A process for purification a hydrocarbon stream including: (a) Providing a hydrocarbon stream having a diene value of at least 1.0, a bromine number of at least 5 g and containing at least 10 wt % of pyrolysis plastic oil; b) contacting the effluent obtained in step a) with a silica gel, clays, alkaline or alkaline earth metal oxide, iron oxide, ion exchange resins, active carbon, active aluminium oxide, molecular sieves, alkaline oxide and/or porous supports, and/or silica gel, or any mixture thereof; c) performing a first hydrotreating step; d) contacting the effluent obtained in step c) with silica gel, clays, alkaline or alkaline earth metal oxide, iron oxide, ion exchange resins, active carbon, active aluminium oxide, molecular sieves, alkaline oxide and/or porous supports and silica gel, or any mixture thereof; e) performing a second hydrotreating step; and f) recovering a purified hydrocarbon stream.