An optical fiber having at least one epoxidized polyolefin based polymer coating. The coating is formed from a crosslinkable composition having (a) at least one epoxidized polydiene oligomer having a first and a second end, the oligomer having at least one hydrocarbon chain that is substantially free of ethylenic double bonds, at least one epoxide group at the first end and at least one reactive functional group at the second end; (b) at least one hydrogenated polydiene oligomer having at least one reactive functional group capable of reacting with the epoxide groups; and (c) at least one photo-initiator. Preferably, the coating is a primary coating coated with a secondary coating.