Catalytic system comprising at least two catalysts, in which - the first catalyst comprises - a content of metal(s) from group VIB of between 2% and 9% by weight of trioxide of the metal (s) from group VIB relative to the total mass of the catalyst, and - at least two metals from group VIII, one of which is the major promoter known as VIII-1 and the other is known as the co-promoter VIII-2, the sum of the contents of metals from group VIII is between 0.3% and 2% by weight of oxide of the metals from group VIII relative to the total mass of the catalyst and - the second catalyst comprises - a content of metal(s) from group VIB strictly more than 9% and less than 17% by weight of trioxide of the metal(s) from group VIB relative to the total mass of the catalyst, and - at least two metals from group VIII, one of which is the major promoter known as VIII-1 and the other is known as the co-promoter VIII-2, the sum of the contents of metals from group VIII is strictly more than 2% and less than 5% by weight of oxide of the metals from group VIII relative to the total mass of the catalyst, in said first and second catalysts, the metal from group VIB being molybdenum and the metals from group VIII being nickel and cobalt, in said first and second catalysts, the elements from group VIII being present in the proportions defined by the atomic ratio [VIII-1/(VIII-1+VIII-2)], said atomic ratio being between 0.5 and 0.85, said atomic ratio being identical for said first and second catalysts, in said first and second catalysts, the respective amounts of metal (s) from group VIB and of metals from group VIII are such that the atomic ratio of metals from group VIII to metal (s) from group VIB (VIII/VIB) is between 0.3:1 and 0.7:1, said atomic ratio being identical for said first and second catalysts. - the first catalyst comprises - a content of metal(s) from group VIB of between 2% and 9% by weight of trioxide of the metal (s) from group VIB relative to the total mass of the catalyst, and - at least two metals from group VIII, one of which is the major promoter known as VIII-1 and the other is known as the co-promoter VIII-2, the sum of the contents of metals from group VIII is between 0.3% and 2% by weight of oxide of the metals from group VIII relative to the total mass of the catalyst and - a content of metal(s) from group VIB of between 2% and 9% by weight of trioxide of the metal (s) from group VIB relative to the total mass of the catalyst, and - at least two metals from group VIII, one of which is the major promoter known as VIII-1 and the other is known as the co-promoter VIII-2, the sum of the contents of metals from group VIII is between 0.3% and 2% by weight of oxide of the metals from group VIII relative to the total mass of the catalyst and - the second catalyst comprises - a content of metal(s) from group VIB strictly more than 9% and less than 17% by weight of trioxide of the metal(s) from group VIB relative to the total mass of the catalyst, and - at least two metals from group VIII, one of which is the major promoter known as VIII-1 and the other is known as the co-promoter VIII-2, the sum of the contents of metals from group VIII is strictly more than 2% and less than 5% by weight of oxide of the metals from group VIII relative to the total mass of the catalyst, in said first and second catalysts, the metal from group VIB being molybdenum and the metals from group VIII being nickel and cobalt, in said first and second catalysts, the elements from group VIII being present in the proportions defined by the atomic ratio [VIII-1/(VIII-1+VIII-2)], said atomic ratio being between 0.5 and 0.85, said atomic ratio being identical for said first and second catalysts, in said first and second catalysts, the respective amounts of metal (s) from group VIB and of metals from group VIII are such that the atomic ratio of metals from group VIII to metal (s) from group VIB (VIII/VIB) is between 0.3:1 and 0.7:1, said atomic ratio being identical for said first and second catalysts. - a content of metal(s) from group VIB strictly more than 9% and less than 17% by weight of trioxide of the metal(s) from group VIB relative to the total mass of the catalyst, and - at least two metals from group VIII, one of which is the major promoter known as VIII-1 and the other is known as the co-promoter VIII-2, the sum of the contents of metals from group VIII is strictly more than 2% and less than 5% by weight of oxide of the metals from group VIII relative to the total mass of the catalyst,