A network polymer that contains: (a) a plurality of polymer chains which are derived from one or more ethylenically-unsaturated monomer(s), and (b) at least one linking group which links the polymer chains and which contains anhydride, carbonate, or uretidinedione moieties. The network polymer and other network polymers which contain similar dissociating groups are useful in curable formulations which contain a curable compound that contains: (a) a central moiety, and (b) a plurality of reactive groups which are bonded to the central moiety and which react with acid, hydroxyl, or isocyanate moieties liberated by dissociation of the anhydride, carbonate, or uretidinedione moieties. The curable composition builds viscosity more slowly and more controllably during curing than equivalent systems which do not contain the network polymer. It is useful in coatings and other uses for curable compositions.