The occurrence of autowaves at the interface as a result of a first-order phase transition had been examined. The linear analysis of a system of the equations for a liquid which contains two components shows that a phase transition at the interface can give rise to autowaves. A spectrum of these autowaves depends on parameters of the system. For a special case of the system parameters an analysis is made of the dependence of the spectrum of autowaves from a temperature gradient the interface. We show that as a result of a interface instability in the bulk solid phase there are various periodic structures of distribution of the component concentration. Surfaces of equal concentration for the spectra of the autowaves are built. A qualitative and quantitative comparison of the numerical calculations with experimental data is made. ©1998 American Institute of Physics.