This Note is concerned with the strict hyperbolicity of the compressible Euler equations equipped with an equation of state that describes the thermodynamical equilibrium between the liquid phase and the vapor phase of a uid. The proof is valid for a very wide class of uids. The argument only relies on smoothness assumptions and on the classical thermodynamical stability assumptions, that requires a de nite negative Hessian matrix for each phase entropy as a function of the speci c volume and internal energy.