Aminomono- or di-[(poly-n-butoxy)-n-butylamino]-(poly-n-butoxy)-n-butylamines of the general formula IH.sub.2 N--[(CH.sub.2 CH.sub.2 CH.sub.2 CH.sub.2 O).sub.x --(CH.sub.2).sub.4 --NH].sub.y --(CH.sub.2 CH.sub.2 CH.sub.2 CH.sub.2 O).sub.x --(CH.sub.2).sub.4 --NH.sub.2 (I)where x is from 1 to 150 and y is 1 or 2, are prepared by a process in which a hydroxy-(poly-n-butoxy)-butanol of the formula IIHO--(CH.sub.2 CH.sub.2 CH.sub.2 CH.sub.2 O).sub.x --(CH.sub.2).sub.4 --OH (II)where x is from 1 to 150, is reacted with from 1.01 to 300 mole equivalents of ammonia per hydroxyl group in the presence of a hydrogenation/dehydrogenation catalyst and hydrogen at from 150.degree. to 300.degree. C. and under from 20 to 400 bar.