A numerical and analytical study has been made to reveal the internal structures of partly dispersed shock waves in pure vapour-droplet media. The results clearly demonstrate the effects of different relaxation phenomena present and their associated time scales on the structure. The study systematically analyses the relative effects of different flow parameters on the structure and thickness of the shock wave. Wherever possible, the structure in a vapour-droplet medium is contrasted against similar structures in more familiar solid particle-laden gas flow. The case of complete evaporation through which a two-phase vapour-droplet medium reverts to a single-phase nonrelaxing one is discussed. Although linearized analyses are often presented for relaxing flows downstream of frozen shocks, they are of limited applicability to vapour-droplet flows. The paper gives many examples of why a linearized analysis is unlikely to be successful in such cases.