Thickeners, which are based on an aqueous preparation of nonionic water-dispersible or water-soluble polyurethanes, it being possible to produce these polyurethanes by reacting(a) one or more hydrophilic polyols (a) which contain, per molecule, at least two OH groups and at least two functional groups which are selected from the functions —O— (ether groups) and —COO— (ester groups), where the molecular weight of these hydrophilic compounds is at least 300,(b) one or more compounds of the formula (I),in which R is a CH3—CH(CH3)— (CH2—CH(CH3))2— group or a C15H31-m group (where m=0, 2, 4 or 6), Y is hydrogen or a methyl group and n is a number in the range from 0 to 10, and (c) one or more at least difunctional isocyanates, in which the compounds a), b) and c) are reacted with one another in the equivalent ratios OHa):OHb):NCOc) of 1:(1+x):2(1+y), with the provisos that the following conditions apply: x is a number in the range from 0.05 to 1.2, y is a number in the range from (0.2 to 1.05)x, and equivalent ratio NCOc)>(OHa)+OHb))are characterized by excellent thickening effect, in particular for aqueous dispersions.