We present the first experimental investigation and pertinent theoretical modeling of an interfacial oscillatory instability in a binary fluid alloy, the Ga-Pb system. It is characterized by spinodal decomposition at elevated temperatures and by a complete wetting transition at liquid-liquid coexistence. For the alloy Ga0.95Pb0.05 the fluid interface has been probed by second harmonic generation (SHG) under UHV conditions at temperatures between 740 and 550 K. At conditions inside the miscibility gap clear oscillations of the SHG-intensity with a period of similar to30 min are found for different cooling cycles and also at constant temperatures. These interfacial oscillatory instabilities simultaneously induce temperature oscillations in the bulk fluid with the same period. This phenomenon can be explained by a periodic variation of the fluid interfacial emissivity. A model has been developed which describes the wetting-dewetting dynamics by hydrodynamic equations within the Reynolds approximation. It is found that the interfacial oscillatory instability is determined by capillary-gravitation instability. The model quantitatively describes the time evolution of the interfacial and temperature oscillations and gives the correct value of the oscillation period. A detailed comparison of the experimental and model results is given. (C) 2004 American Institute of Physics.