A process for preparing amines of the formula, in which m is 1, 2 or 3, where when m is 1 R 1 is an aliphatic C 1-60 hydrocarbon radical or C 4-60 hydrocarbon radical that contains at least one cycloaliphatic or aromatic ring, said C 1-60 or C 4-60 hydrocarbon radical optionally containing one or more heteroatoms independently selected from the group consisting of nitrogen, oxygen, and sulfur, and R 2 is hydrogen, C 1-6 alkyl or phenyl, or R 1, R 2 together are -(CH 2) j -Y-(CH 2) k -, where Y is methylene, oxygen, sulfur, or NR 3 (where R 3 is C 1-4 alkyl) and j and k are independently an integer from 1 to 4, when m is 2 or 3 R 1 is a di- or trivalent C 4-20 hydrocarbon radical that contains at least one cycloaliphatic or aromatic ring, said hydrocarbon radical optionally containing one or more heteroatoms independently selected from the group consisting of nitrogen, oxygen,and sulfur, and R 2 is hydrogen, C 1-6 alkyl or phenyl, and R 4 and R 5 are independently hydrogen or C 1-16 alkyl, R 6 and R 7 are independently hydrogen or C 1-4 alkyl, comprising the steps of 1. reacting an amino alcohol of the formula with a carbonyl compound of the formula and subsequent hydrogenation of the resulting reaction product with hydrogen (H 2) on a heterogeneous hydrogenation catalyst to form an intermediate of the formula 2. reacting the intermediate obtained in step 1 with an amine component of the formula in the presence of hydrogen (H 2) and a heterogeneous hydrogenation catalyst to form a corresponding amine of the formula, where m and the radicals R 1, R 2, R 4, R 5, R 6, and R 7 in the formulas to are as defined in formula. m is 1, 2 or 3, where when m is 1 R 1 is an aliphatic C 1-60 hydrocarbon radical or C 4-60 hydrocarbon radical that contains at least one cycloaliphatic or aromatic ring, said C 1-60 or C 4-60 hydrocarbon radical optionally containing one or more heteroatoms independently selected from the group consisting of nitrogen, oxygen, and sulfur, and R 2 is hydrogen, C 1-6 alkyl or phenyl, or R 1, R 2 together are -(CH 2) j -Y-(CH 2) k -, where Y is methylene, oxygen, sulfur, or NR 3 (where R 3 is C 1-4 alkyl) and j and k are independently an integer from 1 to 4, when m is 2 or 3 R 1 is a di- or trivalent C 4-20 hydrocarbon radical that contains at least one cycloaliphatic or aromatic ring, said hydrocarbon radical optionally containing one or more heteroatoms independently selected from the group consisting of nitrogen, oxygen,and sulfur, and R 2 is hydrogen, C 1-6 alkyl or phenyl, and when m is 1 R 1 is an aliphatic C 1-60 hydrocarbon radical or C 4-60 hydrocarbon radical that contains at least one cycloaliphatic or aromatic ring, said C 1-60 or C 4-60 hydrocarbon radical optionally containing one or more heteroatoms independently selected from the group consisting of nitrogen, oxygen, and sulfur, and R 2 is hydrogen, C 1-6 alkyl or phenyl, or R 1, R 2 together are -(CH 2) j -Y-(CH 2) k -, where Y is methylene, oxygen, sulfur, or NR 3 (where R 3 is C 1-4 alkyl) and j and k are independently an integer from 1 to 4, R 1 is an aliphatic C 1-60 hydrocarbon radical or C 4-60 hydrocarbon radical that contains at least one cycloaliphatic or aromatic ring, said C 1-60 or C 4-60 hydrocarbon radical optionally containing one or more heteroatoms independently selected from the group consisting of nitrogen, oxygen, and sulfur, and R 2 is hydrogen, C 1-6 alkyl or phenyl, or R 1, R 2 together are -(CH 2) j -Y-(CH 2) k -, where Y is methylene, oxygen, sulfur, or NR 3 (where R 3 is C 1-4 alkyl) and j and k are independently an integer from 1 to 4, when m is 2 or 3 R 1 is a di- or trivalent C 4-20 hydrocarbon radical that contains at least one cycloaliphatic or aromatic ring, said hydrocarbon radical optionally containing one or more heteroatoms independently selected from the group consisting of nitrogen, oxygen,and sulfur, and R 2 is hydrogen, C 1-6 alkyl or phenyl, and R 1 is a di- or trivalent C 4-20 hydrocarbon radical that contains at least one cycloaliphatic or aromatic ring, said hydrocarbon radical optionally containing one or more heteroatoms independently selected from the group consisting of nitrogen, oxygen,and sulfur, and R 2 is hydrogen, C 1-6 alkyl or phenyl, and R 4 and R 5 are independently hydrogen or C 1-16 alkyl, R 6 and R 7 are independently hydrogen or C 1-4 alkyl, comprising the steps of 1. reacting an amino alcohol of the formula with a carbonyl compound of the formula and subsequent hydrogenation of the resulting reaction product with hydrogen (H 2) on a heterogeneous hydrogenation catalyst to form an intermediate of the formula 2. reacting the intermediate obtained in step 1 with an amine component of the formula in the presence of hydrogen (H 2) and a heterogeneous hydrogenation catalyst to form a corresponding amine of the formula, where m and the radicals R 1, R 2, R 4, R 5, R 6, and R 7 in the formulas to are as defined in formula. 1. reacting an amino alcohol of the formula with a carbonyl compound of the formula and subsequent hydrogenation of the resulting reaction product with hydrogen (H 2) on a heterogeneous hydrogenation catalyst to form an intermediate of the formula 2. reacting the intermediate obtained in step 1 with an amine component of the formula in the presence of hydrogen (H 2) and a heterogeneous hydrogenation catalyst to form a corresponding amine of the formula, where m and the radicals R 1, R 2, R 4, R 5, R 6, and R 7 in the formulas to are as defined in formula.