The invention relates to compositions for inhibiting the formation of deposits in underground formations such as oil wells, comprising, in a solvent medium, polymers P resulting from the radical copolymerization, preferably controlled and in solution, of a mixture including: monomers having an ethylenically unsaturated structure, selected from monomers that form, by polymerization, a polymer that has an effect of inhibiting the formation of organic and/or inorganic deposits; and polyethylenically unsaturated, cross-linking monomers carrying at least one group that can be cleaved between two ethylene unsaturations, said polymers P being present in the solvent in the form of dispersed nanogels.