A box model is presented to simulate changes in Mediterranean long-term average salinity and Δ18O over the past 20,000 years. Simulations are validated by comparison with observations. Sensitivity tests illustrate robustness with respect to the main assumptions and uncertainties. The results show that relative humidity over the Mediterranean remained relatively constant around 70%, apparently narrowly constrained to the lower end of the range observed globally over sea surfaces by the basin's land-locked character. Isotopic depletion in run off, relative to the present, is identified as the main potential cause of depletions in the Mediterranean Δ18O record. Also, slight increases in relative humidity (of the order of 5%) might have caused very pronounced isotopic depletions, such as that in sapropel S5 of the penultimate interglacial maximum. The model shows distinctly non proportional responses of Δ18O and salinity to environmental change, which argues against the use of isotope residuals in Mediterranean paleosalinity reconstructions. ¿ 1999 American Geophysical Union