The movable contact line between two liquids and a gas phase sensitively reacts to small disturbances in the force equilibrium. The shape of the contact line and the adjoining interfaces is determined by the interface and surface tensions, the contact angles, the density differences (hydrostatic pressure), and the Laplace capillary pressure. When these change, the three-phase contact line can deform and even become unstable. Interface and surface tension depend on the concentration and temperature. During mass transport processes (concentration changes) various forms of the instability of the contact line can be observed: Oscillations of a circular contact line (regular expansion and reduction); Single deformations (bulges) which quickly disappear again; Deformations (bulges) which run along the boundary line; Periodically generated and damped deformations with different modes. The behavior of the three-phase contact line is of practical importance for coalescence processes and for spontaneous emulsification on liquid surfaces.