A process for the continuous manufacture of an aqueous ethylene/vinyl acetate copolymer dispersion which comprises continuously copolymerizing ethylene and vinyl acetate and optionally other .alpha.-olefinically unsaturated monomers, in an aqueous emulsion in the presence of an emulsifier and/or a protective colloid, and in the presence of a free-radical-forming redox catalyst system of a reducing agent and an oxidizing agent as well, optionally, as a heavy metal salt, and recovering said ethylene/vinyl acetate copolymer dispersion, characterized by (a) the presence of a molar excess of at least 3 times, preferably from 3 to 10 times, said reducing agent over said oxidizing agent dosed into the reaction medium and (b) adding the monomers continuously to the reaction mixture at such a rate that the concentration of unreacted monomers at no place in the reaction zone exceeds 15% by weight of the total weight of the reaction mixture.