FIELD: chemical industry, paper industry, survey and a crude oil production. SUBSTANCE: manufacture of homopolymers and copolymers in a water solution using polymerization of monomers with non-saturated olefinic links at the presence of a compound containing an atom of phosphorus with oxidation level below 5, and the hydrogen superoxides, distinguished that, they use a molar quantity of the containing atom of phosphorus compound, equal 0.005 - 0.49 gramme-molecules per 1 gramme-molecule of at least one polymerized monomer, and reaction is conducted with production of a (co)polymer water solution, and at that the contents of residual monomers is below or equal to 300 p / million, and concentration of the polymer in the water solution is no less than 38 % by dry substance irrespective of monomeric composition, in absence of any agent of decomposition of hydrogen superoxide for free radicals and any other free-radicals initiator, as well as in absence of any peracid salt or any other chain-transfer agent. Besides there is a description of a polymer produced by this method and an water suspension of mineral substances containing above-stated polymer. EFFECT: homopolymers and/or copolymers produced by the above-stated method, can be used as an agent of comminution and/or dispersion of water suspension of mineral substances, as a complex-forming agent or an inhibitor of settling and/or formation of mineral sedimentations, as a diluting agent in the water suspensions use as a drilling mud used in process of survey and a crude oil production, as a stabilizer of ceolite suspensions, as a modifying descaling agent in detergent compounds, as an agent retaining water in a paper industry. 19 cl, 14 ex, 10 tbl
