A catalytic process of hydrorefining or hydroconversion of a hydrocarbon-containing feedstock operating at a temperature comprised between 180 and 450° C., a total pressure of 0.5 to 30 MPa, an hourly volume rate of 0.1 to 20 h−1, in the presence of hydrogen with a hydrogen/liquid feedstock ratio of 50 to 2000 Nl/I, wherein the catalyst is supported catalyst, the said catalyst comprising:
- a porous support constituted by an organic-inorganic hybrid material (OIHM), the said OIHM having a covalent bond between the organic and inorganic phases, the said bond conforming to the formula M-O—Z—R where M represents at least one metal constituting the inorganic phase, Z at least one heteroelement from phosphorus and silicon from one or more organic precursor(s) and R an organic fragment of alkyl, aryl, alkoxy, aryl-alkyl type, saturated or not, branched or not, and bearing or not one or more organic functional groups,
- at least one metal of group VIB and/or of group VB and/or of group VIII, the metal of group VIB being chosen from chromium, molybdenum and tungsten, the metal of group VB from vanadium, niobium and the metal of group VIII from iron, cobalt, nickel, ruthenium, palladium, osmium, iridium and platinum,
- said catalyst having an active sulphide phase with the provision that the catalyst contains in % by weight, relative to the mass of the catalyst in oxide form, from 0.01 to 40% by weight of molybdenum oxide or tungsten oxide, from 0.01 to 25% by weight of cobalt oxide or nickel oxide, and from 0.01 to 15% by weight of P2O5.