TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Components: The catalyst in slurry is a sulfurized catalyst containing at least an element comprising molybdenum, iron, nickel, tungsten, cobalt, vanadium or ruthenium. The additive is inorganic oxides, spent catalysts containing at least one supported element of group VIII and/or at least one element of group VIB and/or carbon-containing solids with a low content of hydrogen. The additive has a particle size of lower than 1 mm. The supported catalyst comprises a metal of group VIII comprising nickel, palladium, platinum, cobalt, rhodium and/or ruthenium, optionally a metal of group VIB comprising molybdenum and/or tungsten on an amorphous inorganic support comprising alumina, silica, silica-alumina, magnesia and/or clays.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Process: The residual fraction containing at least a portion of the solid particles of the slurry of catalyst is partly or totally recycled directly to at least one hydroconversion step, preferably to the first hydroconversion step. The residual fraction containing the dispersed solid catalyst particles is recycled, in part or in whole, to the preparation of the slurry of catalyst after undergoing separation(s) and any process(es) for the preparation of catalytic precursors. The liquid fraction(s) devoid of solids obtained by at least a separation undergoes/undergo partly or entirely a stage of hydrotreating and/or hydrocracking via decompression. The liquid fraction(s) devoid of solids obtained by at least a separation undergoes/undergo partly or entirely a stage of hydrotreating and/or hydrocracking without decompression. The liquid fraction(s) devoid of solids and having a distillation point of 180-550 degrees C, preferably 200-550 degrees C is/are recycled, partly or entirely, as a solvent to the stage of preparation of the suspension. The liquid fraction(s) devoid of solids and exiting from the hydroconversion stage undergoes/undergo a hydrotreatment prior to its/their recycling in the suspension. The lignocellulosic biomass and/or one or more components of lignocellulosic biomass comprising cellulose, hemicellulose or lignin undergo a pretreatment including at least one of (a) a stage of drying and/or a stage of torrefaction, and (b) a stage of crushing. The algae undergo a pretreatment including at least one of (a) a stage of demineralization, (b) a stage of drying and (c) a stage of crushing. The biomass is co-treated with a substance comprising oil residues, synthetic crude oils, pollarded crude oils, deasphalted oils, deasphalted resins, deasphalted asphalts, derivatives of conversion process of oil, bituminous sands or their derivatives, bituminous shales or their derivatives, coal(s) or liquid products obtained by liquefaction, hydrocarbon waste and/or industrial polymeric waste, organic waste or domestic plastic waste, plant or animal oils and fats, tar and residues not or hardly undergo beneficiation resulting from the gasification of biomass, coal, gas or oil residues, charcoal, oil of pyrolysis, and/or activated sludge. The effluent resulting from the first stage of hydroconversion is subjected to a separation of a light fraction containing at least 90 vol.% of compounds boiling at most 300 degrees C, preferably at most 450 degrees C, and at least a portion, preferably all, of the residual effluent is treated in the second hydroconversion stage. The first and second hydroconversion stages are performed at a temperature of 300-440 degrees C, a total pressure of 2-35 MPa, at a mass hourly velocity of 0.1-5 per hour and at a hydrogen/charge ratio of 0.1-2 Nm3/kg.