A process for the catalytic hydrodeoxygenation of biomass pyrolysis oil and/or of the ligneous organic phase resulting from the phase separation of biomass pyrolysis oil to which water has been added, comprising a plurality of catalytic beds arranged in series and distributed in one or more reactors which is/are equipped with means for controlling the temperature, and characterized by: • the pressure in the HDO reactor or reactors is between 5 and 20 MPa, • the injection of the pyrolysis oil at the top of the 1 st catalytic bed, • the fractional injection of the hydrogen: • the 1 st injection of hydrogen is carried out at the top of the 1 st catalytic bed by controlling the inlet temperature of the 1 st catalytic bed between 120 and 180 °C by the temperature and/or the flow rate of the H 2 injection, • the other injection or injections of H 2 being carried out between 2 catalytic beds and being chosen so that the temperature difference ΔTmax thus corresponding to the temperature variation of the catalytic bed situated between two successive H 2 injections does not exceed 50°C, ΔTmax ≤ 50°C, and wherein the oulet temperature of the final catalytic bed is controlled by the temperature and/or the flow rate of the different injections of H 2: ∘ between 320 and 380°C, the process comprising at least 4 H 2 injections, when the HDO is extensive, the liquid organic phase resulting from the final HDO catalytic bed comprising less than 10% w/w of the initial amount of oxygen present in the pyrolysis oil employed or when the HDO is total the organic phase at the outlet of the final catalytic bed no longer comprises oxygen, ∘ between 180 and 320°C when the HDO is partial, the liquid organic phase resulting from the final HDO catalytic bed comprising between 10% and 90% w/w of the initial amount of oxygen present in the pyrolysis oil employed, • the separation of the liquid effluents at the outlet of the final catalytic bed into a liquid aqueous phase and an organic phase, it being possible for a portion of the organic phase optionally to be recycled in the reactor, for example to be reinjected with the pyrolysis oil, said process operating continuously. • the pressure in the HDO reactor or reactors is between 5 and 20 MPa, • the injection of the pyrolysis oil at the top of the 1 st catalytic bed, • the fractional injection of the hydrogen: • the 1 st injection of hydrogen is carried out at the top of the 1 st catalytic bed by controlling the inlet temperature of the 1 st catalytic bed between 120 and 180 °C by the temperature and/or the flow rate of the H 2 injection, • the other injection or injections of H 2 being carried out between 2 catalytic beds and being chosen so that the temperature difference ΔTmax thus corresponding to the temperature variation of the catalytic bed situated between two successive H 2 injections does not exceed 50°C, ΔTmax ≤ 50°C, and wherein the oulet temperature of the final catalytic bed is controlled by the temperature and/or the flow rate of the different injections of H 2: ∘ between 320 and 380°C, the process comprising at least 4 H 2 injections, when the HDO is extensive, the liquid organic phase resulting from the final HDO catalytic bed comprising less than 10% w/w of the initial amount of oxygen present in the pyrolysis oil employed or when the HDO is total the organic phase at the outlet of the final catalytic bed no longer comprises oxygen, ∘ between 180 and 320°C when the HDO is partial, the liquid organic phase resulting from the final HDO catalytic bed comprising between 10% and 90% w/w of the initial amount of oxygen present in the pyrolysis oil employed, ∘ between 320 and 380°C, the process comprising at least 4 H 2 injections, when the HDO is extensive, the liquid organic phase resulting from the final HDO catalytic bed comprising less than 10% w/w of the initial amount of oxygen present in the pyrolysis oil employed or when the HDO is total the organic phase at the outlet of the final catalytic bed no longer comprises oxygen, ∘ between 180 and 320°C when the HDO is partial, the liquid organic phase resulting from the final HDO catalytic bed comprising between 10% and 90% w/w of the initial amount of oxygen present in the pyrolysis oil employed, • the separation of the liquid effluents at the outlet of the final catalytic bed into a liquid aqueous phase and an organic phase, it being possible for a portion of the organic phase optionally to be recycled in the reactor, for example to be reinjected with the pyrolysis oil,