The propagation of weak perturbations in an overheated water–air bubble medium is considered in the case where the bubbles contain, in addition to water vapor, an inert gas (e.g., air) which does not undergo phase transitions. Maps of the stability regions of the investigated systems as a function of the degree of overheating of the liquid are constructed. The influence of the initial degree of overheating on the evolution of harmonic waves is analyzed. For unstable systems, the dependence of the increment on bubble radius with increasing degree of water overheating is studied.