TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Components: The first monometallic catalytic bed contains only one group VIB metal element, in oxide form, in a total concentration of 1-25 mass% in relation to a support consisting of meso and macro porosity material. The first catalytic bed contains the element Mo, or W. The support is selected from alumina, silica, silica/alumina, magnesium oxide and carbon.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Process: In the process (P1), the first catalytic bed is charged in the first fixed bed of a reactor of hydrotreating unit (HDT) unit. The first catalytic bed is charged in a pre-reactor of an HDT unit. The second catalytic bed for hydrotreating consists of a bimetallic catalyst capable of promoting the hydrogenation reactions of unsaturated hydrocarbon and removal of the heteroatomic components from the refinery stream of petroleum hydrocarbons. The bimetallic catalyst consists of group VIB metal oxide promoted by elements from group VIII in a support consisting of meso and macro porosity material. The VIB metal elements are selected from Mo and W and the elements from group VIII are selected from element Ni and Co, dispersed in a concentration of 1-25 mass% of the support. The hydrogen stream has a concentration of more than 90 vol.%. The hydrogen stream includes a recycle stream from the gaseous products of the process. The dilution stream includes a recycle stream from the gaseous products of the process. The concentration of hydrogen is adjusted upstream of each catalytic bed subsequent to the first. The concentration of hydrogen in the dilution stream is adjusted to replenish hydrogen consumed from the first reaction mixture upstream of each catalytic bed subsequent to the first. Preferred Components: The biomass oil consists of triglycerides and/or fatty acids with saturated carbon chains. The biomass oil consists of vegetable oils, algae oils and/or animal fat lipids. The vegetable oil is selected from soya oil, Barbados nut oil, castor oil, cottonseed oil, Brazilian palm tree oil, pine oil, sunflower oil, Barbados nut oil, palm oil, coconut oil, rapeseed oil, and/or peanut oil. The triglycerides have ester groups derived from fatty acids having 12-18C and/or the fatty acids have 12-18C carbon chain. EXAMPLE - No suitable example given.