Aqueous polymer dispersions obtainable by incorporating into an aqueous starting dispersion containingA) from 25 to 60% by weight, based on the starting dispersion, of a polymer A as the disperse phase, built up froma) from 3 to 55% by weight of one or more .alpha.,.beta.-monoethylenically unsaturated mono- or dicarboxylic acids containing from 3 to 5 carbon atoms, of an anhydride of these acids or of a mixture of these monomers (monomers a), andb) from 45 to 97% by weight of one or more other copolymerizable monomers (monomer b), in polymerized form and having, in disperse form, a mean particle size of from 20 to 400 nm,B) an effective amount of an emulsifier, andC) water as the remainder, at a temperature below the boiling point of pure water and above the glass transition point of the polymer A, from 5 to 60 mol-%, based on the number of moles of acid functions of the polymer A copolymerized in the form of the monomers a, of one or more of the divalent metals magnesium, calcium and zinc in the form of the oxide, hydroxide, carbonate or bicarbonate or in the form of a mixture of these basic salts, a process for their preparation, binders prepared therefrom, and bitumen-treated roof sheeting produced using these binders.