A process for the rectification of mixtures of high-boiling air- and/or temperature-sensitive substances which require a high separation efficiency is proposed, in particular a process for the working-up of a VE- or VEA-containing product stream. The process includes a first purification stage to separate low-boiling products and unspecified isomers of the useful product from the product stream virtually without loss of useful product and a second purification stage for removing the useful product in a stream having a purity of >97% by weight and a further stream having a purity of >92% by weight.