One-component moisture-curing composition comprising a) at least one polyurethane polymer P which contains isocyanate groups and has an average molecular weight of at least 4000 g/mol, and b) at least one polyaldimine ALD of the formula, where X is the radical of an n-functional polyamine having aliphatic primary amino groups and an average amine equivalent weight of at least 180 g/eq, preferably at least 220 g/eq, following removal of n amino groups; n is 2 or 3, Y 1 and Y 2 either independently of one another are each a monovalent hydrocarbon radical having 1 to 12 C atoms, or together form a divalent hydrocarbon radical having 4 to 20 C atoms which is part of an unsubstituted or substituted carbocyclic ring having 5 to 8, preferably 6, C atoms, and Y3 is a radical of the formula where R 3 is a hydrogen atom or is an alkyl or arylalkyl group and R 5 is either a linear or branched alkyl chain having 11 to 30 carbon atoms, optionally with at least one heteroatom, more particularly with at least one ether oxygen, or a singly or multiply unsaturated linear or branched hydrocarbon chain having 11 to 30 carbon atoms; the isocyanate group content being not more than 3.5% by weight, based on the sum of the isocyanate-group-containing constituents present in the composition; and further comprising at least one catalyst K which accelerates the hydrolysis of the aldimine groups and which is an organic carboxylic acid, an organic carboxylic anhydride, a silyl ester of an organic carboxylic acid, an organic sulfonic acid, a sulfonic ester or another organic or inorganic acid, and the amount of which is 0.005% to 2% by weight, based on the overall polyurethane composition. a) at least one polyurethane polymer P which contains isocyanate groups and has an average molecular weight of at least 4000 g/mol, and b) at least one polyaldimine ALD of the formula, where X is the radical of an n-functional polyamine having aliphatic primary amino groups and an average amine equivalent weight of at least 180 g/eq, preferably at least 220 g/eq, following removal of n amino groups; n is 2 or 3, Y 1 and Y 2 either independently of one another are each a monovalent hydrocarbon radical having 1 to 12 C atoms, or together form a divalent hydrocarbon radical having 4 to 20 C atoms which is part of an unsubstituted or substituted carbocyclic ring having 5 to 8, preferably 6, C atoms, and Y3 is a radical of the formula where R 3 is a hydrogen atom or is an alkyl or arylalkyl group and R 5 is either a linear or branched alkyl chain having 11 to 30 carbon atoms, optionally with at least one heteroatom, more particularly with at least one ether oxygen, or a singly or multiply unsaturated linear or branched hydrocarbon chain having 11 to 30 carbon atoms; where X is the radical of an n-functional polyamine having aliphatic primary amino groups and an average amine equivalent weight of at least 180 g/eq, preferably at least 220 g/eq, following removal of n amino groups; n is 2 or 3, Y 1 and Y 2 either independently of one another are each a monovalent hydrocarbon radical having 1 to 12 C atoms, or together form a divalent hydrocarbon radical having 4 to 20 C atoms which is part of an unsubstituted or substituted carbocyclic ring having 5 to 8, preferably 6, C atoms, and Y3 is a radical of the formula where R 3 is a hydrogen atom or is an alkyl or arylalkyl group and R 5 is either a linear or branched alkyl chain having 11 to 30 carbon atoms, optionally with at least one heteroatom, more particularly with at least one ether oxygen, or a singly or multiply unsaturated linear or branched hydrocarbon chain having 11 to 30 carbon atoms;