A process for preparing N-methyl-2-(3,4-dimethoxyphenyl)-ethylamine comprises hydrogenating 3,4-dimethoxyphenylacetonitrile with a methylamine of the general formula I ##STR1## where R.sup.1 is hydrogen, benzyl or tert-butyl, and hydrogen in the presence of a supported catalyst which comprises from 0.05 to 50% by weight of copper chromite, copper, silver, gold, iron, cobalt, nickel, ruthenium, rhodium, palladium, osmium, iridium, platinum or mixtures thereof, in the presence or absence of water at from 20.degree. to 200.degree. C. under from 1 to 300 bar.