Conventionally, carbon dioxide and hydrogen sulphide are absorbed using aqueous alkanolamines or carbonate solution in column type of equipment. However, in view of the unparallel advantages offered, the use of microporous hollow fiber membrane modules is an attractive alternative. In the present study application of cross-flow membrane contactors for absorption of these gases using aqueous potassium carbonate as a solvent is explored. The carbon dioxide and hydrogen sulphide absorption into aqueous solutions carbonate involves complex chemical reactions. The effect of these chemical reactions on the absorption into a liquid flowing though a hollow fiber membrane may not be described using conventional mass transfer models like e.g. the penetration or surface renewal model due to the lack of a well defined liquid phase bulk and the presence of a laminar velocity profile in the mass transfer zone. Moreover, in the case of cross-flow membrane contactors, the concentrations of both fluids, inside and outside the fibers, vary in both directions i.e. in the direction of flow and in the direction normal to the flow. Hence the theoretical analysis of the cross-flow membrane contactor is more complicated. To describe the effect of the chemical reaction on the absorption rate in the cross-flow hollow fiber contactor, a detailed mathematical model was developed using first principles. A complete scheme of the reversible ionic reactions and equilibria involved was implemented in the model to describe the solute uptake. The experiments were carried out study the effects various parameters such as gas and liquid velocities, bulk concentrations of solute gas and liquid phase reactant. The theoretical predictions were compared with experimental results. An excellent match between experimental results and model predictions was obtained.