A process for converting carbon material into fuel bases comprising two liquefaction stages in the presence of hydrogen in a boiling-bed reactor containing a supported catalyst and integrating a hydrogen production stage generated by non-fossil sources that do not emit CO2. The hydrogen production stage comprises the gasification of biomass and/or the decomposition of water, hydrochloric acid, hydrogen chloride or hydrogen sulfide by thermal, electrolytic, chemical or biological processes. The thus produced hydrogen is sent into at least one of the liquefaction stages.