TECHNOLOGY FOCUS - BIOLOGY - Preferred Components: The crude vegetable or animal oil comprises 95-98 wt.% of triglycerides and 2-5 wt.% of free fatty acids, mono- and diglycerides, phospholipids, tocopherols, sterols, natural dyes and odorous compounds and a compound such as phosphorus, magnesium, calcium, iron and/or zinc in concentrations of up to 2500 ppm, in the form of phospholipids and/or sterols in the case of phosphorus, magnesium and calcium present in the pigments in the case of magnesium and as free sterols and/or soap in the case of iron and/or zinc. Preferred Process: The crude vegetable or animal is pre-refined before the pretreatment process, the prerefining of the crude oil comprising: degumming comprising removing at least a portion of phospholipids or mucilages by precipitation in the presence of acidulated water; neutralizing the degummed oil to neutralize at least one part of free fatty acid present in the oil, in the presence of a sodium hydroxide solution; washing using water to remove the traces of sodium salt; and drying under vacuum.    TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Method: The pretreatment is carried out at a temperature of 160-250 degrees C, under a pressure of 0.3-1 MPa, with a residence time of 0.2-1.5 hour. The pretreatment step is carried out in a reactor with multiple fixed beds placed in parallel and interchangeable. Preferred Components: The adsorbents used in the step (a) of pretreatment step are alumina, optionally activated, and silica-alumina. The adsorbents comprise 100% of the porous refractory oxide comprising alumina, optionally activated and silica-alumina. The adsorbents are present in the form of spherical or extrudates with a diameter of 0.5-10 mm. The adsorbent has a macropore volume, measured by mercury intrusion, a volume of pores whose average diameter is greater than 500A?, of greater than 0.1 ml/g, a total pore volume of greater than 0.60 ml/g and a specific surface area expressed in SBET of 30-320 m2/g. The fixed bed catalyst used in step (b) is a hydrotreatment catalyst having hydro-dehydrogenating function comprising at least one metal of group VIII and/or group VIB and a support comprising alumina, silica, silica-alumina, magnesia, clay and mixtures of at least two of the minerals. In the production of the middle distillates base, the content of the nickel oxide is 0.5-10 wt.%, preferably 1-30 wt.% of the catalyst.