A nonaqueous coating material composition and coatings thereof are provided. The composition contains an oligomeric and/or polymeric compound (A) having at least two hydroxyl groups, an oligomeric and/or polymeric compound (B) having at least two alkylidene-1,3-dioxolan-2-one groups of formula (I′), and a catalyst (D) where # stands for the attachment to the polymer backbone and R1, R2 independently of one another are hydrogen, C1-C6 alkyl, C1-C4 alkoxy-C1-C4 alkyl, C5-C6 cycloalkyl, phenyl or phenyl-C1-C4 alkyl; R3 is hydrogen, C1-C6 alkyl, C1-C4 alkoxy-C1-C4 alkyl, C5-C6 cycloalkyl, phenyl, or phenyl-C1-C4 alkyl; A is a chemical bond or C1-C4 alkanediyl; X is O or NR7; Z is a chemical bond, PO2, SO2, or C═O, Y is a chemical bond, CH2, or CHCH3, and R7 where present is C1-C6 alkyl.