The present invention relates to a cosmetic composition comprising: one or more vinylformamide/vinylformamine copolymers comprising: from 10 to 95 mol % of units of formula A and from 90 to 5 mol % of units of formula B, one or more non-ionic fixing polymers, and one or more cationic surfactants. It also relates to the use of this composition for shaping and/or fixing the hairstyle, to a cosmetic treatment process for the hair using same and also to a particular cosmetic set.