Process for functionalizing a water-soluble or water-dispersible polymeric organic binder, in which unmodified, water-soluble or water-dispersible polymeric organic binders are reacted with one or more polar aprotic swelling agents which are compatible with the binder, with thorough mixing with one or more compounds which have groups capable of free radical polymerization, compositions obtainable thereby and radiation-sensitive mixtures which contain, as essential components, the above composition, at least one photopolymerization initiator, if required one or more ethylenically unsaturated, photopolymerizable low molecular weight compounds which are compatible with the polymeric binder and further conventional additives and/or assistants, and radiation-sensitive letterpress or relief printing plates which can be produced therefrom.