A study is made of the so-called dynamic state of a metastable substance, characterized by the onset of a nonequilibrium energy interaction (interchange), involving various waves, in the excited material. The intensity of the optical emission is used to analyze the dynamic state; an investigation is made of the propagation of its leading and trailing edges. Various propagation characteristics and natural solitary-wave forms are identified; their similarity to ionization waves allows making some assumptions about the essential nature of this process. The observed effects are important for establishing the physical conditions for the formation of the substance of ball lightning and are also interesting for the physics of flames, electrical breakdown, and electrode spots.