As with 'normal' 1H216O water molecules, the two stable water isotopes 1H218O and 1H2H16O (2H=D=Deuterium) are passed through every part of the water cycle in the atmosphere: water evaporates from ocean and land surfaces, is transported by atmospheric circulation, condenses in clouds and finally forms precipitation falling back to the earth's surface. But since HDO and H218O have a different vapour saturation pressure and molecular diffusivity than H216O, fractionation processes occur during every phase transition of any water sample. The heavier isotopes H218O and HDO become enriched in the liquid or solid phase while the vapour phase becomes more depleted in them. The strength of the fractionation processes highly depends on particular physical parameters, such as temperature and humidity. Numerous geophysical studies have used this dependency to infer information about past climates from measurements of the isotopic composition of precipitation stored in paleowater archives, e.g. in ice cores. In the last several years, atmosphere general circulation models (AGCMs) have been used as a helpful tool for studying water isotopes. Incorporating both H218O and HDO explicitly into the water cycle of the AGCM enables analysing the relationship between the isotopic composition of precipitation and climate variables, such as surface temperatures. Different boundary conditions can be prescribed for the model simulations to gain a better understanding of isotope anomalies caused by different states of the climate. This thesis focuses on the variability of H218O and HDO in precipitation falling on Greenland and Antarctica. Over the last two decades, isotope measurements on several ice cores from both polar regions have revealed new insight in the alternating occurrence of stable climate periods, like the Holocene or the last glacial stage, and fast climatic transition phases between, such as the Younger Dryas. The Hamburg AGCM ECHAM-4 was used to investigate several topics related to these isotope records from Greenland and Antarctica. Simulations for both the present climate and the Last Glacial Maximum (LGM, ~21,000 years ago) were performed to test the reliability of H218O (or HDO) as a proxy for past surface temperatures on Greenland or Antarctica. The model results indicate that a strong change in the seasonal timing of precipitation occurred on Greenland during the LGM and that this change has a significant influence on the mean isotopic composition of ice core samples from this period. Further analyses of the major source regions of water vapour transported to the ice sheets explain some additional changes between the present and LGM climate. So far, little is known about the timing and mechanisms of the transition phase between two stable climate stages. The performed ECHAM-4 sensitivity experiments concentrated on the effects of an meltwater event in the North Atlantic, similar to what might have happened during the Younger Dryas period (~ 16,000 years ago). The simulations revealed that several mechanisms influence the isotopic composition of precipitation during such a meltwater event. A simple interpretation of the isotope signal as a proxy for changed surface temperatures would lead to erroneous estimates of climate changes in many regions of the Northern Hemisphere. Finally, the variability of the isotopic composition of polar precipitation for the climate of the last century is investigated: In an ECHAM-4 simulation of the period 1950-1994, only one-third of the modelled interannual variance is related to simultaneous changes in surface temperatures on Greenland or Antarctica. Several other climate variables, e.g. ocean temperatures of the evaporation areas and/or variability in the water vapour transport to the ice sheets, contribute together a non-negligible part of the fluctuations in the isotope signal in polar precipitation. The imprint of the North Atlantic Oscillation and the El Nino/Southern Oscillation phenomenon is detected in the isotopic composition of precipitation falling in Greenland and Antarctica, respectively. As a summary we conclude from our AGCM isotope experiments, that the isotopic composition of polar precipitation can certainly be used as a proxy for paleoclimatic conditions, but that the interpretation of the isotope signal is neither simple nor straightforward. Especially the strong (spatial) correlation between the isotope signal and surface temperatures on the ice sheets, as it is observed for the present climate, might have been different for past climates.