Abstract: There is disclosed a homoplymer of an alkenylsilane having a syndiotactic structure and a copolymer of the alkenylsilane and an .alpha.-olefin. The polymer and the copolymer can be prepared by subjecting the alkenylsilane or the alkenylsilane and the .alpha.-olefin to addition polymerization in the presence of a transition metal compound having asymmetirically interconnected ligands or preferably in the presence of the transition metal compound and aluminoxane. The polymer and the copolymer can be used as a nucleating agent for a crystalline polypropylene.

Abstract: A poly-.alpha.-olefin of novel structure which is an addition polymer of an .alpha.-olefin having 4 carbon atoms or more, wherein (a) by the analysis of the peaks attributable to the side chain methylene groups directly bonded to the main chain in the .sup.13 C-NMR spectrum produced by the measurement in 1,2,4-trichloro-benzene, (i) a novel main peak not attributable to the isotactic structure thereof is positioned on the side of higher magnetic field than is the peak attributable to the isotactic structure, and (ii) the intensity of said main peak is 0.3 or more relative to the sum of the intensities of the total peaks attributable to the side chain methylene groups directly bonded to the main chain, and (b) the molecular weight measured by gel permeation chromatography and calculated as polypropylene is not less than 1,000.