Energy storage is a key technology for many purposes and in particular for air conditioning plants and a successful exploitation of solar energy. Thermal storage devices are usually classified as either variable temperature (“sensible heat”) or constant temperature (“latent heat”) devices. For both models a basic question is to determine the efficiency suitably: Only exergy efficiency appears a proper way. The aim of this paper is to examine exergy efficiency in both variable and constant temperature systems. From a general statement of exergy efficiency by the present author, two types of actual definitions are proposed, depending on the fact that the exergy of the fluid leaving the thermal storage during the charge phase can be either totally lost or utilized elsewhere. In addition, specific remarks are made about the exergy of a system in a periodically varying temperature environment.