A continuous process for the treatment of a hydrocarbon feed containing at least one hydrocarbon fraction with a sulphur content of at least 0.1% by weight, an initial boiling temperature of at least 340°C and a final boiling temperature of at least 440°C, the process comprising the following steps: a) an hydrodemetallization step in the presence of the hydrocarbon feed and hydrogen and a hydrodemetallization catalyst in which at least two permutable reactors are carried out under the following operating conditions: - a temperature in the range 350°C to 430°C, - an absolute pressure in the range 11 MPa to 26 MPa, preferably in the range 14 MPa to 20 MPa, - a HSV (defined as the volumetric flow rate of the feed divided by the total volume of catalyst) in the range 0.1 h -1 to 5 h -1, preferably in the range 0.15 h -1 to 3 h -1, and more preferably in the range 0.2 h -1 to 2 h -1. b) a step for fixed bed hydrotreatment, comprising at least one reactor in which the effluent obtained from step a) is brought into contact with at least one hydrotreatment catalyst at a temperature in the range 350°C to 430°C and under an absolute pressure in the range 14 MPa to 20 MPa, c) a step for fixed bed hydrocracking the effluent obtained from the step b) in the presence of a hydrocracking catalyst, in which at least one by-passable reactor, i.e. a reactor which can be stopped by carrying out a by-pass while the other reactors of the unit are still operating is carried out under the following operating conditions: - temperature in the range 350°C to 430°C, the reactor being stopped as soon as the temperature of said by-passable reactor is between 405°C and 425°C, - absolute pressure in the range 14 MPa to 20 MPa, d) a step for separating the effluent obtained from the hydrocracking step c) in order to obtain at least one gaseous fraction and at least one heavy liquid fraction, said heavy liquid fraction being sent to an atmospheric distillation producing at least one atmospheric distillate and an atmospheric residue, a portion or the entirety of said atmospheric residue being sent to a vacuum distillation producing a vacuum residue, said atmospheric and vacuum residues possibly being sent to a catalytic cracking process or in fact being used as a fuel oil or fuel oil base. a) an hydrodemetallization step in the presence of the hydrocarbon feed and hydrogen and a hydrodemetallization catalyst in which at least two permutable reactors are carried out under the following operating conditions: - a temperature in the range 350°C to 430°C, - an absolute pressure in the range 11 MPa to 26 MPa, preferably in the range 14 MPa to 20 MPa, - a HSV (defined as the volumetric flow rate of the feed divided by the total volume of catalyst) in the range 0.1 h -1 to 5 h -1, preferably in the range 0.15 h -1 to 3 h -1, and more preferably in the range 0.2 h -1 to 2 h -1. - a temperature in the range 350°C to 430°C, - an absolute pressure in the range 11 MPa to 26 MPa, preferably in the range 14 MPa to 20 MPa, - a HSV (defined as the volumetric flow rate of the feed divided by the total volume of catalyst) in the range 0.1 h -1 to 5 h -1, preferably in the range 0.15 h -1 to 3 h -1, and more preferably in the range 0.2 h -1 to 2 h -1. b) a step for fixed bed hydrotreatment, comprising at least one reactor in which the effluent obtained from step a) is brought into contact with at least one hydrotreatment catalyst at a temperature in the range 350°C to 430°C and under an absolute pressure in the range 14 MPa to 20 MPa, c) a step for fixed bed hydrocracking the effluent obtained from the step b) in the presence of a hydrocracking catalyst, in which at least one by-passable reactor, i.e. a reactor which can be stopped by carrying out a by-pass while the other reactors of the unit are still operating is carried out under the following operating conditions: - temperature in the range 350°C to 430°C, the reactor being stopped as soon as the temperature of said by-passable reactor is between 405°C and 425°C, - absolute pressure in the range 14 MPa to 20 MPa, - temperature in the range 350°C to 430°C, the reactor being stopped as soon as the temperature of said by-passable reactor is between 405°C and 425°C, - absolute pressure in the range 14 MPa to 20 MPa, d) a step for separating the effluent obtained from the hydrocracking step c) in order to obtain at least one gaseous fraction and at least one heavy liquid fraction, said heavy liquid fraction being sent to an atmospheric distillation producing at least one atmospheric distillate and an atmospheric residue, a portion or the entirety of said atmospheric residue being sent to a vacuum distillation producing a vacuum residue, said atmospheric and vacuum residues possibly being sent to a catalytic cracking process or in fact being used as a fuel oil or fuel oil base.