The two film theory is often used to evaluate the mass transfer rate in gas-liquid contactors. The analytical solving of the film mass balance equations is often not possible because of the non-linearity of the reaction terms. Therefore, a numerical solution of the equations of the contactor model has to be developed. However, this becomes a heavy task when the bulk phases are not perfectly mixed. An original numerical solving technique is presented here. The technique is based on a Taylor series development of all the unknowns of the contactor model. The technique is presented on three applications. Two of these applications are simple enough to allow the comparison of our results with the results obtained with a classical shooting technique. (C) 2004 Elsevier B.V. All rights reserved.