The complicated periodic bifurcations and chaotic behaviors revealed in a nonlinear electronic system. One class of periodic and dhaotic states alternating sequence and similar structures in different levels is observed experimently. A theorem on the similar structures is presented. A method to classify periodic and chaotic alternating sequences by their levels for a class of nonlinear dynamical systems is suggested. The structure regularity for each level periodic sequence and the relationships between periodic and chaotic states of diffe-rent levels are predicted.