The present invention relates to a process for the production of polyurethanes where (a) polyisocyanate, (b) polymeric compounds having groups reactive toward isocyanates, (c) catalysts, (d) polymer P formed from ethylenically unsaturated monomers and having an average of more than 2 functional groups of the formula —O—NH2 and optionally (e) blowing agent, (f) chain extender and/or crosslinking agent, and (g) auxiliaries and/or additives are mixed to give a reaction mixture, and the reaction mixture is allowed to complete a reaction to give the polyurethane. The present invention further relates to polyurethanes produced by this process and to the use of these polyurethanes in the interior of means of transport.