A cosmetic composition for the hair comprises at least one water-soluble crosslinked polymer obtained by crosslinking a polyamino-polyamide with a crosslinking agent, said polyamino-polyamide being prepared by the polycondensation of (a) an acidic compound selected from the group consisting of (i) organic dicarboxylic acid, (ii) ethylenically unsaturated aliphatic mono- or di-carboxylic acid, (iii) ester of said acids of (i) and (ii), and (iv) mixtures of (i), (ii) and (iii) on (b) a polyamine selected from the group consisting of bis-primary and mono- or bis-secondary polyalkylene polyamines, said polyamine (b) being replaceable by a member selected from the group consisting of (1) 0-20 mole percent hexamethylene diamine, (2) 0-40 mole percent bis-primary amine and (3) 0-40 mole percent bis-secondary amine, said crosslinking agent being selected from the group consisting of (a') simple bi-functional compounds selected from bis-halohydrins, bis-azetidinium, bis-haloacyl diamine and alkyl bis-halides, (b') oligomers obtained by the reaction of (1') a compound selected from the group consisting of the compounds in (a') above or an epihalohydrin, a bis-epoxide, or a bis-unsaturated derivative with (2') a compound reactive with the compound in (1'), and (c') the quaternized compounds comprising said crosslinked polymer alkylated with an alkylating agent selected from the group consisting of (a) epoxides, (b) ethylenically unsaturated compounds, (c) chloroacetic acid, and (d) alkane sultone selected from the group consisting of propane sultone and butane sultone. The crosslinking agent is employed in amounts of 0.025-0.35 mole per amine group in said polyamino-polyamide. The said crosslinked polymer is soluble in water in amounts of 10 weight percent thereof without essentially any gel formation and a 10 weight percent aqueous solution of the said crosslinked polymer has a viscosity greater than 3 centipoises at 25.degree. C.