A roller comprising a roller core and a roller covering being composed of an elastomer or elastic plastic material is characterized in that the elastomer or elastic plastic material of the roller covering cadditionally comprises fluorinated polyolefin. Preferably, from 0.2 to 25% by weight of a fluorocarbon plastic, in particular of polytetrafluoroethylene powder or fiber, is incorporated into the roller coating material to improve the ink-repellent properties of the roller covering. In one embodiment, the fluorinated polyolefin is employed in the form of a fibrous material, e.g. a web or the like, provided with the coating material and wrapped around the roller to form a surface layer.