The invention describes a catalyst comprising at least one material with a hierarchical porosity comprising silicon and at least one hydrodehydrogenating element from group VIB and/or group VIII of the periodic table of the elements. Said material with a hierarchical porosity comprising silicon is constituted by at least two elementary spherical particles, each of said spherical particles comprising zeolitic nanocrystals having a pore size in the range 0.2 to 2 nm and a matrix based on silicon oxide, which is mesostructured, having a pore size in the range 1.5 to 30 nm and having amorphous walls with a thickness in the range 1 to 30 nm, said elementary spherical particles having a maximum diameter of 100 μm. The matrix based on silicon oxide may contain aluminum. The catalyst also optionally comprises at least one doping element in a controlled quantity selected from phosphorus, boron and silicon, optionally at least one element from group VB of the periodic table of the elements, and optionally an element from group VIIA. The invention also concerns hydrocracking/hydroconversion and hydrotreatment processes employing said catalyst.