Process for hydrocracking and/or hydrotreatment of hydrocarbon feeds utilizing a catalyst comprising at least one hydro-dehydrogenating element of group VIB and of non-precious group VIII used alone or mixed, and a support comprising at least one porous mineral matrix and at least one dealuminated USY zeolite having an overall silicon-to-aluminium atomic ratio comprised between 2.5 and 10, a fraction by weight of extra-network aluminium atom greater than 10% relative to the total mass of the aluminium present in the zeolite, a mesopore volume measured by nitrogen porosimetry greater than 0.07 ml.g−1, and a crystal parameter a0 of the elemental mesh greater than 24.28 Å, in which a quantity of the element nickel comprised between 0.5 and 3% by weight relative to the total mass of the zeolite is deposited on said USY zeolite and in which said catalyst is in the sulphide form.