Medicinal white oils and medicinal paraffins are prepared from petroleum fractions containing aromatics and nitrogen, oxygen and sulfur compounds, e.g. light and heavy atmospheric gas oils, vacuum gas oils and residues, which have been pretreated in a first stage by acid treatment or catalytic hydrogenation, by hydrogenation in a second stage over a nickel-containing catalyst under from 50 to 200 bar and at elevated temperatures, by a process in which the catalyst used in the second stage and present in the oxide form is reduced with a hydrogen-containing gas, passivated and then again activated with hydrogen, before the hydrogenation to medicinal white oils or paraffins is carried out.