In a process for preparing 3-aminomethyl-3,5,5-trimethylcyclohexylamine (isophoronediamine, IPDA) having a cis/trans isomer ratio of at least 70/30 from 3-cyano-3,5,5-trimethylcyclohexanone (isophoronenitrile, IPN), NH.sub.3 and H.sub.2, the hydrogenation is carried out at from 50 to 200.degree. C. and a pressure of from 50 to 300 bar in the presence of a hydrogenation catalyst having an alkali metal content of .ltoreq.0.03% by weight, calculated as alkali metal oxide referring to the total weight of the catalyst.The alkali metal content is made up of the contents of Li, Na, K, Rb and Cs; in particular, the alkali metal content is the Na content.A process for producing hydrogenation catalysts having an alkali metal content (in particular a sodium content) of .ltoreq.0.03% by weight, calculated as alkali metal oxide/sodium oxide referring to the total weight of the catalyst, and the hydrogenation catalysts themselves are also provided by the invention.