Disclosed is a method for making nongelled functional addition polymers from linear unsaturated anhydrides. The method subjects a linear unsaturated anhydride compound, an active hydrogen compound, and an epoxide compound to reaction conditions such that each of the following three reactions occur: (i) polymerization of polymerizable C.dbd.C bonds, (ii) ring opening of an anhydride functional group of the linear unsaturated anhydride compound by the active hydrogen compound to create an acid functional group, and (iii) reaction of the acid functional group resulting from the anhydride ring opening with the epoxide compound. At the time of reaction (iii), the acid functional group resulting from the anhydride ring opening may be selected from an ethylenically unsaturated monomer, a polymer, or both. In one embodiment, the method does not include the physical removal of any acid functional monomers or polymerization products. Also disclosed are a curable coating composition and a coated substrate.