Soluble polyacetals containing acetaldehyde acetal units are obtainable by cationically initiated addition polymerization of(a) compounds containing at least 3 hydroxyl groups, and(b) divinyl ethers containing terminal vinyl ether groups, or mixtures of such divinyl ethers and monovinyl ethers, in the presence or absence of(c) dihydroxy compounds and/or monohydroxy compounds, and are useful as admixture in phosphate-reduced and phosphate-free detergents and cleaners and as dispersant for finely divided minerals.