An in situ or one-pot process for the preparation of the compounds of formula (I) uses a compound of general formula (I): ##STR00001## and includes:a) the hydrogenation of a nitrile group of the compound of general formula (II): ##STR00002## in which R.sub.1 to R4 are especially H or alkyl and n varies from 0 to 4, in the presence of a hydrogenation catalyst, a methylating agent and an organic acid as solvent, and at a temperature Ta below the initiation temperature of a reductive amination reaction, to give a primary amine from the nitrile group; andb) the reductive amination of the primary amine in the presence of hydrogen, at a temperature Tb above Ta, to give the dimethylated amine of general formula (I) by activation of the methylating age.