A method of hydroprocessing a heavy hydrocarbon oil, comprising: (a) contacting in a first hydroprocessing step the heavy hydrocarbon oil with hydrogen in the presence of a first catalyst having activity for hydrocracking asphaltenes in the heavy hydrocarbon oil in order to produce a hydroprocessed heavy hydrocarbon oil having fewer asphaltenes than the heavy hydrocarbon feed, and (b) contacting the hydroprocessed heavy hydrocarbon oil with hydrogen in the presence of a second catalyst having activity for hydrodesulfurizing the hydroprocessed heavy hydrocarbon feed and a composition and pore size distribution different from the first catalyst; wherein (i) the first catalyst comprises a porous inorganic carrier loaded with 7 to 20 wt.% of the oxide of a Group VI(b) metal and 0.5 to 6 wt. % of the oxide of a Group VIII metal, respectively based on the weight of the catalyst, said catalyst having a specific surface area of 100 to 180 m 2 /g, a total pore volume of 0.55 ml/g or more, and a pore size distribution wherein the proportion of the volume of the pores having diameters of 200 10 -10 m (200 Å) and more is 50% or more based on the total pore volume, and the proportion of the volume of the pores having diameters of 2000 10 -10 m (2000 Å) and more is 10 to 30%, based on the total pore volume, (ii) the second catalyst is a supported catalyst, with the support containing 2 wt.% to 40 wt.% silica based on the total weight of the support and being loaded with 5 to 30 wt.% of the oxide of a Group VI(b) metal, and 0.5 to 30 wt % of the oxide of a Group VIII metal, respectively based on the weight of the catalyst, said catalyst having a specific surface area of 150 to 400 m 2 /g, and a total pore volume of 0.3 to 1.2 ml/g, a pore size distribution having a peak in the range of 40 10 -10 m (40 Å) diameter to 200 10 -10 m (200 Å) diameter, with said peak representing pores that together contain 35% to 90% of the total pore volume of the catalyst, and the pores of said peak within a diameter range of ± 20 10 -10 m (±20 Å) from the peak position contain at least 50% of the volume in the diameter range of 40 10 -10 m (40 Å) to 200 10 -10 m (200 Å). (a) contacting in a first hydroprocessing step the heavy hydrocarbon oil with hydrogen in the presence of a first catalyst having activity for hydrocracking asphaltenes in the heavy hydrocarbon oil in order to produce a hydroprocessed heavy hydrocarbon oil having fewer asphaltenes than the heavy hydrocarbon feed, and (b) contacting the hydroprocessed heavy hydrocarbon oil with hydrogen in the presence of a second catalyst having activity for hydrodesulfurizing the hydroprocessed heavy hydrocarbon feed and a composition and pore size distribution different from the first catalyst; (i) the first catalyst comprises a porous inorganic carrier loaded with 7 to 20 wt.% of the oxide of a Group VI(b) metal and 0.5 to 6 wt. % of the oxide of a Group VIII metal, respectively based on the weight of the catalyst, said catalyst having a specific surface area of 100 to 180 m 2 /g, a total pore volume of 0.55 ml/g or more, and a pore size distribution wherein the proportion of the volume of the pores having diameters of 200 10 -10 m (200 Å) and more is 50% or more based on the total pore volume, and the proportion of the volume of the pores having diameters of 2000 10 -10 m (2000 Å) and more is 10 to 30%, based on the total pore volume, (ii) the second catalyst is a supported catalyst, with the support containing 2 wt.% to 40 wt.% silica based on the total weight of the support and being loaded with 5 to 30 wt.% of the oxide of a Group VI(b) metal, and 0.5 to 30 wt % of the oxide of a Group VIII metal, respectively based on the weight of the catalyst, said catalyst having a specific surface area of 150 to 400 m 2 /g, and a total pore volume of 0.3 to 1.2 ml/g, a pore size distribution having a peak in the range of 40 10 -10 m (40 Å) diameter to 200 10 -10 m (200 Å) diameter, with said peak representing pores that together contain 35% to 90% of the total pore volume of the catalyst, and the pores of said peak within a diameter range of ± 20 10 -10 m (±20 Å) from the peak position contain at least 50% of the volume in the diameter range of 40 10 -10 m (40 Å) to 200 10 -10 m (200 Å).