A process for the preparation of amines of the general formula I ##STR1## in which R.sup.1, R.sup.2, R.sup.3, R.sup.4, R.sup.5, R.sup.6 denote 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 together denote a saturated or unsaturated C.sub.3 -C.sub.9 alkylene dichain and R.sup.3 or R.sup.5 denotes C.sub.21 -C.sub.200 alkyl, C.sub.21 -C.sub.200 alkenyl or they together form a C.sub.2 -C.sub.12 alkylene dichain, by the reaction of olefins of the general formula II ##STR2## in which R.sup.3, R.sup.4, R.sup.5, and R.sup.6 have the above meanings, with ammonia or primary or secondary amines of the general formula III ##STR3## in which R.sup.1 and R.sup.2 have the above meanings, at temperatures ranging from 200.degree. to 350.degree. C. and pressures ranging from 100 to 300 bar in the presence of a heterogeneous catalyst, wherein the heterogeneous catalyst used is a zeolite of the type SSZ-37.