The different relaxation processes in a two-phase, vapour-droplet mixture are discussed. It is shown that, for most common pure vapour-droplet media, the relaxation times governing three relaxation processes are widely different in magnitude. This disparity can be exploited to understand the physical structure of shock waves in such a medium. Three different types of fully dispersed waves are identified and the reason for their existence elucidated. The unsteady process through which a shock wave attains its final, stable structure is analyzed by considering the piston and cylinder problem. It is shown how, depending on the piston velocity, the final structure may be partly or fully dispersed..