A curable composition for coating an optical fiber that includes an aliphatic-aromatic oxyglycidyl(meth)acrylate monomeric component, an aliphatic-(hetero)cyclic oxyglycidyl(meth)acrylate monomeric component, or a combination thereof, and an ethylenically unsaturated urethane or urea oligomeric component. Cured products of the composition and optical fibers that contain cured primary coatings formed from such compositions are also disclosed. The resulting optical fibers and optical fiber ribbons containing them can be used for data transmission in telecommunications systems.