In this paper we study structure and representations of cyclic automata. Corresponding to Green's equivalences in semigroup theory, we introduce three binary relations say L, R and H on cyclic automata. An automaton is said to be strict if L is an equivalence on the set of states. Some properties of these relations are established for giving characterizations of three subclasses of strict automata. Also, we provide representations of strict automata by representing the states as vectors and describing the state transitions in terms of matrix operations. These results generalize and extend Ito's representations of strongly connected automata.