A process for direct hydroliquefaction of biomass selected from algae, lignocellulosic biomass and/or of one or more constituents of lignocellulosic biomass selected from the group comprising cellulose, hemicellulose and/or lignin for producing fuel bases comprising two successive hydroconversion stages under high hydrogen pressure in ebullating bed reactors. Hydroconversion takes place in the presence of a supported catalyst of the type for hydroconversion of petroleum residue and a suspension composed of the biomass and a solvent, preferably a hydrogen donor solvent and preferably recycled from the process. The biomass can undergo a pretreatment of drying and/or roasting and/or grinding and/or demineralization prior to hydroliquefaction.