A process for the conversion of a heavy hydrocarbon feed, said process comprising the following steps: a) a step for hydroconversion of the heavy hydrocarbon feed in the presence of hydrogen in at least one or more three-phase reactors disposed in series or in parallel, containing at least one hydroconversion catalyst, the hydroconversion step a) being carried out under an absolute pressure in the range 2 to 35 MPa, a temperature in the range 300°C to 550°C, and under a quantity of hydrogen mixed with the feed in the range 50 to 5000 normal cubic metres (Nm 3) per cubic metre (m 3) of feed, in a manner such as to obtain a liquid effluent with a reduced Conradson carbon, metals, sulphur and nitrogen content, b) one or more optional steps for separating the effluent obtained from step a) in order to obtain at least one light liquid fraction boiling at a temperature of less than 350°C and a heavy liquid fraction boiling at a temperature of more than 350°C, c) a step for hydroconversion of the liquid effluent obtained from the hydroconversion step a) in the case in which the separation step b) is not carried out, or of the heavy liquid fraction obtained from the separation step b) when said step b) is carried out, in the presence of hydrogen in at least one or more three-phase reactors disposed in series or in parallel, containing at least one hydroconversion catalyst, the hydroconversion step c) being carried out under an absolute pressure in the range 2 to 38 MPa, at a temperature in the range 300°C to 550°C, and under a quantity of hydrogen in the range 50 to 5000 normal cubic metres (Nm 3) per cubic metre (m 3) of liquid feed under standard temperature and pressure conditions, in which process the overall hourly space velocity employed is in the range 0.05 to 0.09 h -1, and in which the hydroconversion catalyst of step a) and step c) is a catalyst comprising an alumina support and at least one metal from group VIII selected from nickel and cobalt, said element from group VIII being used in association with at least one metal from group VIB selected from molybdenum and tungsten, and is used in the form of extrudates or beads. a) a step for hydroconversion of the heavy hydrocarbon feed in the presence of hydrogen in at least one or more three-phase reactors disposed in series or in parallel, containing at least one hydroconversion catalyst, the hydroconversion step a) being carried out under an absolute pressure in the range 2 to 35 MPa, a temperature in the range 300°C to 550°C, and under a quantity of hydrogen mixed with the feed in the range 50 to 5000 normal cubic metres (Nm 3) per cubic metre (m 3) of feed, in a manner such as to obtain a liquid effluent with a reduced Conradson carbon, metals, sulphur and nitrogen content, b) one or more optional steps for separating the effluent obtained from step a) in order to obtain at least one light liquid fraction boiling at a temperature of less than 350°C and a heavy liquid fraction boiling at a temperature of more than 350°C, c) a step for hydroconversion of the liquid effluent obtained from the hydroconversion step a) in the case in which the separation step b) is not carried out, or of the heavy liquid fraction obtained from the separation step b) when said step b) is carried out, in the presence of hydrogen in at least one or more three-phase reactors disposed in series or in parallel, containing at least one hydroconversion catalyst, the hydroconversion step c) being carried out under an absolute pressure in the range 2 to 38 MPa, at a temperature in the range 300°C to 550°C, and under a quantity of hydrogen in the range 50 to 5000 normal cubic metres (Nm 3) per cubic metre (m 3) of liquid feed under standard temperature and pressure conditions, in which process the overall hourly space velocity employed is in the range 0.05 to 0.09 h -1, and in which the hydroconversion catalyst of step a) and step c) is a catalyst comprising an alumina support and at least one metal from group VIII selected from nickel and cobalt, said element from group VIII being used in association with at least one metal from group VIB selected from molybdenum and tungsten, and is used in the form of extrudates or beads.