The concept of parity of Kekule structures is critically examined. While it appears to be desirable to have a discriminatory device to classify Kekule structures into those with a predominant stabilizing effect and those which destabilize a system relative to an appropriate hypothetical acyclic structure with the same number of CC double bonds, the concept of parity as introduced in the early development of valence theory is found unsatisfactory. A remedy for the situation is proposed which is based on a closer examination of the conjugated circuits present in a system. It is shown that while in many instances the new criterion gives the same classification of Kekule structures as the concept of parity, in other situations where the parity classification leads to ambiguities or unacceptable results the new scheme works well.