Abstract: Two-stage low pressure catalytic hydrotreatment of heavy petroleum hydrocarbons having a high content of contaminants (metals and asphaltenes), is conducted under operating conditions with low-pressure, in a fixed bed or ebullated bed reactor to limit the formation of sediments and sludge in the product and obtain a hydrotreated hydrocarbon of improved properties, with levels of contaminants, API gravity and distillates within the ranges commonly reported in the feedstocks typical to refining schemes. A hydrotreatment catalyst, whose principal effect is the hydrodemetallization and the hydrocracking of asphaltenes of the heavy hydrocarbons of petroleum is used in the first stage, and the second reaction stage employs a hydrotreatment catalyst for a deeper effect of hydrodesulfurization of the heavy petroleum hydrocarbon whose content of total sulfur is reduced to a level required for its treatment in the conventional refining process or for its sale as a hydrocarbon of petroleum with improved properties.