1. A simple method is described for calculating the free concentrations of all species in a mixture of several ionic components that associate at equilibrium to any extent and with any stoicheiometry. 2. It can readily be adapted to take account of species such as protons for which the free rather than the total concentrations are controlled. 3. It was applied to mixtures of adenine nucleotides, Mg2+ and other ions relevant to the study of glucokinase (EC 2.7.1.2), but the qualitative conclusions are not peculiar to this system. 4. ATP exists in a high and nearly constant proportion (about 80%) as MgATP2- in solutions in which the total MgCl2 concentration exceeds the total ATP concentration by 1-10 mM. 5. By contrast, the proportion of ATP present as MgATP2- varies greatly if the total MgCl2 and total ATP concentrations are varied in constant proportion.