Propylene-ethylene copolymers are obtained by two-stage polymerization from the gaseous phase in an agitated fixed bed by means of a Ziegler-Natta catalyst system that contains in addition to a titanium-containing solid component also an aluminum compound as co-catalyst, wherein as Ziegler-Natta catalyst system a system is used which, following the reaction of the titanium-containing solid component with the co-catalyst, is deactivated by reaction with carbon dioxide. The copolymers are used for producing fibers, films and moldings.