A process for cracking a polyolefin containing material, in particular a polyolefin containing material which contains at least 60 % by dry weight of one or more polyolefins and optionally at least one thermally more stable polymer, in which process said material is thermally cracked to be converted into one or more gaseous cracking products thereby leaving a solid residue, characterised in that said polyolefin containing material is cracked stepwise in at least two successive cracking phases, including a first cracking phase and a final cracking phase, in one tank reactor which contains a liquid phase and a gaseous phase, the liquid phase being cracked in each of the cracking phases to produce a gaseous cracking product which is removed from the tank reactor during the production thereof, during the first cracking phase the tank reactor being continuously fed with said polyolefin containing material whilst during the final cracking phase feeding of said polyolefin containing material in the tank reactor is interrupted and the liquid phase remaining in the tank reactor at the end of said first cracking phase being further cracked during the final cracking phase to produce a final gaseous product and a solid residue, in which process: - the liquid phase contained in said tank reactor is kept during said first cracking phase at a first temperature of between 420°C and 510°C and is cracked during said first cracking phase in said tank reactor at said first temperature to produce a first gaseous cracking product; - the first gaseous cracking product is removed during the first cracking phase from the tank reactor during the production thereof and is subsequently at least partially condensed; - the liquid phase which remains at the end of the first cracking phase in said tank reactor is heated during said final cracking phase to a final temperature of at least 525°C and is cracked during said final cracking phase to produce said final gaseous cracking product and said solid residue; - the final gaseous cracking product is removed during the final cracking phase from the tank reactor during the production thereof and is subsequently at least partially condensed; - after having produced the solid residue, it is removed from the tank reactor; and - after having removed the solid residue from the tank reactor, the first cracking phase is restarted. said polyolefin containing material is cracked stepwise in at least two successive cracking phases, including a first cracking phase and a final cracking phase, in one tank reactor which contains a liquid phase and a gaseous phase, the liquid phase being cracked in each of the cracking phases to produce a gaseous cracking product which is removed from the tank reactor during the production thereof, during the first cracking phase the tank reactor being continuously fed with said polyolefin containing material whilst during the final cracking phase feeding of said polyolefin containing material in the tank reactor is interrupted and the liquid phase remaining in the tank reactor at the end of said first cracking phase being further cracked during the final cracking phase to produce a final gaseous product and a solid residue, in which process: - the liquid phase contained in said tank reactor is kept during said first cracking phase at a first temperature of between 420°C and 510°C and is cracked during said first cracking phase in said tank reactor at said first temperature to produce a first gaseous cracking product; - the first gaseous cracking product is removed during the first cracking phase from the tank reactor during the production thereof and is subsequently at least partially condensed; - the liquid phase which remains at the end of the first cracking phase in said tank reactor is heated during said final cracking phase to a final temperature of at least 525°C and is cracked during said final cracking phase to produce said final gaseous cracking product and said solid residue; - the final gaseous cracking product is removed during the final cracking phase from the tank reactor during the production thereof and is subsequently at least partially condensed; - after having produced the solid residue, it is removed from the tank reactor; and - after having removed the solid residue from the tank reactor, the first cracking phase is restarted. - the liquid phase contained in said tank reactor is kept during said first cracking phase at a first temperature of between 420°C and 510°C and is cracked during said first cracking phase in said tank reactor at said first temperature to produce a first gaseous cracking product; - the first gaseous cracking product is removed during the first cracking phase from the tank reactor during the production thereof and is subsequently at least partially condensed; - the liquid phase which remains at the end of the first cracking phase in said tank reactor is heated during said final cracking phase to a final temperature of at least 525°C and is cracked during said final cracking phase to produce said final gaseous cracking product and said solid residue; - the final gaseous cracking product is removed during the final cracking phase from the tank reactor during the production thereof and is subsequently at least partially condensed; - after having produced the solid residue, it is removed from the tank reactor; and - after having removed the solid residue from the tank reactor, the first cracking phase is restarted.