The dynamics of two horizontal inviscid liquid layers induced by a vertical wavemaker is studied analytically, followed by a numerical analysis. The focus is put on the time dependent motion of the two interfaces, formed between the two liquid layers and between the upper layer and the air above. The singularities that would appear in the two contact lines (the three-phase lines formed by the wavemaker, the liquids, and the air) in most variable-separating techniques are suppressed by a Fourier-integral method, which generates uniformly valid solutions; the surface elevations at the contact lines remain finite for all time. Various wavemaker velocities are considered for realistic applications of the results. The study is initially prompted by the oil-skimming problem, one of the main issues of which is to determine the optimum speed of the oil skirt, without leaving the spilt oil behind. By obtaining the locations of the two interfaces though this study, the motion of the oil layer (upper liquid) can be determined precisely, based on conservation laws.