PROBLEM TO BE SOLVED: To provide a composition for hair excellent in feeling at an application time, showing excellent conditioning effect of damaged hair from the application time until a rinsing time followed by drying, and having little irritation and excellent biodegradability.SOLUTION: This composition for hair contains (A) (A4) an N-hydroxyalkyl amine compound obtained by subjecting (A2) ethylene oxide and (A3) propylene oxide to an addition reaction to (A1) primary amine having 16-40C straight chain or branched chain alkyl or alkenyl group which may be substituted with amide, ester, ether or hydroxy group, in each specific range of 0
