A process for preparing polyamines, which comprises converting compounds of the formula NC-Z m - n -Y where Z corresponds to the CH 2 -CH 2 -NR- group, m = 0 or 1, where in the case that m = 0 NC- is bonded directly to X, in the case that m = 1 and n = 1 NR is bonded to X and R = H or CH 2 -CH 2 -CN, or in the case that m = 1 and n = 0 either R of NR is selected from the group consisting of CH 3, phenyl, CH 2 -CH 2 -CN and CH 2 -CH 2 -CH 2 -NH 2 or the nitrogen of the NR is part of a heterocycle selected from the group of piperazines, (benz)imidazoles, pyrazoles, triazoles and diazepanes, in which another nitrogen of the heterocycle is bonded to Y, X is selected from the group of alkyl group-substituted or unsubstituted methylene, ethylene, propylene, butylene, pentylene, hexylene, heptylene, octylene, nonanylene, decanylene, undecanylene, dodecanylene groups, of alkyl group-substituted or unsubstituted 1,2-, 1,3- or 1,4-benzyl groups, 1,4'-bicarbonyl groups, 9,10-anthracenyl groups, alkyl group-substituted or unsubstituted 1,2-, 1,3- or 1,4-cycloalkyl groups, substituted or unsubstituted phenyl-N group, of piperazines, (benz)imidazoles, pyrazoles, triazoles and diazepanes, where the bond to CN or Z and Y or H in each case is via the two nitrogen atoms of the ring, one to two methylene groups that may be substituted by linear or branched C 1 - to C 12 -alkyl, C 6 - to C 10 -aryl, C 7 - to C 12 -aralkyl, C 3 - to C 8 -cycloalkyl, and at least one methylene group may be replaced by 0, NH or NR, where R has the same definition as above and the C 1 - to C 12 -alkyl, C 6 - to C 10 -aryl, C 7 - to C 12 -aralkyl, C 3 - to C 8 -cycloalkyl groups may in turn be substituted by alkyl groups, n is 0 or a natural number from 1 to 10, Y in the case that m = 0 and n = 1 or higher is CN, CH 2 -NH 2 or CH 2 -CH 2 -CN or in the case that m = 1 and n = 1 or higher is NH 2 or NR-CH 2 -CH 2 -CN or in the case that m = 1 and n = 0 is H, CH 2 -CH 2 -CN, CH 2 -CH 2 -CH 2 -NH 2, alkyl group-substituted or unsubstituted benzyl or cycloalkyl group, or in the case that m = 0 and n = 0 is CH 2 -CN, CH 2 -CH 2 -CN, CH 2 -CH 2 -CH 2 -CN, CH 2 -CH 2 -CH 2 -CH 2 -CN, CH 2 -CH 2 -CH 2 -CH 2 -CH 2 -CN, CH 2 -NH 2, CH 2 -CH 2 -NH 2, CH 2 -CH 2 -CH 2 -NH 2, in one stage at temperatures in the range from 100 to 200°C and pressures in the range from 20 to 200 bar in the presence of hydrogen and a heterogeneous catalyst, the same heterogeneous catalyst if two or more reactors are used, comprising one or more elements of transition group 8 of the Periodic Table. Z corresponds to the CH 2 -CH 2 -NR- group, m = 0 or 1, where in the case that m = 0 NC- is bonded directly to X, in the case that m = 1 and n = 1 NR is bonded to X and R = H or CH 2 -CH 2 -CN, or in the case that m = 1 and n = 0 either R of NR is selected from the group consisting of CH 3, phenyl, CH 2 -CH 2 -CN and CH 2 -CH 2 -CH 2 -NH 2 or the nitrogen of the NR is part of a heterocycle selected from the group of piperazines, (benz)imidazoles, pyrazoles, triazoles and diazepanes, in which another nitrogen of the heterocycle is bonded to Y, X is selected from the group of alkyl group-substituted or unsubstituted methylene, ethylene, propylene, butylene, pentylene, hexylene, heptylene, octylene, nonanylene, decanylene, undecanylene, dodecanylene groups, of alkyl group-substituted or unsubstituted 1,2-, 1,3- or 1,4-benzyl groups, 1,4'-bicarbonyl groups, 9,10-anthracenyl groups, alkyl group-substituted or unsubstituted 1,2-, 1,3- or 1,4-cycloalkyl groups, substituted or unsubstituted phenyl-N group, of piperazines, (benz)imidazoles, pyrazoles, triazoles and diazepanes, where the bond to CN or Z and Y or H in each case is via the two nitrogen atoms of the ring, one to two methylene groups that may be substituted by linear or branched C 1 - to C 12 -alkyl, C 6 - to C 10 -aryl, C 7 - to C 12 -aralkyl, C 3 - to C 8 -cycloalkyl, and at least one methylene group may be replaced by 0, NH or NR, where R has the same definition as above and the C 1 - to C 12 -alkyl, C 6 - to C 10 -aryl, C 7 - to C 12 -aralkyl, C 3 - to C 8 -cycloalkyl groups may in turn be substituted by alkyl groups, n is 0 or a natural number from 1 to 10, Y in the case that m = 0 and n = 1 or higher is CN, CH 2 -NH 2 or CH 2 -CH 2 -CN or in the case that m = 1 and n = 1 or higher is NH 2 or NR-CH 2 -CH 2 -CN or in the case that m = 1 and n = 0 is H, CH 2 -CH 2 -CN, CH 2 -CH 2 -CH 2 -NH 2, alkyl group-substituted or unsubstituted benzyl or cycloalkyl group, or in the case that m = 0 and n = 0 is CH 2 -CN, CH 2 -CH 2 -CN, CH 2 -CH 2 -CH 2 -CN, CH 2 -CH 2 -CH 2 -CH 2 -CN, CH 2 -CH 2 -CH 2 -CH 2 -CH 2 -CN, CH 2 -NH 2, CH 2 -CH 2 -NH 2, CH 2 -CH 2 -CH 2 -NH 2,