This invention relates to doped catalysts on an aluminosilicate substrate with a low content of macropores and the hydrocracking/hydroconversion and hydrotreatment processes that use them. The catalyst comprises at least one hydro-dehydrogenating element that is selected from the group that is formed by the elements of group VIB and group VIII of the periodic table and a dopant in a controlled quantity that is selected from among phosphorus, boron, and silicon and a non-zeolitic substrate with a silica-alumina base that contains a quantity of more than 15% by weight and of less than or equal to 95% by weight of silica (SiO.sub.2).