The invention describes a process for start-up of a hydrotreatment or hydroconversion unit carried out in the presence of hydrogen, in at least 2 catalytic beds, process in which At least one bed contains at least one presulfurized and preactivated catalyst and at least one catalytic bed that contains a catalyst whose catalytic metals are in oxidized form, A so-called starting feedstock, which is a hydrocarbon fraction that contains at least 0.5% by weight of sulfur, lacking olefinic compounds and not containing an added sulfur-containing compound, passes through a first catalytic bed that contains said presulfurized and preactivated catalyst and then passes through at least one catalytic bed that contains a catalyst whose catalytic metals are in oxidized form, And the first presulfurized and preactivated catalyst bed reaches a temperature of at least 220° C.