Polyurethanes having improved curing are prepared by reactinga) organic and/or modified organic diisocyanates and/or polyisocyanates withb) polyether polyols based on aromatic amines, able to be prepared by reacting specific amine combinations and, if desired, further coinitiators in a stage wise molecular addition of alkylene oxide, and also, if desired, further relatively high molecular weight compounds containing at least two reactive hydrogen atoms and, if desired,c) low molecular weight chain extenders and/or crosslinkers in the presence ofd) blowing agents,e) catalysts and, if desired,f) further auxiliaries and/or additives,wherein the specific amine combination used is a mixture of amines of the diphenylmethane series consisting of from 5 to 20% by weight of 4-ring amine, from 15 to 30% by weight of 3-ring amine, from 20 to 35% by weight of amines having more than 4 rings and from 25 to 50% by weight of 2-ring amine, wherein the proportions add up to 100% by weight, in combination with further aromatic amines.