The paper presents theoretical methodology that allows determination of thermodynamic state functions of the under-potential deposition of hydrogen, UPD H, and semiconductor or metallic species, UPD M. The experimental approach involves temperature dependence of the UPD by application of cyclic-voltammetry or chronocoulometry. The theoretical approach is based on a general electrochemical adsorption isotherm and numerical calculations which lead to determination of the Gibbs free energy of adsorption, ΔG°a ds , as a function of Τ and θ. Temperature dependence of ΔG°a ds , (for θ = const) leads to appraisal of the entropy of adsorption, ΔS°a ds , whereas coverage dependence of ΔG°a ds (for Τ = const) allows assessment of the nature of the lateral interactions between the adsorbed species; knowledge of ΔG°a ds and ΔS°a ds leads to determination of ΔH°a ds . The paper presents new approach which permits elucidation of the bond energy between the substrate, S, and H UPD or S and M UPD , E S-HUPD and E S-MUPD , respectively. Comprehension of E S-HUPD is essential in assessment of the strength of the S-H UPD bond and the adsorption site of H UPD .Knowledge of E S-MUPD is of importance in: (i) evaluation of the strength of the cohesive forces acting between S and M UPD that are responsible for the adhesion of the adsorbate to the substrate; and (ii) comparison of the S-M UPD bond with that observed for the 3-D bulk deposit of M. The UPD H on Rh and Pt electrodes from aqueous H2SO4 solution is discussed as an example of application of this methodology.The under-potential deposition, UPD, of hydrogen, H, and semiconductors and metals, abbreviated by M, of the ρ and d blocks of the periodic table on transitionmetal has been a subject of intense studies in electrochemical surface science (1-15).