Heavy hydrocarbon charges are converted in a deasphalting section in the presence of solvents and obtaining two streams, one consisting of deasphalted oil and the other one containing asphaltenes, mixing the deasphalted oil stream with a hydrogenation catalyst and passing the thus obtained mixture to a hydroprocessing section containing hydrogen or hydrogen/H2S, mixing the stream consisting of asphaltenes discharged from the deasphalting section with an appropriate hydrogenation catalyst and passing the obtained mixture to a second hydroprocessing section where it is reacted with hydrogen or a mixture of hydrogen and H2S, passing both the stream containing the reaction product with dispersed catalyst from the hydroprocessing section and the stream containing the reaction product with dispersed catalyst from the second hydroprocessing section, to one or more distillation or flash stages, whereby the more volatile fractions are separated from the distillation residue (tar) or from the liquid discharged from the flash unit, sending the distillation residue (tar) or the liquid discharged from the flash unit, containing the catalyst in the dispersed phase, with a high content of metal sulphides, produced by demetallization of the charge, to a second deasphalting section thereby obtaining deasphalted oil and asphaltenes.