In 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,R.sup.6 are 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 -alkyl-cycloalkyl, C.sub.4 -C.sub.20 -cycloalkyl-alkyl, aryl, C.sub.7 -C.sub.20 -alkylaryl or C.sub.7 -C.sub.20 -aralkyl, R.sup.1 and R.sup.2 together form a saturated or unsaturated, divalent C.sub.3 -C.sub.9 -alkylene chain and R.sup.3 and R.sup.5 are C.sub.21 -C.sub.200 -alkyl, C.sub.21 -C.sub.200 -alkenyl or together form a divalent C.sub.2 -C.sub.12 -alkylene chain, by reating olefins of the formula II ##STR2## where R.sup.3, R.sup.4, R.sup.5 and R.sup.6 are as defined above, with ammonia or primary or secondary amines of the formula III ##STR3## where R.sup.1 and R.sup.2 are as defined above, at from 200.degree. to 350.degree. C. and a pressure of from 100 to 300 bar in the presence of a heterogeneous catalyst, the heterogeneous catalysts being mesoporous oxides having a high surface area.