Abstract: A distributor or transfer roller is provided for printing machines, in particular for offset printing machines. The roller has at least a substantially rigid core and a cover made of a polymeric material applied on and permanently fixed to the core. The cover is applied directly on the core or on a hard-elastic intermediate layer having a hardness of ?10 Shore D, optionally by an adhesion promoting layer. The cover is at least substantially made of a fluorinated polymer and has a hardness of ?15 Shore D and/or a scratch hardness according to ISO 15184 of 6B or harder. The polymeric material can be a duroplastic material, a fluorinated polyurethane resin, polyester resin, epoxy resin, acrylate resin and/or polyether resin, a highly cross-linked non-elastic fluoropolymer, a fluorothermoplastic, a polymeric non-elastic fluorosilicone, or a fluoropolymer lacquer.