A method for breaking down polyolefins, comprising the steps a) producing a melt of synthetic polyolefins, in particular of dry synthetic polyolefins, b) purifying the polyolefin melt by passing the polyolefin melt through at least one melt filter, c) transferring the purified polyolefin melt into at least one first reactor, wherein the purified polyolefin melt in the at least one first reactor is conducted from a lower region (sump region) to an upper region (head region) of the reactor with heating to temperatures between 300°C and 370°C, preferably 330°C to 360°C, particularly preferably 350°C, wherein the polyolefins in the at least one first reactor are cleaved into oligomers, d) transferring the oligomer mixture formed in the at least one first reactor to at least one second reactor, wherein the oligomer mixture in the at least second reactor is conducted from a lower region (sump region) to an upper region (head region) of the reactor with heating to 380°C to 450°C, preferably 400°C to 430°C, in particular 410°C, wherein the oligomers in the at least one second reactor are broken down to short-chain hydrocarbons in the presence of at least one clay mineral as depolymerization catalyst, e) removing the short-chain hydrocarbons having C3-C22 that are formed in the at least one second reactor to at least one precondenser, wherein the short-chain hydrocarbons exiting from the at least one second reactor are cooled in the at least one precondenser; and f) introducing the short-chain hydrocarbons that are cooled in the at least one precondenser into at least one main condenser, wherein the short-chain hydrocarbons exiting from the at least one precondenser are liquefied in the at least one main condenser. a) producing a melt of synthetic polyolefins, in particular of dry synthetic polyolefins, b) purifying the polyolefin melt by passing the polyolefin melt through at least one melt filter, c) transferring the purified polyolefin melt into at least one first reactor, wherein the purified polyolefin melt in the at least one first reactor is conducted from a lower region (sump region) to an upper region (head region) of the reactor with heating to temperatures between 300°C and 370°C, preferably 330°C to 360°C, particularly preferably 350°C, wherein the polyolefins in the at least one first reactor are cleaved into oligomers, d) transferring the oligomer mixture formed in the at least one first reactor to at least one second reactor, wherein the oligomer mixture in the at least second reactor is conducted from a lower region (sump region) to an upper region (head region) of the reactor with heating to 380°C to 450°C, preferably 400°C to 430°C, in particular 410°C, wherein the oligomers in the at least one second reactor are broken down to short-chain hydrocarbons in the presence of at least one clay mineral as depolymerization catalyst, e) removing the short-chain hydrocarbons having C3-C22 that are formed in the at least one second reactor to at least one precondenser, wherein the short-chain hydrocarbons exiting from the at least one second reactor are cooled in the at least one precondenser; and f) introducing the short-chain hydrocarbons that are cooled in the at least one precondenser into at least one main condenser, wherein the short-chain hydrocarbons exiting from the at least one precondenser are liquefied in the at least one main condenser.