FIELD: method of production of polymers and copolymers of olefins CH2 = CHR, where R is hydrogen or C1-12 alkyl in the presence of catalyst including product of reaction of alkyl-aluminum compound with solid catalytic component having at least one bond Ti-halogen and magnesium dihelide in active form. SUBSTANCE: gas-phase process is run in at least two reactors with fluidized or mechanically mixed bed operating under various reaction conditions to produce different polymers in different reactors. The method is distinguished by the fact that polymer at least partially recirculates between different reactors with recirculation velocity-unloading rate ratio between 2 and 6. In addition to production of polymers and copolymers with a wide range of molecular weight, the method may be used in production of polymeric compositions in which polymer or copolymer of different compositions is produced in two or more stages. EFFECT: higher efficiency. 30 cl, 4 dwg, 3 tbl
