The invention provides a polymer composition comprising a polyolefin or a diene elastomer, and an unsaturated compound (A) containing at least two groups each comprising an olefinic —C═C— bond or acetylenic —C≡C— bond, characterized in that each group comprising an olefinic —C═C— bond or acetylenic —C≡C— bond in the unsaturated compound (A) contains an aromatic ring or a further olefinic double bond or acetylenic unsaturation, the aromatic ring or the further olefinic double bond or acetylenic unsaturation being conjugated with the olefinic —C═C— or acetylenic —C≡C— unsaturation. The use of a multifunctional unsaturated compound (A) containing an aromatic ring or a further olefinic bond conjugated with the olefinic —C═C— or acetylenic —C≡C— unsaturation of the multifunctional unsaturated compound gives enhanced crosslinking and/or branching yield and/or less degradation of the polymer compared to crosslinking with a multifunctional unsaturated compound not containing an aromatic ring or a further olefinic bond.