A theoretical model is derived to account for the deuterium--oxygen 18 relationship measured in meteorice waters. A steady state regime is assumed for the evaporation of water at the ocean surface and the subsequent formation of precipitation. The calculations show that the deuterium and oxygen 18 content in precipitation can be taken as linearly related. From the slope and the intercept (known as the deuterium excess) of the ΔD-Δ18O linear relationship for precipitation we compute the mean values on a global scale of the evaporating ocean surface temperature and the relative humidity of the air masses overlying the oceans. The deuterium excess is primarily dependent on the mean relative humidity of the air masses formed above the ocean surface. Paleoclimatic data may be obtained by this isotopic method from the analysis of old water and ice samples. A moisture deficit of the air over the ocean, equal to only 10%, in comparison to 20% for modern conditions, is deduced from the deuterium--oxygen 18 distribution measured in groundwater samples older than 20,000 years.