This invention relates to a catalyst for hydrorefining and/or hydroconversion of hydrocarbon-containing feedstocks that contain compounds whose boiling point is higher than 520.degree. C. and that contain sulfur and possibly metals, as well as its use in hydrorefining and/or hydroconversion processes of heavy feedstocks. A petroleum residue of atmospheric distillation (RA) or of vacuum distillation (RSV) or a deasphalted oil (DAO) are representative feedstocks of the feedstocks treated within the scope of this invention.