TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Process: The first hydroconversion step operates at a temperature of 325-375 degrees C, at a total pressure of 16-20 MPa, and the second hydroconversion step operates at a temperature of 350-425 degrees C and a total pressure of 16-20 MPa. The temperature of the second hydroconversion step is at least 10 degrees C higher than that of the first hydroconversion step. The lignocellulosic biomass or one or more constituents of lignocellulosic biomass comprising cellulose, hemicellulose and/or lignin undergo pre-treatment comprising: drying, which is carried out at a temperature of less than 250 degrees C, preferably less than 200 degrees C, and/or a roasting step, where the roasting is carried out at a temperature of 200-300 degrees C, preferably 225-275 degrees C in the absence of air; and grinding step. The effluent obtained from the first hydroconversion is subjected to a separation of the light fraction and at least a part, preferably totality of the residual effluent is treated in the second hydroconversion step. The effluent obtained from the second hydroconversion step undergoes a separation step for separating a gas phase, an aqueous phase, at least one light fraction of liquid hydrocarbons such as naphtha, kerosene and/or diesel, heavy fraction of vacuum gas oil, vacuum residue fraction and a solid fraction which can be in the vacuum residue. The heavy fraction of vacuum gas oil is recycled entirely or partly towards the step of forming a suspension. The at least partially the light fraction and/or the heavy fraction obtained after separation undergo hydrotreatment and/or hydrocracking step. At least one part of the effluent obtained after the second hydroconversion directly undergoes hydrotreatment and/or hydrocracking step without intermediary decompression. The used catalyst of the first hydroconversion is directly withdrawn in the second hydroconversion step or in which the used catalyst of the second hydroconversion step is directly withdrawn in the first hydroconversion step. Preferred Components: The biomass particles have humidity of 1-50%, preferably 5-10% and a particle size of less than 600 microns, preferably less than 150 microns. The solvent comprises vacuum distillate, preferably vacuum gas oil, and optionally atmospheric distillate, where the weight ratio of solvent/biomass is 0.1-3, the solvent is a solvent obtained from a separation step carried out after two hydroconversion steps, and the solvent is recycled upstream of the two hydroconversion steps. The lignocellulosic biomass comprises cellulose, hemi-cellulose and/or lignin. The lignocellulosic biomass or its one or more constituents are co-treated with a charge comprising petroleum residues, crude oils, synthetic crude, topped crude oils, deasphalted oils, deasphalting resins, deasphalting asphalts, derivatives from conversion of petroleum, bituminous sands or their derivatives, oil shale or their derivatives, coal, hydrocarbon waste and/or industrial polymer, organic waste or household plastics, vegetable or animal oil and fat, tars and non- or poorly recovered recyclable residues obtained from biomass gasification, coal or petroleum residues, coal from wood, pyrolysis oil or mixtures of such charges. The catalyst comprises a group VIII metal comprising nickel, palladium, platinum, cobalt, rhodium and/or ruthenium, optionally a group VIB metal comprising molybdenum and/or tungsten group, on an amorphous mineral support comprising alumina, silica, silica-aluminas, magnesia, clays and mixtures of at least two of the minerals.