Polyamines containing at least two nitrogen atoms monosubstituted with pendant arms capable of coordinating metal cations, or with precursors of such pendant arms, all nitrogen atoms of the polyamines except two being fully substituted and the remaining two bearing one H atom each, are cyclized by reaction with a bridging agent that contains two sites that each bear a reactive group capable of undergoing a nucleophilic attack by one of the two N-H groups on the polyamine. Unlike the prior art, cyclization occurs in preference over polymerization of the polyamine, even in reaction mixtures in which the polyamine is at high concentration. A process is also disclosed whereby linear polyamines in which the terminal amine groups are primary amines are substituted with methylenephosphonate ester groups, with one such substituent on each nitrogen atom of the polyamine. The process involves the use of a trialkyl or triaryl phosphite, and unlike the prior art, monosubstitutions at all nitrogen atoms are achieved in preference over disubstitutions at the terminal primary amines. Finally, a novel class of N,N′,N″-tris(methylenephosphonate or methylephosphonic acid-substituted)-1,4,7-triazaheptanes are disclosed as new compositions of matter.