A process for aqueous, free-radically initiated, continuous emulsion polymerization of A) at least one vinyl ester and optionally at least one (meth)acrylic ester, B) ethylene, and C) 0 to 10% by weight of one or more ethylenically unsaturated, functionalized comonomers, in the presence of 3.0 to 12.5% by weight of one or more emulsifiers, where at least 50% by weight are nonionic emulsifiers, and 0 to 10% by weight of one or more protective colloids, in a stirred tank cascade with at least two pressure reactors connected in series and with at least one low-pressure reactor connected downstream.