Linear crosslinkable polyurethanes obtained from (a) at least one diisocyanate having 2 to 30 carbon atoms, (b) at least one aliphatic or cycloaliphatic diol having 2 to 30 carbon atoms, to whose carbon chain at least one carboxyl group is covalently bonded, and some or all of said carboxyl groups have been esterified with an olefinically unsaturated C.sub.3-C.sub.8alcohol or with the glycidyl ester of an olefinically unsaturated C.sub.3-C.sub.8carboxylic acid, and (c) optionally at least one aliphatic or cycloaliphatic diol having 2 to 30 carbon atoms, to whose carbon chain at least one carboxyl group is covalently bonded. The polyurethanes are suitable, alone or as a mixture with other reactive components, for thermal and/or photochemical crosslinking in crosslinkable compositions for the production of mouldings, coatings and in particular solder masks.