Waves in liquid/gas and liquid/vapour two-phase systems have various wave modes, curious propagation characteristics and peculiar mechanisms for destabilizing and stabilizing, due to the composite structure of two-phase systems, the accumulated effects of the local and instantaneous interactions between the phases, and the phase transitions. Knowledge of such waves is important, to understand the fundamental properties of two-phase systems and to prove the validity of models. This book discusses recent results on possible wave modes, their structure and propagation characteristics, and mechanisms for destabilizing and stabilizing in liquid/gas and liquid/vapour two-phase systems.