Polyurethane foams are produced by reactinga) organic and/or modified organic diisocyanates and/or polyisocyanates withb) at least one relatively high molecular weight compound containing at least two reactive hydrogen atoms,c) at least one compound containing from three to eight, preferably from three to six, reactive hydrogen atoms andd) low molecular weight chain extenders and/or crosslinkers containing at least two reactive hydrogen atomsin the presence ofe) blowing agentsf) catalysts and, if desired,g) further auxiliaries and additives,wherein (c) are ethylene oxide-rich adducts having an ethylene oxide content of more than 50% by weight and an OH number of from 200 to 800 mg KOH/g and (d) are polyfunctional chain extenders and/or crosslinkers having an OH number of more than 700 mg KOH/g.The polyurethane foam produced by this process can be used as upholstery material.