Provided is a conditioner composition, which comprises a tertiary amine represented by the following formula (1): ##STR00001## wherein, R.sup.1 represents a linear or branched C.sub.6-24 alkyl or alkenyl group, R.sup.2 and R.sup.3 are the same or different and each represents a C.sub.1-6 alkyl group or a group -(AO).sub.nH (in which A represents a C.sub.2-4 alkylene group, and n stands for a number of from 1 to 6 with the proviso that n pieces of A are the same or different and are arranged in any order); or a salt thereof. The conditioner composition can impart fiber or hair with good suppleness and smoothness during wetting and after drying and is particularly excellent in imparting hair or fiber with smoothness after drying.