Abstract: A process is described for hydroconversion of a mixture of organic oils of different origins in a conventional hydrotreatment unit, constituted by at least two catalyst beds, under moderately severe process conditions to obtain diesel fuel oil. The process includes injection of a stream of oil of animal or plant origin, with independently adjusted flow rates, from the second catalyst bed of the hydrotreatment unit onwards, in accordance with the variations in temperature observed in each of the catalyst beds after the first bed. The process is applicable to conventional hydrotreatment units, and makes it possible to overcome the effects of the highly exothermic nature of hydroconversion reactions in oils of animal and/or plant origin in hydrotreatment process for obtaining specified diesel fuel oil.