According to the present invention, aqueous multi-stage polymer dispersions comprising an acid-functional first polymer and an epoxy-functional second polymer, wherein 90 mole % or more of the said epoxy groups, based on the moles of epoxy groups in the monomer mixture used to form the second polymer, are retained in the aqueous dispersion after said dispersion is stored in a sealed container for 10 days at 60.degree. C. Further, methods of making the aqueous multistage polymer dispersion comprise polymerizing the monomers used to make the second polymer in the presence of an aqueous dispersion of the first polymer. Preferably, the second polymer is formed in the presence of 0.3 wt. % or less, based on the total weight of the first polymer and the ingredients to form the second polymer, of one or more strong acid surfactant, and 3) 0.1 wt. % or less, based on the total weight of the first polymer and the ingredients to form the second polymer, of one or more initiator that contains strong acid groups or generates strong acid groups under the conditions of aqueous emulsion polymerization. The aqueous dispersions provide non-toxic, odor free storage stable coating compositions that form coatings having excellent film toughness and hardness.