A carbamate or terminal urea functional vinyl polymer is prepared by reacting a compound having an hydroxyl group and a carbamate group, terminal urea group, or a group that can be converted to a carbamate or terminal urea group, with a cyclic carboxylic acid anhydride group to form an ester bond and a free acid group from the anhydride; and reacting the free acid group with a compound having an epoxide group. The cyclic carboxylic acid anhydride group may be pendant to a vinyl polymer, or one of the compound having an hydroxyl group, a compound having the cyclic carboxylic acid anhydride group, and the compound having an epoxide group may have polymerizable ethylenic unsaturation that is polymerized, optionally with one or more copolymerizable monomers to form a vinyl polymer. When the compound having an hydroxyl group has a group that can be converted to a carbamate or terminal urea group, the group is converted to the carbamate or terminal urea group after step (a). The carbamate or terminal urea functional vinyl polymer may be included in a coating composition. The coating composition may be applied to a substrate and cured to form a cured coating on the substrate.