A new type of membrane bioreactor is proposed for the transformation of lactose into lactic acid by Lactobacillus rhamnosus. The reactor is tubular and contains two coaxial porous alumina tubes. The internal one supports an alpha alumina membrane (mean pore size : 2.0 x 10(-7) m) on its internal wall, the external one has the same membrane on its external face. The bacteria are fixed into the support macroporosity and confined in the annular space defined by the two separating walls. The substrate solution is fed into the reactor inner compartment whereas the liquid percolates in the radial direction across the two membranes. This original configuration allows the transformation of lactose into lactic acid in the porous space contained between the two microfiltration layers. A model is developed in cylindrical coordinates and takes into account the mass transfer phenomena coupled with biological reaction in the membrane annulus. The continuous decrease of permeate flow rate is introduced into the theoretical calculation by a Michaels type law relating the permeate flux evolution to the bacteria population growth. The theoretical results are in good agreement with experiments and the bacteria population growth evolution could be simulated in order to choose the experimental conditions for the best productivity. This membrane reactor can be operated for 90 h, producing a total substrate conversion at high contact time. However, a continuous decrease of permeate flux was observed as a result of membrane plugging by the bacteria population growth.