The invention relates to processes for preparing 3-aminomethyl-3,5,5-trimethylcyclo-hexylamine (isophoronediamine, IPDA) having a high cis/trans isomer ratio. IPDA having a cis/trans isomer ratio in the range from 63/37 to 66/34 can be obtained in any desired cis/trans isomer ratio, irrespective of temperature, by reacting IPDA with H.sub.2 and NH.sub.3 in the presence of a hydrogenation catalyst. IPDA having a cis/trans isomer ratio of at least 73/27 which is an important starting material for the synthesis of polyurethanes and polyamides can be obtained by combining this isomerization process with distillative processes.