A novel, impact-resistant, rubber-modified plastic material having good aging resistance can be produced by polymerizing 40 to 99 parts by weight of at least one ethylenically unsaturated monomer capable of forming a plastic material having a glass transition temperature of 10*C or higher, in the presence of 1 to 60 parts by weight of an olefin-acrylate copolymer comprising as the essential components an olefin having 3 to 20 carbon atoms and an acrylate in which the alcohol moiety has 1 to 20 carbon atoms, particularly an alternating copolymer of the olefin and the acrylate, or an alternating interpolymer of the olefin, the acrylate in which the alcohol moiety has no ethylenic unsaturation, and 0.1 to 30 mole percent of the acrylate in which the alcohol moiety has ethylenic unsaturation.