Consider a vertical plate with a leading edge. The temperature of the plate is above the spontaneous nucleation temperature, so that vapor completely covers the plate, Two-dimensional quasi-parallel theory is used to examine the stability of the two-phase system. Numerical calculations show that the main parameter determining the thickness of the vapor film and its stability is the difference between the temperature of the heated vertical plate and the saturation temperature of the liquid. As the thickness of the vapor film is made smaller, the nose of the neutral curve approaches that of the corresponding one-phase liquid. The overall temperature difference between the plate and liquid bulk does not strongly influence stability properties.