Hexokinase was purified 680-fold from erythrocytes of man. The preparation was not contaminated by other glycolytic enzymes.Initial reaction rate measurements were performed at pH 7.2, ionic strength 0.15 and 37 "C by use of coupled optical assays. The experimental data were used to construct a kinetic model of the enzyme, the kinetic parameters of which were estimated by means of a computer-fit program.The hexokinase of erythrocytes operates by a rapid-equilibrium random mechanism. The dissociation constant of the E . glucose complex is 0.038 to 0.054 mM, of the F, -MgATP complex 1.0 to 2.1 mM. Uncomplexed Mg2+ up to 4 mM is capable of activating the enzyme velocity twofold (Knrgl+ = 1.0 mM). An inhibition was observed a t higher Mg2+ concentrations. a-D-Glucose 6-phosphate and &-D-glUCoSe 1,6-bisphosphate inhibit the hexokinase competitive to MgATP with dissociation constants of 0.069 mM. The enzyme is also inhibited by 2,3-bisphosphoglycerate competitive with respect to MgATP with a K P~G = 2.7 mM. An inhibition by uncomplexed ATP was not detected. The parameters of the kinetic model of the enzyme in conjunction with the free intracellular Concentrations of substrates and effectors were used to calculate the actual intracellular activity of the hexokinase in dependence on variations of pH, temperature and the state of haemoglobin oxygenation. The calculated hexokinase activities correspond to the glycolytic flux in all conditions considered, except a t pH 8.