Alternative explanations are proposed for the results of the three types of remote sensing experiments in which water ice is supposed to be found on the surfaces of atmosphereless celestial bodies: (1) measurements of hydrogen content by the neutron spectrometer on Lunar Prospector, (2) observations of the absorption bands near 3 μm in reflectance spectra of asteroids, and (3) radar observations of polar regions of Mercury. Calculations have shown that in the first two types of observations solar wind protons chemically trapped by oxygen atoms in hydroxyl groups or other radiation defects in oxygen-bearing particles on the surfaces of atmosphereless bodies can be mistaken for water. Higher hydrogen content in the lunar polar regions, especially in polar craters, as compared to equatorial zones can be due to sharp decrease of escape probability with temperature. Spots of high hydrogen content in equatorial zones of the Moon can be explained by variations of degassing rates in different materials. Solar wind origin of OH groups may account for 3-μm absorption by asteroids of M and E classes thought to be differentiated. Strong, highly depolarized radar echoes from polar and lower latitude craters of Mercury can be explained by decrease of the dielectric loss of silicate material with temperature, which solves the problems of delivery and thermal stability of low-loss material on Mercury surface, being consistent with the observed regional variations of radar brightness. The possibilities considered in the paper should be taken into account in interpretation of the observations aimed on search of water. ¿ 2001 American Geophysical Union