Phosphonates are important compounds in water treatment, research, and medicine. The acid-base and alkaline-earth metal ion complex solution chemistry of the polyphosphonate diethylenetriaminepentakis(methylenephosphonic acid) (DTPMP) has been determined up to 2 m ionic strength and from 25 to 90 90-degrees-C. The phosphonate acid-base and metal complex stability constants were modeled with a simple polymer-type model permitting the solution chemistry to be viewed either as a polymer or as discrete steps. This facilitates interpretation and comparison with previously published discrete constants. Two of the three sp3-hybridized nitrogen atoms are protonated first with stability constants K1N = 10(12.58 +/- 0.05) and K2N = 10(11.18 +/- 0.03); the third nitrogen is too weak of a base to be protonated under most solution conditions. The stepwise proton association constants of the phosphonate groups were modeled with the following one parameter model : log(K(i)) = b(H+)q(i-1), where K(i) is the ith proton association constant (molality), q(i-1) is the value of the charge on the (i - 1)th species, and b(H+) was found to be about 1.04 with slight ionic strength and temperature dependence. A one-parameter model has been used to describe multiple metal complexation stability constants : log(K(ij)) = b(M2+q(ij-1), where q(ij-1) is the value of the charge on the phosphonate species, H(i)M(j-1)Phn and b(M2+) was found to be about 0.63, again with small dependence on ionic strength and temperature. Results are shown to be consistent with the electrostatic theory of complex formation. These results have been used to establish the existence of a new and highly insoluble calcium phosphonate phase. Applications of these results to other metals and phosphonates are discussed along with several practical examples.