The invention relates to a process for converting heavy hydrocarbon feedstocks, at least 50% by weight of which boils at a temperature of at least 300 ° C., and in particular residues under vacuum. The feeds are subjected to a first step a) of deep hydroconversion, optionally followed by a step b) of separation of a light fraction, and a heavy residual fraction resulting from step b) is obtained, of which at least 80% by weight has a boiling point of at least 250 ° C. Said faction resulting from step b) or the effluent resulting from step a) is then subjected to a second step c) of deep hydroconversion. The overall hourly space velocity for steps a) to c) is less than 0.1 hr-1. The effluent from step c) is fractionated to separate a light fraction. The heavy fraction obtained, 80% by weight of which boils at a temperature of at least 300 ° C., is sent to a deasphalting step e). The DAO deasphalted fraction is then preferably converted in a step f) chosen from hydroconversion in an ebullating bed, catalytic cracking in a fluidized bed and hydrocracking in a fixed bed.
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