This study compares, experimentally and theoretically, five different modes of supplying oxygen to a membrane-aerated biofilm reactor (MABR), and search for the more efficient ways of treating wastewaters. A single-tube MABR was used to measure the decrease of an organic substrate (sodium acetate) in water by supplying oxygen in different modes, namely: (1) by feeding the membrane tube either with oxygen or air (or none of them); (2) in some cases by simultaneous sparging air to the residual water. The dynamics of the substrate and oxygen consumption were measured during the batch experiment, and two mathematical models are developed to predict their transient responses using a Monod kinetic with dual substrate limitation. The models predict biomass growth and the production of extracellular polymer substances (EPS), which in turn causes the biofilm to grow; they account for the counter-diffusion of substrate and oxygen within the EPS structure that contains the cells, and one of them incorporates the mass transport by convection and diffusion in the surrounding liquid contained inside the interconnected pores and channels within the biofilm. Transport and kinetic parameters are estimated from experiments, and both models successfully predict concentration measurements in some of the set of experiments. It was found that all of the modes of oxygen supplied in a MABR were more efficient than the traditional suspended cell process. (c) 2006 Elsevier Ltd. All rights reserved.