Polyurethanes suitable as coating materials or components thereof are essentially composed of A) a.sub.1) from 40 to 100 mol % of bis(4-isocyanatocyclohexyl)methane, the trans/trans content of (a.sub.1) being up to 18 mol %, based on the amount of (a.sub.1), and a.sub.2) from 0 to 60 mol % of further polyfunctional aliphatic, cycloaliphatic, araliphatic or aromatic isocyanates of 4 to 30 carbon atoms and B) b.sub.1) from 20 to 100 mol % of a nonaromatic diol and b.sub.2) from 0 to 80 mol % of further polyfunctional compounds having reactive groups which can react with the isocyanate groups (A), the reactive groups being hydroxyl or primary or secondary amino groups.