A process for the preparation of polymers is described, wherein at least one first ethylenically unsaturated monomer is subjected to a free radical polymerization in the presence of stable free radicals or sources of stable free radicals and of a compound having at least one free thiol group to give a polymer, and wherein the molar ratio of compound having a free thiol group to stable free radicals is from 0.05 to 1.1. The polymerization rate is substantially increased by the compound having a free thiol group.