NOVELTY - Hydrocarbons feedstock processing using thermal or catalytic cracking of raw-material comprises conducting cracking within the reaction system embracing two reaction zones; introducing hydrocarbons feedstock in a liquid state into first reaction zone where a temperature is maintained which enables running cracking reaction; and carrying vapors of cracking products away from upper part of first zone while liquid reaction mixture from lower part of this zone flows into lower part of second zone, where reaction mixture flowing in from below is divided in streams flowing upwards.    USE - For hydrocarbons feedstock processing, useful in processing waste raw materials containing waste plastics, including polyethylene, polypropylene, polystyrene and PVC, used lubricating oils and lubricants, distillation residues, impure heavy hydrocarbon fractions of various origin or used and fresh vegetable and animal fats as applicable in production of fuels.    ADVANTAGE - The method avoids the occurrence of large differences in temperatures on a surface of the heat exchange that cause undesirable phenomenon of coking. It provides high productivity of the most valuable target products, low consumption of energy and long periods of continuous operation of the installation free from any disturbances caused by settling of coke on the surface of any equipment.    DETAILED DESCRIPTION - Hydrocarbons feedstock processing using thermal or catalytic cracking of raw-material to receive hydrocarbons with lower molecular weights and consisting of conducting the cracking reaction in the mass of the liquid hydrocarbons feedstock under conditions specific for running such a reaction and in the presence of the catalyst or without it, when the gas-steam mixture of reaction products is received, comprises conducting cracking within the reaction system embracing the two reaction zones; introducing hydrocarbons feedstock in a liquid state into the first reaction zone where a temperature is maintained which enables running cracking reaction; and carrying vapors of cracking products away from the upper part of the first zone while the liquid reaction mixture from the lower part of this zone flows into the lower part of the second zone, where the reaction mixture flowing in from below is divided in streams flowing upwards. Into every liquid stream, a stream of gas is introduced from below which, along with the reaction mixture, forms a liquid-gas mixture which is heated when flowing upwards by indirect exchange of heat with the heating medium and then the heated mixture flowing out up above from the second zone is turned back into the first reaction zone and the vapors of products as carried away up above from the first zone are submitted to separation. An INDEPENDENT CLAIM is also included for a system for hydrocarbons feedstock processing using thermal or catalytic cracking for hydrocarbons with lower molecular weights, containing the tank-type reactor (1) and tubular reactor (5) situated one next to each other, the tank-type reactor being provided with the inlets to feed raw-materials and a catalyst, outlets to carry away the products and remove impurities while the tubular reactor is provided with the parallel tubes (6) mounted in the casing and directed from below to the top. The tubes along with the lower chamber (6a) combining the lower open ends of the tubes and with the upper chamber (6b) combining the upper open ends of the tubes form a separate tubular space in the casing, which is connected with the tank-type reactor by pipes such that one pipe connects the lower part of the tank-type reactor with the lower inlet into the tubular space, while the second pipe (12) connects the upper outlet from the tubular space with the tank-type reactor, where the inlet of the second pipe leading to the tank-type reactor is above the lower part of the tank-type reactor. Each tube of the tubular reactor has a small tube (7) installed on its lower end, with an inlet directed in principal coaxially to the tube's surface. Inlet ends of the small tubes are connected with the collector (8). The diameter of the small tubes is less than the diameter of the tubes. The casing of the tubular reactor has an inlet and an outlet to feed and to carry away the heating medium.    DESCRIPTION OF DRAWING(S) - The figure presents the system of hydrocarbons feedstock processing based on the cracking method.    Tank-type reactor (1)    Tubular reactor (5)    Tubes (6)    Lower chamber (6a)    Upper chamber (6b)    Small tube (7)    Collector (8)    Second pipe (12)