We have previously demonstrated that Na+,K(+)-ATPase can be phosphorylated by 100 microM ATP and 5 mM Mg2+ and in the absence of Na+, provided that 40% dimethylsulfoxide (Me2SO) is present. Phosphorylation was stimulated by K+ up to a steady-state level of about 50% of Etot (Barrabin et al. (1990) Biochim. Biophys. Acta 1023, 266-273). Here we describe the time-course of phosphointermediate (EP) formation and of dephosphorylation of EP at concentrations of Mg2+ from 0.1 to 5000 microM and of K+ from 0.01 to 100 mM. The results were simulated by a simplified version of the commonly accepted Albers-Post model, i.e. a 3-step reaction scheme with a phosphorylation, a dephosphorylation and an isomerization/deocclusion step. Furthermore it was necessary to include an a priori, Mg(2+)- and K(+)-independent, equilibration between two enzyme forms, only one of which (constituting 14% of Etot) reacted directly with ATP. The role of Mg(2+) was two-fold: At low Mg2+, phosphorylation was stimulated by Mg2+ due to formation of the substrate MgATP, whereas at higher concentrations it acted as an inhibitor at all three steps. The affinity for the inhibitory Mg(2+)-binding was increased several-fold, relative to that in aqueous media, by dimethylsulfoxide. K+ stimulated dephosphorylation at all Mg(2+)-concentrations, but at high, inhibitory [Mg2+], K+ also stimulated the phosphorylation reaction, increasing both the rate coefficient and the steady-state level of EP. Generally, the presence of Me2SO seems to inhibit the dephosphorylation step, the isomerization/deocclusion step, and to a lesser extent (if at all) the phosphorylation reaction, and we discuss whether this reflects that Me2SO stabilizes occluded conformations of the enzyme even in the absence of monovalent cations. The results confirm and elucidate the stimulating effect of K+ on EP formation from ATP in the absence of Na+, but they leave open the question of the molecular mechanism by which Me2SO, inhibitory Mg2+ and stimulating K+ interact with the Na+,K(+)-ATPase.