1. Process for converting a first feedstock comprising pyrolysis oil obtained from a steam
cracking unit and a second heavy hydrocarbon-based feedstock, said process comprising
the following steps:
a) a step of hydroconverting said feedstocks in at least one reactor, in the presence of hydrogen and of at least one hydroconversion catalyst, with the reactor being fed with the first feedstock at a feed temperature T1 of between 80 and 200°C and with the second feedstock at a feed temperature T2 greater than 250°C, producing a hydroconverted liquid effluent;
b) a step of separating at least a portion of the hydroconverted liquid effluent obtained from step a) into at least a naphtha fraction, a gas oil fraction, a vacuum gas oil fraction and an unconverted residue fraction;
c) a hydrocracking step in a fixed-bed reactor in the presence of a catalyst for hydrocracking at least a portion of the vacuum gas oil fraction obtained from step b), producing a hydrocracked liquid effluent;
d) a step of fractionating at least a portion of the hydrocracked liquid effluent obtained from step c) into a naphtha fraction, a gas oil fraction and an unconverted vacuum gas oil fraction;
e) a step of steam cracking of at least a portion of the naphtha fraction obtained from step d) and optionally of a portion of the unconverted vacuum gas oil fraction obtained from step d) to obtain a steam-cracked effluent;
f) a step of fractionating at least a portion of the steam-cracked effluent obtained from step e) into an ethylene fraction, a propylene fraction, a butadiene and C4 olefin fraction, a pyrolysis gasoline fraction and a pyrolysis oil fraction;
g) a step in which at least a portion of the pyrolysis oil fraction obtained from step f) is sent into the hydroconversion step a).

2. Process according to the preceding claim, characterized in that, in step g), the pyrolysis oil fraction obtained from step f) is sent to the hydroconversion step a), either directly or after at least one intermediate treatment chosen from deasphalting and steam stripping and/or hydrogen stripping.
3. Process according to either of the preceding claims, characterized in that the first feedstock comprising pyrolysis oil obtained from a steam cracking unit is introduced at the end of the hydroconversion step a).

4. Process according to Claim 1, characterized in that the introduction of all or part of the first
feedstock is shifted from the hydroconversion step a) to the separation step b).
5. Process according to one of the preceding claims, characterized in that the
hydroconversion step a) in the presence of hydrogen is performed in at least one ebullated-
bed three-phase reactor.
6. Process according to one of the preceding claims, characterized in that it also comprises a step h) of deasphalting by liquid/liquid extraction of at least a portion of the unconverted residue fraction from step b), so as to obtain an asphalt phase and a deasphalted unconverted residue, said deasphalted unconverted residue being at least partly sent to the hydrocracking step c).
7. Process according to the preceding claim, characterized in that the deasphalting step h) is performed in two successive steps so as to obtain an asphalt phase, a light deasphalted unconverted residue and a heavy deasphalted unconverted residue, said light deasphalted unconverted residue being sent at least partly to the hydrocracking step c), said heavy deasphalted unconverted residue preferably being sent at least partly to step a) in the second feedstock.
8. Process according to one of the preceding claims, characterized in that it also comprises a step a') of deasphalting the pyrolysis oil obtained from the liquid/liquid extraction step f), so as to obtain an asphalt phase and a deasphalted pyrolysis oil, said deasphalted pyrolysis oil being at least partly sent to the hydroconversion step a) as first feedstock.
9. Process according to the preceding claim, characterized in that the pyrolysis oil deasphalting step a') is performed by liquid/liquid extraction in two steps, so as to obtain an asphalt phase, a light deasphalted pyrolysis oil and a heavy deasphalted pyrolysis oil, said light deasphalted pyrolysis oil preferably being at least partly or totally sent to the hydrocracking step c), and said heavy deasphalted pyrolysis oil preferably being at least partly sent to the hydroconversion step a) in the first feedstock.

10. Process according to one of the preceding claims, characterized in that it also comprises a step i) of deasphalting by liquid/liquid extraction of the pyrolysis oil obtained from step f) and of at least a portion of the unconverted residue obtained from step b), so as to obtain an asphalt phase and a deasphalted oil DAO cut, said deasphalted oil cut being at least partly sent to the hydroconversion step a) in the first feedstock.
11. Process according to the preceding claim, characterized in that the deasphalting step i) is performed by liquid/liquid extraction in two steps, so as to obtain an asphalt phase, a light

deasphalted oil cut and a heavy deasphalted oil cut, said light deasphalted oil cut being at least partly sent to the hydrocracking step c), and said heavy deasphalted oil cut being at least partly or totally sent to the hydroconversion step a) in the first feedstock.
12. Process according to one of the preceding claims, characterized in that the hydroconversion step a) is performed in the presence of a colloidal or molecular catalyst, and of a porous supported catalyst.
13. Process according to one of the preceding claims, characterized in that it also comprises at least one of the following additional steps:

- a hydrotreatment step j), performed in a reactor in the presence of at least one fixed-bed hydrotreatment catalyst, of at least a portion of the naphtha fraction obtained from step b), optionally followed by a step k) of recycling of at least a portion of the hydrotreated naphtha fraction obtained from step j) into the steam cracking step e);
- a hydrotreatment step l), performed in a reactor in the presence of at least one fixed-bed hydrotreatment catalyst, of at least a portion of the gas oil fraction obtained from step b), optionally followed by a step m) of recycling of at least a portion of the hydrotreated gas oil fraction obtained from step l) into the hydrocracking step c).

14. Process according to one of the preceding claims, characterized in that the proportion of pyrolysis oil of the first feedstock relative to the total feedstock of the hydroconversion step a) is greater than or equal to 5% by weight, preferably greater than or equal to 10% by weight, and/or preferably less than or equal to 50% by weight, notably less than or equal to 25% or 40% by weight.
15. Process according to one of the preceding claims, characterized in that the second feedstock of the hydroconversion step a) comprises hydrocarbons chosen from at least one of the following hydrocarbons: hydrocarbons obtained from the atmospheric distillation or vacuum distillation of crude oil, residual fraction obtained from the direct liquefaction of coal, vacuum gas oil, residual fraction obtained from the direct liquefaction of lignocellulosic biomass alone or as a mixture with coal, residual petroleum fraction.