The dynamics of wetting a hydrocarbon self-assembled monolayer by water/DMSO (dimethyl sulfoxide) mixtures and the resulting structure are studied by molecular dynamics computer simulations. A mixture of the two liquids in contact with a methyl terminated C18H37 self-assembled monolayer shows preferential wetting of the surface by the DMSO molecules over a wide range of concentrations. The dynamics of the water desorption and DMSO adsorption starting from a nonequilibrium state are followed. The process is shown to involve a continuous replacement of approximately four water molecules for every single DMSO molecule. In the final equilibrium state, the DMSO methyl groups are oriented toward the surface while the SO bonds form hydrogen bonds with the water. This gives rise to an overlayer of water adjunct to the DMSO surface layer.