Method of thermal destruction of polyethylene and polypropylene waste, implemented in both periodic and continuous modes of the above-mentioned plastics waste processing, and which includes loading of pre-crushed and impurities-free waste of the above-mentioned plastics in a pyrolysis furnace containing a thermal destruction reactor and a furnace with a fuel burner, their heating with a fuel burner in a thermal destruction reactor within 450 - 480 °C, thermal decomposition of the initial crushed and purified raw material in the thermal destruction reactor without air access, resulting in the thermal destruction of the vapor-gas mixture at the outlet from the reactor, feeding it to the catalyst column, besides, after the degradation products fractionating, gas and liquid fuel are obtained, subsequent cooling of the fractionated products in heat exchangers and unloading coke from the thermal destruction reactor, wherein the gasoline and water formed are separated due to the differences in their densities, and separation of the liquid components and hydrocarbon gas from the vapor-gas mixture of hydrocarbons formed in the process of thermal destruction is carried out in stages, characterized in that in periodic mode no less than two thermal destruction reactors are used, which are used in sequence during the operation, and in this case firing with a fuel burner is performed which is a portable one, and after disconnecting the hot furnace from the thermal destruction reactor, the latter is put into cooling mode with a possibility of cooling with air supplied from the burner gas-blower or fan, simultaneously connecting still hot furnace to the second cold thermal destruction reactor, during the thermal destruction reactor heating, preheating and maintaining the preset temperature is ensured in the boiler of the hydrocarbon collecting tank and in the boiler of the rectification column cube by supplying fuel gases, formed from the fuel burning in thermal destruction reactor fuel burner, wherein the supply of fuel gas, formed from the fuel burning, is stopped when temperature in the collecting tank reaches 300-360 °C, and in the rectification column tank the temperature is maintained within 160-220 °C and controlled by changing the temperature of the vapor-gas mixture after dewaxer and at the top of the rectification column, wherein the separation or fractionation of the liquid components from the vapor-gas mixture of hydrocarbons formed in the process of thermal destruction is carried out in four stages, where at the first stage, high-boiling components of the vapor-gas mixture are condensed in the heat exchanger, cooled with water at a temperature of 300-360 °C, which is regulated by changing the water supply to the heat exchanger, at the second stage, paraffins are condensed in the column serving as the dewaxer, at a temperature of 180 - 300°C, which is regulated by feeding water to the dewaxer dephlegmator, wherein the condensed high-boiling hydrocarbons and paraffins forming the heating fuel fraction are maintained in the collecting tank at the temperature of 300-360 °C, providing stripping of light fractions, at the third stage, the fractions of gasoline and diesel fuel are divided in the rectification column, providing the temperature mode within 35-100 °C at the top of the rectification column, and 160-220 °C at the bottom of the rectification column, at the fourth stage, gasoline and water vapors are condensed in the heat exchanger at the temperature of 20-3 5 °C upon that the heterogeneous catalyst is used as a catalyst in the form of titanium strands twisted in spiral, besides, each spiral is returned in one or in different directions, forming in the secon case left and right rotation spirals, besides strands are used turned with a spiral in one direction each, or turned all with spirals in different directions each, titanium strands are placed in the collecting tank, in the tubes of the heat exchanger, where high-boiling components of a vapor-gas mixture are condensed, in the tubes of the dewaxer dephlegmator and in the tubes of the rectification column dephlegmator.