The anelastic behaviour of some porous media has been studied as a function of their water content. The investigated systems (oxides, calcite, carbon) have been chosen to provide various chemical as well as physical environments to the fluid. From the chemical point of view, the hydrophilic/hydrophobic balance has been considered. The hydrophilic character of the oxides has been varied by heat treatments. Naturally hydrophobic graphite has been made hydrophilic by oxidation. The experimental results point to the large influence of the fi rst water monolayer on the anelastic properties of the composite media. The main physical character taken into account is the crack aspect ratio i.e. the ratio of the smallest to largest dimension of the pores. Two models have been considered. In the first one anelasticity results from the molecular motion of the adsorbate inside the fluid phase. The second one is a grain-to-grain contact model which takes into account the known variations of the coefficient of friction with hydration of the surfaces. The physical state of water in the low content range is discussed: it is conjectured to be liquid. The maximum in the damping efficiency of the composite as the water content is varied is still a matter of debate.