NOVELTY - Production of lipids from biomass including at least one polysaccharide comprises: subjecting the biomass, including at least one polysaccharide to acid hydrolysis obtaining a first mixture comprising a first solid phase and a first aqueous phase; feeding the first aqueous phase to a fermentation device; subjecting the first solid phase to acid hydrolysis; feeding the second aqueous phase to the fermentation device; subjecting at least a part of the second fermentation broth to microfiltration obtaining a retentate and a permeate; and feeding the retentate to the fermentation device.    USE - The process is useful for producing lipids from biomass including at least one polysaccharide (claimed).    ADVANTAGE - The process efficiently produces lipids used in the production of biodiesel or green diesel which can be used as such or in a mixture with other fuels for motor vehicles.    DETAILED DESCRIPTION - Production of lipids from biomass including at least one polysaccharide comprises: subjecting the biomass, including at least one polysaccharide to acid hydrolysis obtaining a first mixture comprising a first solid phase and a first aqueous phase; feeding the first aqueous phase to a fermentation device in the presence of at least one oleaginous yeast obtaining a first fermentation broth comprising a first oleaginous cellular biomass; subjecting the first solid phase to acid hydrolysis or to enzymatic hydrolysis obtaining a second mixture comprising a second solid phase and a second aqueous phase; feeding the second aqueous phase to the fermentation device in the presence of the first fermentation broth obtaining a second fermentation broth comprising a second oleaginous cellular biomass including lipids; subjecting at least a part of the second fermentation broth to microfiltration obtaining a retentate and a permeate; and feeding the retentate to the fermentation device. An INDEPENDENT CLAIM is biodiesel or green diesel obtained from the lipids produced through the process.