TECHNOLOGY FOCUS - BIOLOGY - Preferred Process: The lignocellulosic biomass and/or their constituents including cellulose, hemicellulose and/or lignin undergo a pretreatment comprising at least one of: a drying stage carried out at 250 degrees C (preferably below 200 degrees C), and/or a stage of roasting, where the roasting is carried out at 200-300 degrees C (preferably 225-275 degrees C) in the absence of air; and a grinding stage. The algae are subjected to a pre-treatment comprising at least one of a demineralization stage, a drying stage carried out at below 250 degrees C (preferably below 200 degrees C), and a grinding stage. Preferred Components: The particles of biomass have a water content of 1-50%, preferably 5-10% and a particle size of less than 600 (preferably less than 150) microns.    TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Components: The catalyst comprises: group VIII metal comprising nickel, palladium, platinum, cobalt, rhodium and/or ruthenium; and optionally group VIB metal comprising molybdenum and/or tungsten, on an amorphous mineral support comprising alumina, silica, silica-aluminas, magnesia, clays and mixtures of at least two of these minerals.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Process: The first hydroconversion stage takes place at 325-375/ degrees C and a total pressure of 16-20 MPa, and the second hydroconversion stage takes place at 350-425 degrees C and a total pressure of 16-20 MPa, where the temperature of the second hydroconversion stage is at least 10 degrees C higher than that of the first hydroconversion stage. The solvent is preferably a solvent obtained from a separation stage carried out after the two hydroconversion stages, and the solvent is recycled upstream of the two hydroconversion stages. The biomass is co-processed with a feed including petroleum residues, petroleum crudes, synthetic crudes, topped petroleum crudes, deasphalted oils, resins from deasphalting, asphalts from deasphalting, derivatives from petroleum processing, bituminous sands or their derivatives, bituminous shales or their derivatives, coal or liquefied products obtained from coal by hydroliquefaction, hydrocarbon and/or polymer industrial waste, household organic or plastic waste, vegetable or animal oils and fats, tars and residues that can be optionally upgraded with difficulty (originating from gasification of biomass), coal or petroleum residues, charcoal and/or pyrolysis oil. The effluent obtained at the end of the first hydroconversion stage is subjected to separation of the light fraction and at least a proportion, preferably all, of the residual effluent is treated in the second hydroconversion stage. The effluent obtained at the end of the second hydroconversion stage undergoes a separation stage for separating a gaseous phase, an aqueous phase, at least one light fraction of liquid hydrocarbons of the naphtha, kerosene and/or diesel, a vacuum gas oil heavy fraction of hydrocarbons, a vacuum residue fraction and a solid fraction that can be in the vacuum residue. The vacuum gas oil heavy fraction of hydrocarbons is recycled wholly or partly to the stage for preparation of a suspension. In the process: at least partially the light fraction(s) and/or the heavy fraction(s) obtained after separation undergo a hydrotreating and/or hydrocracking stage; and at least a proportion of the effluent obtained at the end of the second hydroconversion stage directly undergoes hydrotreating and/or hydrocracking stage without intermediate decompression. The spent catalyst from the first hydroconversion stage is withdrawn wholly or partly directly to the second hydroconversion stage, or vise versa. Preferred Components: The solvent comprises vacuum distillate (preferably vacuum gas oil), and optionally atmospheric distillate, where the solvent/biomass weight ratio is 0.1:3. EXAMPLE - No suitable example given.