Amines of the general formula I ##STR1## where R.sup.1, R.sup.2, R.sup.3, R.sup.4, R.sup.5 and R.sup.6 : are each hydrogen, C.sub.1 -C.sub.20 -alkyl, C.sub.2 -C.sub.20 -alkenyl, C.sub.2 -C.sub.20 -alkynyl, C.sub.3 -C.sub.20 -cycloalkyl, C.sub.4 -C.sub.20 -alkylcycloalkyl, C.sub.4 -C.sub.20 -cycloalkylalkyl, aryl, C.sub.7 -C.sub.20 -alkylaryl or C.sub.7 -C.sub.20 -aralkyl,R.sub.1 and R.sup.2 together are a saturated or unsaturated C.sub.3 -C.sub.9 -alkylene chain andR.sup.3 or R.sup.5 is C.sub.21 -C.sub.200 -alkyl or C.sub.21 -C.sub.200 -alkenyl or R.sup.3 and R.sup.5 together are a C.sub.2 -C.sub.12 -alkylene chain,are prepared by reacting an olefin of the general formula II ##STR2## where R.sup.3, R.sup.4, R.sup.5 and R.sup.6 have the abovementioned meanings, with ammonia or a primary or secondary amine of the general formula III ##STR3## where R.sup.1 and R.sup.2 have the abovementioned meanings, at from 200.degree.0 to 350.degree. C. and from 100 to 300 bar in the presence of a heterogeneous catalyst, wherein the heterogeneous catalyst used is an NU-85 zeolite.