A process for producing a polymer, which comprises polymerizing a vinyl
compound (I) represented by the general formula CH.sub.2.dbd.CH--R,
wherein steric parameters Es and B1 of the substituent R are respectively
-1.64 or less and 1.53 or more, or a vinyl compound (II) represented by
the general formula CH.sub.2.dbd.CH--R', wherein a substituent R' is a
secondary or tertiary alkyl group, in the presence of a catalyst obtained
by combining:
(A) a transition metal compound represented by the general formula [1]
##STR1##
(B) an organoaluminum compound and
(C) a boron compound.
