Recent work on gravitational geons is extended to examine the stability properties of gravitational and electromagnetic geon constructs. All types of geons must possess the property of regularity, self-consistency and quasi-stability on a time-scale much longer than the period of the comprising waves. Standard perturbation theory, modified to accommodate time-averaged fields, is used to test the requirement of quasi-stability. It is found that the modified perturbation theory results in an internal inconsistency. The time-scale of evolution is found to be of the same order of magnitude as the period of the comprising waves. This contradicts the requirement of slow evolution. Thus not all of the requirements for the existence of electromagnetic or gravitational geons are met though perturbation theory. From this result it cannot be concluded that an electromagnetic or a gravitational geon is a viable entity. The broader implications of the result are discussed with particular reference to the problem of gravitational energy.