Compositions and processes permanent shape human hair for the permanent waving of human hair with an excellent waving effect as well as for the straightening of curled hair. A composition for permanently shaping hair has at least one reducing agent or at least one oxidizing agent and a cross linked copolymer of vinylpyrrolidone, vinylimidazol, 3-methyl-1-vinylimidazolium chloride and methacrylic acid. A process for permanent shaping hair wherein a composition comprising at least one reducing agent is applied and rinsed off from hair after a processing time of 1 to 30 min and at a temperature of 20 to 45° C. and a composition comprising at least one oxidizing agent is applied and processed for 1 to 20 min at a temperature range of 20 to 45° C. and rinsed off from hair wherein at least one of the compositions has a cross linked copolymer.
