1. The ATP sites. Homotropic interactions between ATP sites have been studied in a very large range of Na+ and K+ concentrations. The ( Na+, K+)-activated ATPase displays Michaelis-Menten kinetics for ATP under standard concentration conditions of Na+ (100 mM) and K+ (10 mM). The steady-state kinetics behavior changes at very low concentrations of K+ where negative cooperativity is observed. The existence of a high affinity and a low affinity site for ATP was clearly demonstrated from the study of the ATP stimulated hydrolysis of p-nitrophenylphosphate in the presence of Na+ and K+. The ratio of apparent affinities of high and low affinity sites for ATP is 86 at pH 7.5. 2. The Na+ sites. The binding of Na+ to its specific stimulatory sites (internal sites) is characterized by positive cooperativity with a Hill coefficient n(H(Na+))=2.0. Homotropic interactions between Na+ sites are unaffected by variations of the K+ concentration. 3. The K+ sites. (a) Binding of K+ to the (external) stimulatory site of the ATPase has been analyzed by following the (Na+, K+)-ATPase activity as well as the p-nitrophenylphosphatase activity in the presence of Na+ and K+ (with or without ATP). Binding is characterized by a Hill coefficient of 1.0 and a K(0.5(K+))=0.1 to 0.8 mM. The absence of positive or negative cooperativity persists between 5 mM and 100 mM Na+. (b) The analysis of the p-nitrophenylphosphatase or of the 2, 4 dinitrophenylphosphatase activity in the presence of K+ alone indicates the existence of low affinity sites for K+ with positive homotropic interactions. The characteristics of stimulation in that case are, K(0.5)=5 mM, n(H)=1.9. The properties of this family of site(s) are the following: firstly, saturation of the low affinity site(s) by K+ prevents ATP binding to its high affinity internal site. Secondly, saturation of the low affinity sites for K+ prevents binding of Na+ to its internal sites. Thirdly, this family of sites disappears in the presence of ATP, p-nitrophenylphosphate or of both substrates, when Na+ binds to its internal sites. Na+ binding to its specific stimulatory sites provokes the formation of the high affinity type of site for K+. 4. Mg2+ stimulation of the (Na+, K+)-ATPase is characterized by a Hill coefficient n(H(Mg2+))=1.0 and a K(0.5(Mg2+))=1 mM stimulation is essentially a V effect. Heterotropic effects between binding of Mg2+ and substrate to their respective sites are small. Heterotropic interactions between the Ms2+, Na+ and K+ sites are also small. 5. The fluidity of membrane lipids also controls the (Na+, K+)-ATPase activity. Phase transitions or separations in the membrane hardly affect recognition properties of substrates, Na+, K+ and Mg2+ for their respective sites on both sides of the membrane. Only the rate of the catalytic transformation is affected.