Localized states are a universal phenomenon in spatially extended dissipative nonlinear systems. Recently, also temporally localized states have gained some attention, mainly driven by applications in various optical systems, where the dynamics of short optical pulses, i.e. a temporal localization of optical fields, can be described by delay differential equations. We present a theory for such states, which appear as periodic solutions with a period close to the large delay of the system. We study such solutions by using the limit of large delay, derive a desingularized equation for the solution profile, and provide a classification of the Floquet spectrum into point and pseudo-continuous spectrum. In particular, we point out some analogies and differences to the classical theory for spatially localized states in partial differential equations.
