Disclosed herein is a process for producing polymers of an N-vinyl carboxamide, including the steps of flowing a reaction mixture containing an aqueous liquid containing at least one polymerization initiator, N-vinyl carboxamide monomer or a monomer mixture containing N-vinyl carboxamide into a reactor system, and polymerizing the monomer or monomer mixture to produce the polymer of a N-vinyl carboxamide. The polymers resulting therefrom may be hydrolyzed to provide polymers containing vinyl amine units. Also disclosed herein is an apparatus suitable for producing the polymers.