The invention relates to a process for the hydroconversion of a plastic feedstock, comprising: (a1) a non-catalytic hydroconversion step of the feedstock in the presence of
hydrogen in contact with a source of free radicals, the source comprising
sulfur and introduced such that the
sulfur content is between 3% and 20% by weight of the feedstock, to produce a first conversion product; (a2) a step of catalytic hydroconversion of the first conversion product in the presence of
hydrogen in contact with at least one hydroconversion catalyst comprising, alone or as a mixture, at least one hydrogenation-
dehydrogenation element selected from the group consisting of non-
noble metal elements of Group VIB and Group VIII of the
Periodic Table; and a porous support containing a porous
mineral matrix and at least one
zeolite, said steps (a1) and (a2) being carried out at a pressure between 1 MPa and 38 MPa absolute, at a temperature greater than or equal to 200 DEG C and less than 400 DEG C, at an hourly
space velocity relative to each hydroconversion reactor between 0.05 h-1 and 10 h-1, and at a
hydrogen amount between 50 and 5000 Sm3 / m3.