The invention relates to polymeric phosphinic acids and their salts of the formula (I) where X is hydrogen or 1/m of a metal of valency m, or is a protonated nitrogen base, R1 and R2 are identical or different and are hydrogen, a carboxy group, a carboxylic acid derivative, an unsubstituted or substituted alkyl group having from 1 to 10 carbon atoms, phenyl, benzyl, or alkyl-substituted aromatic systems, R3 and R4 may be identical or different and are an unsubstituted or substituted alkyl group having from 2 to 20 carbon atoms, or are OX, with the above meaning for X, and ū is the average number of monomer units. The invention further relates to a process for preparing the abovementioned compounds, and to their use.