NOVELTY - Hydroliquefaction of biomass including algae, lignocellulosic biomass and/or at least one constituent of lignocellulosic biomass including cellulose, hemicellulose and/or lignin for producing fuel bases comprises: (a) stage of preparation of suspension of particles of biomass in solvent; (b) first stage of hydroconversion in presence of hydrogen of suspension in at least one reactor containing ebullating bed catalyst; and (c) second stage of hydroconversion in the presence of hydrogen of a proportion of effluent in at least one reactor containing ebullating bed catalyst.    USE - The method is useful for hydroliquefaction of biomass including algae, lignocellulosic biomass and/or at least one constituent of lignocellulosic biomass including cellulose, hemicellulose and/or lignin for producing fuel bases.    ADVANTAGE - The process: provides high yields of fuel bases; reduces the production of phenols and increases the degree of conversion and quality of the biofuels, due to the better deoxygenation of the biomass by high hydrogen pressure; and provides isothermal operation, as it utilizes ebullating bed catalyst.    DETAILED DESCRIPTION - Hydroliquefaction of biomass including algae, lignocellulosic biomass and/or at least one of constituent of lignocellulosic biomass including cellulose, hemicellulose and/or lignin for producing fuel bases comprises: (a) a stage of preparation of a suspension of particles of biomass in a solvent, preferably a hydrogen donor solvent: (b) a first stage of hydroconversion in the presence of hydrogen of the suspension in at least one reactor containing an ebullating bed catalyst and operating at 300-440 degrees C, at a total pressure of 15-25 MPa, at an hourly mass velocity of 0.1-5 per hour and at a hydrogen/feed ratio of 0.1- 2 Nm3/ kg; and (c) a second stage of hydroconversion in the presence of hydrogen of at least a proportion of the effluent obtained in stage (b) in at least one reactor containing an ebullating bed catalyst and operating at 350-470 degrees C, at a total pressure of 15-25 MPa, at an hourly mass velocity of 0.1-5 per hour and a hydrogen/feed ratio of 0.1-2 Nm3/kg.