NOVELTY - Hydroconversion of biomass (1) to produce fuel bases comprises: (a) preparing a suspension of biomass particles in a solvent; (b) hydroconversion of the suspension in the presence of hydrogen in at least one reactor (3) containing a supported catalyst in an ebullated hydroconversion bed and hydroconversion in the presence of hydrogen in at least one reactor containing a slurry of catalyst in it and optionally a solid additive; (c) separating the effluent from the two stages of hydroconversion for separating gas, a residual fraction and one or more liquid fractions devoid of solid fraction.    USE - The process is useful for hydroconversion of biomass comprising algae, lignocellulosic biomass and/or one or more components of lignocellulosic biomass comprising cellulose, hemicellulose or lignin to produce fuel bases.    ADVANTAGE - The process provides higher conversion rates compared to the use of the two hydroconversion technologies separately, while maintaining an excellent rate of deoxygenation. The operability, in particular the duration of the cycle, is significantly improved. The process involves flexible operating conditions. The catalysts used in the two technologies are different and thus do not present the same aptitude for the coking nor do not completely support the same reactions of hydrotreating, hydrocracking or hydroconversion. The process provides liquid products of good quality with an oxygen content of 0.1-5% at low treatment and production cost.    DETAILED DESCRIPTION - Hydroconversion of biomass (1) comprising algae, lignocellulosic biomass and/or one or more components of lignocellulosic biomass comprising cellulose, hemicellulose or lignin to produce fuel bases comprises: (a) preparing a suspension of biomass particles in a solvent; (b) hydroconversion of the suspension in the presence of hydrogen in at least one reactor (3) containing a supported catalyst in an ebullated hydroconversion bed and hydroconversion in the presence of hydrogen in at least one reactor containing a slurry of catalyst in it and optionally a solid additive; (c) separating the effluent from the two stages of hydroconversion for separating gas, a residual fraction containing at least a portion of the solid particles of the slurry of catalyst, and one or more liquid fractions devoid of solids of naphtha, kerosene, gas oil and vacuum gas oil type.    DESCRIPTION OF DRAWING(S) - The figure shows the schematic view of the process for hydroconversion of biomass via the sequence of ebullated bed hydroconversion then slurry hydroconversion.    Biomass (1)    Furnace (3) Reactor containing a supported catalyst in an ebullated hydroconversion bed (2)    Crusher (22)    Chamber for forming suspension. (23)