Pd overlayers with (111) and (100) morphology and with average thicknesses between one and ten monolayers were deposited onto Au(111) and Au(100), respectively. In the case of Pd on Au(111), the film growth was characterized by in situ STM. Due to a significant overpotential for hydrogen absorption in the Pd thin films, adsorption of hydrogen can be studied without being masked by the absorption reaction. H adsorption on Pd(111) films with an average thickness of about five monolayers occurs in two steps up to a total amout of about one monolayer, whereas for thicknesses of 10 monolayers and above as well as for all Pd''(100)'' films only a single adsorption peak is observed. The H adsorption process is strongly influenced by the anion of the supporting electrolyte with respect to its thermodynamics as well as kinetics. The maximum amount of adsorbed hydrogen increases with the average film thickness and the H/Pd-ratio reaches a limiting value of around 0.6 in acid electrolytes for thicknesses well above 10 monolayers. The influence of organic molecules and of upd Tl on hydrogen adsorption, absorption and evolution is shown and briefly discussed.