Abstract: An improved multilayer continuous biological membrane reactor and a process to eliminate diffusional limitations in membrane reactors in achieved by causing a convective flux of nutrient to move into and out of an immobilized biocatalyst cell layer. In a pressure cycled mode, by increasing and decreasing the pressure in the respective layers, the differential pressure between the gaseous layer and the nutrient layer is alternately changed from positive to negative. The intermittent change in pressure differential accelerates the transfer of nutrient from the nutrient layers to the biocatalyst cell layer, the transfer of product from the cell layer to the nutrient layer and the transfer of byproduct gas from the cell layer to the gaseous layer. Such intermittent cycling substantially eliminates mass transfer gradients in diffusion inhibited systems and greatly increases product yield and throughput in both inhibited and noninhibited systems.