Production of an aqueous polymer dispersion involves moving the reaction emulsion through an external cycle (9) leading from and returning to a reaction vessel. The cycle (9) has a shearing-deficient pump and a heat exchanger (8) having a laminar flow profile. Production of an aqueous polymer dispersion comprises radically polymerizing compounds (I) having individual solubility in water of at least 0.001 wt.%, and comprising polymer particles containing compounds (II), whose water solubility is less than 0.001 wt.%. An oil-in -water mixture (emulsion I) is produced from a mixture of compound (I) including the compounds (II). An Independent claim is also included for the apparatus used to carry out production process.