NOVELTY - The anaerobic digestion process comprises extracting a main product from a first vegetable material. The anaerobic digestion is carried out in a liquid phase containing suspension materials such as a co-product using a high yield digester including a fluidized, recirculated or expanded granular sludge bed, a culture reactor fixed on a movable/immovable support and having a fluidized biomass bed, and Anapulse, Anaflux and Anafiz digesters. The effluent (40-95%) from the digestion is subjected to stripping and decarbonation. A fraction of decarbonated effluent is recycled.    USE - The process is useful for anaerobic digestion of water from a liquid phase containing suspension materials such as a co-product, and for the production of biofuel.    ADVANTAGE - The process ensures economical and rapid anaerobic digestion of water from a liquid phase containing suspension materials such as a co-product with high performance and without risk of infection and blockage in biological activity, and allows large production of high quality biofuel with less number of process steps.    DETAILED DESCRIPTION - The anaerobic digestion process comprises extracting a main product from a first vegetable material. The anaerobic digestion is carried out in a liquid phase containing suspension materials such as a co-product using a high yield digester including a fluidized, recirculated or expanded granular sludge bed, a culture reactor fixed on a movable/immovable support and having a fluidized biomass bed, and Anapulse, Anaflux and Anafiz digesters. The effluent (40-95%) from the digestion is subjected to stripping and decarbonation. A fraction of decarbonated effluent is recycled to the digestion process and then filtered to obtain bacteria having a size of 0.2 mu m. The recycled fraction of the effluent comprises 0-400 mass% of residues and phlegm. The filtration is carried out by reverse osmosis. The fraction of decarbonated effluent is subjected to biological treatment for carbonated and nitrogenized pollution and a physio-chemical treatment for phosphorized pollution, before the filtration step. Carbon dioxide gas is used for neutralization of lime to produce carbonated lime and for partial replacement of an acid for extraction of main product. The filtration provides a retentate subjected to evaporation-concentration. Condensates are recovered after evaporation concentration and used as water.    DESCRIPTION OF DRAWING(S) - The figure shows a flowchart of a process for producing a product and a co-product in liquid phase (Drawing includes non-English language text).