TECHNOLOGY FOCUS - CHEMICAL ENGINEERING - Preferred Composition: The organic feedstock contains or consists of organic substance(s) chosen from polysaccharide, such as cellulose, hemicellulose or starch, and lignocellulose. The biofilm, dependent on the organic feedstock, contains a strain of aerobic microorganisms, which produce cellulase for the decomposition of cellulose to fermentable sugars, a strain of aerobic microorganisms, which produce amylase for the decomposition of starch to fermentable sugars, and a strain of aerobic microorganisms, which produce lignin-modifying enzymes for the decomposition of lignin. Preferred Method: The fermentation product is removed from the fermentation compartment, particularly by transporting the fermentation products through the membrane into the oxygen supply compartment. The oxygen-permeable membrane separates oxygen supply compartment and fermentation compartment. Oxygen is transported from the oxygen supply compartment to the fermentation compartment through the membrane, and an oxygen zone is formed in the fermentation compartment adjacent to the membrane. The aerobic microorganism of biofilm is located adjacent to the membrane in the aerobic zone and an oxygen gradient with decreasing oxygen content with increasing distance from the membrane is established within the biofilm located on the membrane. The biofilm contains a consortium of at least two strains of microorganisms, and at least one of these strains of microorganisms is a strain of aerobic microorganism located adjacent to the surface of the membrane in the aerobic zone of the fermentation compartment for the production of enzymes. At least one of these strains of microorganisms for the fermentation of fermentable sugars is a strain of anaerobic microorganism located on the membrane in the biofilm in an oxygen depleted, preferably anaerobic zone and optionally also in the base material mixture, which contains organic feedstock and which is supplied to the fermentation compartment. The base material mixture is brought in contact with the biofilm. The anaerobic microorganism in the biofilm and optionally also in the suspension ferment fermentable sugar into fermentation products. The supply of oxygen through the membrane is controlled such that the oxygen content within the biofilm or within a zone in the base material mixture located next to the membrane and containing the biofilm decreases with increasing distance from the membrane to a level at which anaerobic condition are established, preferably decreases to approximately zero, so that the conditions in the base material mixture in the fermentation compartment beyond this zone are anaerobic. The fermentation products are removed from the fermentation compartment by transporting them through the membrane into the oxygen supply compartment. The fermentation products are removed from the oxygen supply compartment and separated from a gas or liquid phase, e.g. by condensation, adsorption or distillation. The oxygen and/or fermentation products are transported through the membrane by solution diffusion process. Preferred Arrangement: The reactor contains a unit for continuously or discontinuously supplying gaseous oxygen or oxygen dissolved in a liquid into the oxygen supply compartment, and a unit for continuously or discontinuously supplying a base material mixture containing organic feedstock into the fermentation compartment. The membrane is a tubular component and an oxygen supply compartment lies outside the tubular membrane, and the fermentation compartment lies in the tube-like space within the tubular membrane or vice versa.