The selective removal of H2S from gases containing several acidic components by absorption in aqueous alkanolamines is determined by the ratio of the partial mass transfer resistances in the gas and liquid phase and the solubility (physical and chemical) of these gases in the absorption liquid. The influence of the mass transfer resistances is experimentally studied in the present study. The simultaneous absorption of H2S and CO2 in aqueous solutions of methyl-di-ethanol amine (MDEA) was studied in a stirred cell with flat, horizontal microporous wetted or non-wetted membranes which increase the partial mass transfer resistances in the liquid or gas phase, respectively. It was found that non-wetted membranes do not increase the H2S flux because the located in the gas phase, is reduced, while the CO2 transport is not affected significantly. Wetted membranes reduce the transport of the amine to the gas-liquid interface which introduces an additional transport limitation of the amine. Therefore the H2S and CO2 flux are both determined by the mass transfer in the liquid phase which is generally not the case for H2S with a gas-liquid interface without a membrane. The introduction of a non-wetted membrane in the gas-liquid interface has no effect on the values of the liquid phase mass transfer coefficients, despite the different hydrodynamic situation at the interface. In this case however, a considerable difference was observed for the gas phase mass transfer coefficients. The influence of physical and chemical solubility is studied in the second part of the present paper in which a liquid membrane of pure MDEA is investigated.