The object of the present invention is to provide a process for producing
an ethylene-.alpha.-olefin-polyene copolymer by continuous multistage
polymerization which can give an ethylene-.alpha.-olefin-polyene
copolymer excellent in a form retention property during extrusion. The
process for producing an ethylene-.alpha.-olefin-polyene copolymer
comprises continuously polymerizing ethylene, .alpha.-olefin, and the
following polyene (A) and polyene (B) in a solvent in the presence of an
olefin polymerization catalyst using a polymerization reaction apparatus
comprising two tanks of polymerization reactors connected in series,
wherein the polymerization is carried out under specific conditions:
polyene (A): at least one polyene selected from norbornadienes and
vinylnorbornenes, polyene (B): polyene other than the polyene (A).