The effect on intra-membrane oxygen pressure at a constant carbon substrate loading rate on the development of bio®lms of Vibrio natrigens in a membrane aerated bio®lm reactor (MABR) was investigated experimentally and by mathematical modelling. A recently reported technique (Zhang et al., 1998. Biotechnol. Bioeng. 59: 80±89) for the in situ measurement of the substrate diffusion coef®cients in a growing bio®lm and the mass transfer coef®cients in the boundary layer at the bio®lm liquid interface was used. This aided the study of the effect of the heterogeneous bio®lm structure and also improved the reliability of the model predictions. The different intramembrane oxygen pressures used, 12.5, 25 and 50 kPa, with acetate as the carbon substrate, showed a marked effect on the initial bio®lm growth rate, on acetate removal rate, particularly in thick bio®lms and on bio®lm structure. The model predicted the substrate limitation regimes, the location of the active biomass layer within the bio®lms and the trends in oxygen uptake rate through the membrane into the bio®lms. During the development of the bio®lms, the bio®lm thickness and the intra-membrane oxygen pressure were found to be the most important parameters in¯uencing the MABR performance while the effect of bio®lm structure was less marked.List of symbols C x,f bio®lm density, kg m )3 D diffusion coef®cient in water, m 2 s )1 D c diffusion coef®cient in bio®lm, m 2 s )1 H Henry's law constant, Pa m 3 mol )1 k L mass transfer coef®cient in the concentration boundary layer at the bio®lm-liquid interface, m s )1 k o overall mass transfer coef®cient, m s )1 P M membrane permeability, mol m )1 s )1 Pa )1 r i inner radius of membrane, m r M outer radius of membrane, m Y x/s yield coef®cient of biomass on substrate, kg kg )1 d bio®lm thickness, m k dimensionless bio®lm thickness cParameter de®ned in Eq.(3) eParameter de®ned in Eq. (4) m dimensionless location of the active biomass layer in the bio®lm l max maximum speci®c growth rate of the bio®lm, h )1