Finite Automata are commonly used in Hybrid Systems, however these are frequently continuous time systems while the classical finite automata theory deals with discrete time. The main objective of this talk is to lift basic concepts of automata theory from discrete to continuous time. Functions computed by finite automata will be considered rather than the sets accepted by these and examples of such devices over non-Zeno signals will be given. At last, a function algebra for a special class of functions over non-Zeno signals will be discussed and some examples of circuits given.