The invention relates to polymeric phosphinic acids and their salts of the formula (I) in which X is hydrogen or a 1/m metal of valency m, R1 and R2 are identical or different and are hydrogen, a carboxyl group, a carboxylic acid derivative, an unsubstituted or substituted alkyl group having 1 to 10 carbon atoms, phenyl, benzyl or alkyl-substituted aromatics, R3 and R4 are identical or different and are hydrogen or a vinyl group of the formula (VI) —CR1═CHR2  (VI) in which R1 and R2 have the abovementioned meaning, and {overscore (u)} is the average number of monomer units. The invention also relates to a process for the preparation of the abovementioned compounds and their use.