Low molecular weight poly(acrylic acid-co-vinyl aminomethylene phosphonic acid)s were prepared by consecutively applying the Hofmann degradation and the Mannich reaction to polyacrylamide and poly(acrylamide-co-acrylic acid)s. H-1-NMR, P-31-NMR, and microanalysis were used for structural analyses. These polymers were tested as anti-scalent and they showed better anti-scalent effect than commercial poly(acrylic acid)s. The scale inhibition properties of copolymers increased with increasing amount of aminomethylene phosphonic acid groups.