Gas-liquid mass transfer has been studied in a membrane module with non-wetted microporous fibres in the laminar flow regime. This new type of gas/liquid contactor can be operated stabily over a large range of gas and liquid flows because gas and liquid phase do not influence each other directly. Therefore foam is not formed in the module, gas bubbles are not entrained in the liquid flowing out of the reactor and the separation of both phases can be achieved very easily. These phenomena often limit the applicability of conventional contactors, e.g. a bubble column which was also studied in the present work. The large mass transfer area of a bundle of small fibres offers the possibility of creating a compact gas/liquid mass exchanger. However, owing to the small channels in and around the fibres the flow of either gas or liquid becomes laminar which reduces the mass transfer capacity of the module. Therefore the mass transfer coefficients in the laminar flow regime were determined experimentally. For mass transfer determined by the transport in the liquid phase it was found that the active mass transfer area is equal to the total membrane area, regardless the porosity of the fibre. For processes with liquid flowing through the fibres, the influence of fibre diameter, diffusivity in the liquid, liquid viscosity and liquid velocity on mass transfer can be correlated extremely well with the Graetz-Lévèque solution derived for the analogous case of heat transfer. For liquid flowing around regularly packed fibres mass transfer was described satisfactory with a correlation derived from a numerical solution for the similar heat transfer problem [Miyatake and Iwashita, Int. J. Heat Mass Transf., 33 (1990) 416]. Correlating mass transfer in liquid flowing around irregularly packed fibres was not possible because of the undefined dimensions of the different channels between the fibres.