We present simulations of water-stable isotopes from the LMDZ general circulation model (the LMDZ-iso GCM) and evaluate them at different time scales (synoptic to interannual). LMDZ-iso reproduces reasonably well the spatial and seasonal variations of both δ18O and deuterium excess. When nudged with reanalyses, LMDZ-iso is able to capture the synoptic variability of isotopes in winter at a midlatitude station, and the interannual variability in mid and high latitudes is strongly improved. The degree of equilibration between the vapor and the precipitation is strongly sensitive to kinetic effects during rain reevaporation, calling for more synchronous vapor and precipitation measurements. We then evaluate the simulations of two past climates: Last Glacial Maximum (21 ka) and Mid-Holocene (6 ka). A particularity of LMDZ-iso compared to other isotopic GCMs is that it simulates a lower d excess during the LGM over most high-latitude regions, consistent with observations. Finally, we use LMDZ-iso to explore the relationship between precipitation and δ18O in the tropics, and we discuss its paleoclimatic implications. We show that the imprint of uniform temperature changes on tropical δ18O is weak. Large regional changes in δ18O can, however, be associated with dynamical changes of precipitation. Using LMDZ as a test bed for reconstructing past precipitation changes through local δ18O records, we show that past tropical precipitation changes can be well reconstructed qualitatively but not quantitatively. Over continents, nonlocal effects make the local reconstruction even less accurate.