Abstract: Polyolefins having better particle properties are obtained by polymerizing olefins in the presence of a catalyst comprising a solid catalyst component and an organometallic compound, the said solid catalyst component being prepared by reacting the following components [I] and [II] and further reacting the resulting reaction product with the following component [III]:[I] a reaction product obtained by reacting:(1) a silicon oxide and/or an aluminum oxide, and(2) a titanium compound, or a titanium compound and a vanadium compound, and further reacting the resulting reaction product with:(3) an organoaluminum compound;[II] a reaction product obtained by the reaction of:(1) a magnesium halide, and(2) a compound represented by the general formula Me(OR).sub.n X.sub.z-n wherein Me represents an element of Groups I to IV in the Periodic Table, z represents the valence of the element Me, n is 0<n.ltoreq.

Abstract: Provided is a polymer composition having a melt index of 0.01 to 5.0 and a density of 0.880 to 0.940 prepared by blending 10 to 80 parts by weight of an ethylene/.alpha.-olefin copolymer having an intrinsic viscosity determined in decalin at 135.degree. C. of 2.0 to 10 dl/g and a density of less than 0.91 which copolymer is obtained by copolymerizing ethylene with an .alpha.-olefin of C.sub.3 to C.sub.12 in vapor phase condition, with 20 to 90 parts by weight of an ethylene polymer having an intrinsic viscosity determined in decalin at 135.degree. C. of not higher than 1.7 dl/g and a density not less than 0.950.