Aqueous solutions of poly(maleic acid) (PMA) exhibit a phase separation when neutralized with monovalent bases, prior to the complete neutralization, irrespective of the presence or absence of added salts. The values of the critical degree of neutralization (alpha(tau)) at which the precipitation develops were measured for the PMA aqueous solutions neutralized with various kinds of monovalent counterions, as a function of polymer (C(p)) and added salt concentrations (C(s)). It was found that, at constant C(s), a(tau) decreases sharply with increasing C(p) and that, at constant a(tau), the critical NaCl concentration (C(s)BAR) decreases linearly with increasing C(p). This phenomenon is attributable to the strong binding of monovalent counterions to ionized sites of a polyion and can be analyzed in terms of a site-binding model. The phase separation was shown to occur even in a salt-free solution when the amount of strongly bound Na+ became a certain value, C(p)gamma, where gamma = 0.58. Addition of monovalent salts facilitates the phase separation. At a low degree of neutralization, PMA was found to be quite soluble, in accordance with the neutralization dependence of the solubility of its monomer unit, maleic acid, which was also examined together with that of fumaric acid.