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The adsorption potential theory was applied to study the adsorption isotherms of hydrogen on four kinds of zeolites above critical temperature and under a wide range of pressure. An approximate treatment was used to obtain the pseudo-saturated pressure of supercritical hydrogen and the affinity coefficients of adsorption systems under study. A formula for the generalized adsorption function to describe supercritical adsorption of hydrogen on zeolites was derived by the analysis of the functional dependence of the adsorption amount on the adsorption potential and the affinity coefficients. The study showed that the affinity coefficients had a linear relation with the adsorption heat, which could be used as a parameter of the generalized adsorption function in characterization of an adsorption system. The fittings of the generalized adsorption function to experimental data exhibited that the hydrogen adsorption on zeolites above critical temperature could be satisfactorily described by the generalized adsorption function.