Graft copolymers based on a polyamide which was reacted with maleic anhydride and which has at least one vinylically unsaturated side chain are proposed, this grafted side chain containing at least one representative selected from a) N-vinylcaprolactam and/or b) N-vinylpyrrolidone. Inter alia, natural but also synthetic polyamides are provided as preferred polyamide components. Such graft copolymers, but also generally polyamide-based graft copolymers composed of at least one side chain containing ethylenically unsaturated compounds, are in general suitable in construction chemistry applications but also in the development, exploitation and completion of underground mineral oil and natural gas deposits and in deep wells and moreover in the extraction and the transport of oil or gas and here in particular as a gas hydrate inhibitor.