XXXVIII. Abstract 1993), but the best known are those in Russel crater at 54°S. The hill and dune gullies are longer than others making the aquifers explanation for their formation unlikely (Balme, M., Mangold, N., Baratoux, D., Costard, F., Gosselin, M., Masson, P., Pnet, P., Neukum, G. [2006]. J. Geophys. Res. 111. doi:10.1029/2005JE002607). Recently it has been noted that thin liquid films of interfacial water can play a role in rheological processes on the surface of Mars (Moehlmann, D. [2008]. Icarus 195, 131–139. Kereszturi, A., Moehlmann, D., Berczi, Sz., Ganti, T., Kuti, A., Sik, A., Horvath, A. [2009]. Icarus 201, 492–503.). Here we try to answer the question whether interfacial liquid water may occur on Mars in quantities large enough to play a role in formation of gullies. To verify this hypothesis we have calculated thermal models for hills and dunes of various steepness, orientation and physical properties. We find that within a range of average expected values of parameters it is not possible to have more than a few monolayers of liquid water at depths greater than a centimeter. To create subsurface interfacial water film significantly thicker and hence to produce conditions for the slope instability, parameters have to be chosen to have their extreme realistic values or an additional source of surface heating is needed. One possibility for additional heating is a change of atmospheric conditions due to a local dust storm. We conclude that if interfacial water is responsible for the formation of the hill-slope gullies, our results may explain why the hill gullies are rare.