Analysis of phase transformation processes observed in most hydrogen-absorbing materials (pure metals, alloys or compounds) is still a matter of active research, in view of electrochemical or chemical hydrogen storage applications. Most metal hydride systems present a large and irreducible hysteresis, indicating that non-linear phenomena are taking place during hydrogen sorption/desorption reactions. Investigation of hydriding kinetics therefore requires non-harmonic spectroscopies to fulfill the requirements of linearity and time invariance imposed by the theory of systems. The purpose of this paper is to report on the insertion of atomic hydrogen into a palladium foil. The process is analyzed using electrochemical (the electrolyte is the source of hydrogen) and pneumato-chemical (the gas phase is the source of hydrogen) experimental spectroscopies. Pneumato-chemical impedance spectroscopy (PIS) provides additional information to electro-chemical impedance spectroscopy (EIS) since (i) there is no electrolyte and no electrified interface; (ii) experiments can be performed over long periods of time, without any pollution (closed systems); (iii) there is no parasite reaction such as hydrogen evolution encountered in electrochemical experiments; (iv) the temperature range of investigation is larger; (v) there is no kinetic limitations on the electrolyte side of the interface. Results obtained in single and two-phase domains of the model PdH system, using both EIS and PIS spectroscopies, are reported and discussed. Surface and bulk microscopic rate parameters are compared.