  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 in 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.
