The invention provides a process using olefin polymerization catalysts exhibiting excellent polymerization activities. The olefin polymerization catalysts of the invention contain a transition metal compound typified by formula (I) and at least one of an organometallic compound, an organoaluminum oxy-compound or a compound which reacts with said transition metal compound to form an ion pair. The process using the inventive catalysts is useful in producing .alpha.-olefin/conjugated diene copolymers having specific properties ##STR00001##