Results of an extensive survey of the time evolution of the light output of thin‐film ac electroluminescent devices fabricated from alkaline‐earth‐sulfide phosphors with different activators are presented. Light output increases slowly until a steady state, which depends on voltage and drive frequency, is reached. It is shown that the slow evolution is due to tunneling of electrons from deep states and eventual trapping of these electrons in shallow states. The dynamics of the device is determined by the supply of electrons.