A general kinetic model of multicomponent pressure swing adsorption which describes the operation of multicolumn PSA installations is presented. Single columns can be packed with several layers of different adsorbents. All the steps of complex PSA cycles are taken into account; the systems modelled can be non-isothermal, with non-linear adsorption isotherms. Based on the model developed, typical processes involving the separation of hydrogen from gaseous mixtures are analysed (the separation of hydrogen and methane on activated carbon and the separation of coke gas).