  We calculate the fluxes of radio, hard X-rays and gamma-ray emission from
clusters of galaxies, in the context of a secondary electron model (SEM). In
the SEM the radiating electrons are produced by the decay of charged pions in
cosmic ray (CR) interactions with the intracluster medium, while gamma ray
emission is mainly contributed by the decay of neutral pions. We specifically
applied our calculations to the case of the Coma cluster, and found that the
combined radio and hard X-ray fluxes can be explained in the SEM only if very
small values of the intracluster magnetic field ($B\sim 0.1\mu G$) are assumed,
which in turn imply a large energy density of the parent CRs. The consequent
gamma-ray fluxes easily exceed the EGRET limit at 100 MeV. This conclusion can
be avoided only if most of the hard X-ray emission from Coma is not produced by
Inverse Compton Scattering (ICS).
