Polyurethanes are made by reacting a polyisocyanate with a compound containing at least two isocyanate-reactive hydrogen atoms having a molecular weight of from 400 to 10,000 in the presence of a catalyst containing tertiary amino groups. The required catalyst corresponds to the formula ##STR1## in which R, R.sup.1, R.sup.2, R.sup.3, R.sup.4, R.sup.5, R.sup.6 and R.sup.7 represent a specified group or radical. A blowing agent and/or stabilizer and/or chain extending agent and/or other additives commonly used in the production of polyurethanes may optionally be included in the reaction mixture. The catalyst employed in the process is particularly advantageous in that it does not have a noticeable amine odor.