A process for preparing amines of the 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.sup.1 and R.sup.2 are together a saturated or unsaturated C.sub.3 -C.sub.9 -alkylene dichain, and R.sup.3 or R.sup.5 is C.sub.21 -C.sub.200 -alkyl or C.sub.21 -C.sub.200 -alkenyl or together they are a C.sub.2 -C.sub.12 -alkylene dichain, by reacting olefins of the formula II ##STR2## where R.sup.3, R.sup.4, R.sup.5 and R.sup.6 are each as defined above, with ammonia or primary or secondary amines of the formula III ##STR3## where R.sup.1 and R.sup.2 are each as defined above, at temperatures from 200.degree. to 350.degree. C. and pressures from 100 to 300 bar in the presence of a heterogeneous catalyst using a heterogeneous catalyst comprising hexagonal faujasite.