A constrained-layer construction comprising a stiff layer or substrate and a layer of a viscoelastic polymer which is the reaction product of (a) 25 to 75 weight percent of an acryloyl or methacryloyl derivative of at least one oligomer, said oligomer having a glass transition temperature of less than 25.degree. C. and a molecular weight per oligomer of 600 to 20,000, and (b) 75 to 25 weight percent of a copolymerizable monomer whose homopolymer has a glass transition temperature of at least 50.degree. C., the copolymer being suitable for damping vibrations at relatively high temperatures, e.g., 50.degree.-150.degree. C., is disclosed. Also included is a process for damping vibrations in component parts of devices used in automotive, aerospace, and computer industries.