Polyurethane foams having a yellowness index of less than 30, determined according to EN ISO 4892-2, and a tensile strength of at least 60 kPa, determined according to DIN 53571, are prepared by reacting (a) at least one aliphatic or cycloaliphatic isocyanate with (b) at least one compound which contains at least two hydrogen atoms reactive toward isocyanates in two stages by the prepolymer method, in which either i) in a first stage, the total amount of the isocyanate (a) is reacted with a portion of the compound (b) to give a prepolymer and, in a second stage, the prepolymer is reacted with the remaining amount of the compound (b) to give the finished polyurethane, or ii) in a first stage, the total amount of the compound (b) is reacted with a portion of the isocyanate (a) to give a prepolymer and, in a second stage, the prepolymer is reacted with the remaining amount of the isocyanate (a) to give the finished polyurethane, process for their production, modified open-celled hydrophilic aliphatic polyurethane foams obtainable by reaction of (a) aliphatic polyisocyanates with (b) at least one compound having at least two isocyanate-reactive hydrogen atoms in the presence of a surfactant and/or treating a polyurethane foam with a surfactant or treating a polyurethane foam with a polymer containing primary and/or secondary amino groups and having a molar mass of at least 300, and the sue of said polyurethane foams in furniture, floor coverings, in hygiene articles, for insulation purposes and for packaging.