In a process for the preparation of copolymers containing vinyl esters and ethylene or ethylenically unsaturated monomers by aqueous, free radical polymerization at a pressure of from 5 to 100 bar absolute by the emulsion or suspension polymerization method, after the end of the polymerization, the reaction mixture is let down to a pressure of from 0.1 to 5 bar absolute and recovery of unconverted monomers is effected by multistage fractional low-temperature condensation from the residual gas.