This paper is devoted to measurements of hydrogen sorption into Pd and Li-ion insertion into the transition metal oxides (lambda -MnO2 in particular) performed under strict equilibrium and quasi-equilibrium conditions, respectively. The related charging-discharging curves show common features to the two systems such as potential plateaus, which can be ascribed to highly attractive interactions between the intercalation sites, leading, eventually, to first-order phase transitions. Fitting an equilibrium charging curve to a simple Frumkin-type isotherm for a highly defective Pd lattice demonstrates a rather good agreement between the curves within the whole region of compositions 0 < x < 1. In the case of LixMn2O4,we found a clearly expressed hysteresis, which does not disappear even at the lowest rate of charge and discharge used. We believe that this kind of behavior is due to the combined effect of slow Butler-Volmer kinetics for Li-ion transfer and the true interaction parameter g, which may be more negative than the critical value - 4. It was found that treating averaged charging and discharging curves of the LixMn2O4 electrode, the modified thermodynamic relations and the corresponding equation for the sorption isotherm should be used with the term x(2)/(1 - x) substituted for x/(1 - x) in the simple isotherm under discussion.