The linear relationship observed between the water isotopic contents of precipitation and surface air temperatures leads to the use of the water isotopes, H218O and HDO, in paleoclimatology. Applied to the measurements of the isotopic content of paleowaters, like groundwaters and deep ice cores, this relationship is used to infer paleotemperatures. However, this interpretation of paleo-isotopic contents is only valid if the isotope-temperature relationship is not affected by climate change. To address this problem, we have developed a water isotope modeling inside an atmospheric general circulation model (AGCM) and performed simulations of both the present-day and Last Glacial Maximum (LGM) climatic conditions. AGCMs are indeed the only appropriate tools able to account the whole complexity of the atmospheric circulation. For the present-day climate, preliminary results for January were presented by Joussaume et al. (1984) and are complemented by new simulations performed for both February and August climatic conditions with a higher-resolution version of the model. Model results are well corroborated by observations. They also exhibit some effects of the atmospheric circulation on the isotopic fields. For the simulated LGM climate, the model results compare well with paleoclimatic data of water isotopic contents, except for a higher than observed spatial variability. The overall patterns of the simulated δ18O-temperature relationship for the LGM climate are practically unchanged, which tends to comfort the use of water isotopes in paleoclimatology. However, concerning the deuterium excess, i.e., the relationship between oxygen 18 and deuterium, the model results are not sufficiently valid to allow a discussion of the use of deuterium excess in paleoclimatology.