Alkylated polymeric or copolymeric N-vinyl lactams are obtained by heating one mole of a polymeric or copolymeric N-vinyl lactam with 0.05 to 12 moles of an a -olefin containing at least 2 carbon atoms or with 0.05 to 12 moles of a halo-a -olefin containing 2 carbon atoms, the halo-a -olefin being a chloro-fluoro-a -olefin or a fluoro-a -olefin, in a solution of an organic solvent common to the said polymeric or copolymeric lactam and the said a -olefin or halo-a -olefin in the presence of 0.025 to 0.30 mole of an organic peroxide catalyst per mole of the said a -olefin or halo-a -olefin at a temperature ranging from 80 DEG to 200 DEG C. A long list of suitable comonomers is given, those exemplified are vinyl acetate and ethyl acrylate. The a -olefins may have molecular weights ranging from 28 to 2500.