This invention relates to a process for stabilizing and at the same time phase compatibilising plastics or plastic compositions by incorporating polymeric compounds obtainable by reacting a compound selected from the group consisting of the sterically hindered phenols, sterically hindered amines, lactones, sulfides, phosphites, benzotriazoles, benzophenones and 2-(2-hydroxyphenyl)-1,3,5-triazines, which compounds contain at least one reactive group, with a compatibilisator.