Pervaporation and vapor permeation experiments have been performed in order to investigate separately the effect of feed density and concentration on the material transport from the bulk feed to the bulk permeate. Measurements have been carried out for the azeotropic mixtures ethanol/water, 1,4-dioxane/water and 2-propanol/water at 333 and 353 K using a hydrophilic PVA/PAN-composite-membrane. In particular the influence of the feed density on the fluxes has been investigated close to and at the azeotrope where the feed concentration is almost the same in both processes. The fluxes observed are smaller and the selectivity is larger in vapor permeation compared to pervaporation. Using the same hydrophilic membrane additional pervaporation experiments for binary mixtures of 1-butanol/water and 1-pentanol/water have been performed at 333 K, and for diethyl ether/water at 323 K in the vicinity of the LLE boundary phases. Although the concentrations in the two corresponding equilibrium phases are different almost identical permeate fluxes and selectivities are obtained.