We establish the equations of motion of an isothermal viscous Cahn-Hilliard fluid and we investigate the dynamics of fluids having moving contact lines under this theory. The force singularity arising in the classical model of capillarity is no longer present. This removal is due to a mass transfer across the interface combined with a finite thickness of the interface. A numerical simulation of the flow in the immediate vicinity of the contact line shows the connection between the static contact angle, the dynamic angle and points out the influence of the velocity