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Abstract

A catalyst for .alpha.-olefin polymerization which comprises the following components (A) and (B): component (A), which is a transition metal compound represented by the formula Q(C.sub.5 H.sub.4-m R.sup.1.sub.m)(C.sub.5 H.sub.4-n R.sup.2.sub.n)MeXY wherein (C.sub.5 H.sub.4-m R.sup.1.sub.m) and (C.sub.5 H.sub.4-n R.sup.2.sub.n) respectively represent a conjugated five-membered ring ligand coordinating to a metal Me; R.sup.1 and R.sup.2 which may be the same or different and a plurality of each of which can be bonded together, respectively represent a hydrocarbyl group having 1 to 20 carbon atoms, a halogen atom, an alkoxy group, a silicon-containing hydrocarbyl group, a phosphorus-containing hydrocarbyl group, a nitrogen-containing hydrocarbyl group or a boron-containing hydrocarbyl group; Q represents a bonding group which crosslinks the two conjugated five-membered ring ligand; Me represents a transition metal of the IVB-VIB group in the Periodic Table; X and Y, which may be the same or different, respectively represent hydrogen, a halogen atoms, a hydrocarbyl group, an alkoxy group, an amino group, a phosphorus-containing hydrocarbyl group or a silicon-containing hydrocarbyl group; m denotes an integer of 0.ltoreq.m.ltoreq.4 and n denotes an integer of 0.ltoreq.n.ltoreq.4; component (B), which is a methylisobutylalumoxane which satisfies the following conditions (a), (b) and (c): (a) the molar ratio of a methyl group to an isobutyl group being in the range of 4:1 to 1:4, (b) the chemical shift of .sup.27 Al-NMR being in the range of 160 ppm to 250 ppm and the peak having a half-height width of no smaller than 3000 Hz, and (c) it has a repeating unit of Al--O in an amount of 2 to 100. The methylisobutylalumoxane is assumed to be novel.

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