  Models for the integrated relativistic electron population in clusters of
galaxies are presented. The results depend on the history of electron
acceleration in the cluster. If there is no present particle acceleration or
other sources, then no high energy electrons (gamma >~ 300, E >~ 150 MeV)
should be present due to inverse Compton (IC) losses. High energy electrons are
present if particle acceleration is occurring at present, perhaps as a result
of a cluster merger shock. The resulting IC, synchrotron, and gamma-ray
emission from these models has been calculated. In the models, extreme
ultraviolet (EUV) and very soft X-ray emission are a nearly ubiquitous feature,
because this emission comes from IC by electrons with the longest lifetimes in
clusters. Diffuse UV and optical emission is also expected in most clusters,
but at levels which will be difficult to observe. Hard X-ray tails and diffuse
radio synchrotron emission are only expected in clusters with recent or current
particle acceleration; for example, this acceleration might be due to
intracluster merger shocks. Gamma-ray observations at energies of around 100
MeV should detect both the dominant population of relativistic electrons and
the corresponding ions. The predicted fluxes are easily detectable with GLAST.
