In certain adsorption processes, several different adsorbents may be used, each more or less specialized for a particular task of selectively taking up certain components. The different adsorbents may be packed in different columns, or, alternatively, in the same column as superposed layers. In the latter case, they necessarily experience the same conditions in terms of throughput, pressure and temperature. The dynamic behaviour, and therefore the optimal design and operation of such beds, Is different from that of single adsorbent beds. The passage of concentration waves from one layer to the other and the flow reversal induce particular refraction, dispersion and interference phenomena. We propose a method of analysis and representation of these phenomena, based on pseudo-characteristics defined as lines propagating constant values of particular concentrations. The pseudo-characteristics do not in general coincide with the classical lines generated by the method of characteristics within the framework of equilibrium models, except in some ideal situations (quasi-equilibrium without dispersion and without pressure and velocity changes). These lines can be generated by computer simulations using non-ideal complex models, and offer a convenient and compact way to analyse the start-up and convergence towards the cyclic regime, to represent the essential features of the concentration profiles at all times, to adjust the operating times and to optimize the layer thickness. This analysis is illustrated using the example of hydrogen purification from a four-component mixture, using a two-bed two-adsorbent six-step PSA process.