Homopolymers and/or copolymers are manufactured by polymerizing ethylenically monounsaturated monomer(s) in an aqueous solution in a reaction vessel containing compounds which contain a phosphorus atom of degree of oxidation less than 5, phosphorous compounds being introduced in amounts of 0.005-0.49 gram-atom phosphorus per mol of unsaturation in said ethylenically unsaturated monomer(s) in the presence of hydrogen peroxide and in the absence of any agent(s) which decomposes hydrogen peroxide thereby forming free radicals, in the absence of any other generator of free radicals, and in the absence of any per salt and/or any other transfer agent.