The preparation of alkoxylates of oligoamines or polyamines by a two-stage procedure where, in the first stage, one molecule of alkylene oxide per NH group is added onto the oligoamines or polyamines in the presence of water, alcohols or acids or a mixture thereof in the absence of a neutral or basic catalyst and, in the second stage, after removal of water and acids reaction with further alkylene oxide is carried out in the presence of a conventional neutral or basic catalyst, entails, before the second stage is carried out, an organic solvent or diluent or a mixture thereof from the group of (a) alcohols and phenols and their alkoxylates, (b) polyalcohols based on ethylene oxide, propylene oxide, butylene oxide or a mixture thereof, (c) N-substituted carboxamides, (d) alkanolmonoamines and alkanolpolyamines and their alkoxylates, (e) other alkoxylates of oligoamines or polyamines, (f) aromatic hydrocarbons, (g) aliphatic hydrocarbons, (h) ethers and (i) sulfones or sulfoxides being added.