Process for obtaining an aqueous dispersion, formed by a polymer and making available particles composed of finely divided inorganic solid substance, in which at least one ethylenically unsaturated monomer is distributed in the aqueous medium in a dispersed form and polymerized by at least one polymerization initiator by means of radicals in the presence of at least one inorganic solid substance, finely divided and distributed in a dispersed form and at least one dispersant according to the method of aqueous emulsion polymerization by means of radicals, characterized in that a) an aqueous and stable dispersion of at least one inorganic solid substance is used, which is characterized in that it contains in an initial solid product concentration of 1% by weight, based on the aqueous dispersion of at least one solid substance, still one hour after obtaining more than 90% by weight of the substance s Dispersed liquid in its origin in dispersed form and its dispersed solid substance particles show an average diameter by weight at 100 nm, b) the dispersed solid substance particles of at least one inorganic solid substance shown in an aqueous normalized potassium chloride solution at a pH value, the pH value of the aqueous reaction medium at the start of emulsion polymerization, an electrophoretic mobility other than zero, and c) the radical generating component of at least one polymerization initiator by means of radicals and / or the dispersing effect component of at least one dispersant shows at least one electric charge, whose polarity is opposite to the polarity of the electrophoretic mobility of the dispersed solid substance particles of at least one solid substance, which show these in a solution of normalized and aqueous potassium chloride a pH value, which corresponds to the pH value of the aqueous reaction medium so at the beginning of emulsion polymerization.
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