Oscillatory wetting-dewetting instabilities at the liquid/vapour interface of Ga-Pb and, for the first time, of Ga-Bi alloys have been studied employing second harmonic generation and kinetic ellipsometry. Alloy samples prepared at x-T conditions inside the respective miscibility gap (Ga 0.8 Bi 0.2 : T = 520 K; Ga 0.95 Pb 0.05 : T = 595 K) show oscillations on the timescale of typically hours. The surface transforms back and forth from a Ga-rich non-wetting state to a complete wetting state where the Ga-rich bulk is covered with a Bi-rich (or Pbrich) film. In the case of Ga-Bi the change of the wetting film thickness was characterized quantitatively with the aid of the ellipsometric measurements. It is consistent with a wetting-dewetting mechanism whereby the wetting film varies periodically between macroscopic and microscopic values. The phenomenon can be understood taking different emissivities of the wet and the nonwet state into account. They cause at otherwise constant conditions different temperatures of the sample, which has to adopt its phase compositions according to the respective phase diagram. This results in mass transport to and away from the surface. A model calculation on Ga-Bi taking these effects into account recovers in good quantitative agreement the oscillation period and the oscillations of the temperature as well as of the film thickness. Similarities and differences between Ga-Bi and Ga-Pb are finally considered.