  We explore the possibility of detecting the excess of the cosmic radio
background (CRB) toward galaxy clusters due to its Compton scattering by
electrons of the hot intergalactic gas. When mapping the background
fluctuations at frequencies < 800 MHz, this effect gives rise to a radio source
at the cluster location. At higher frequencies, where the microwave (CMB or
relic) radiation dominates in the background, a 'negative' source is observed
at this location due to the transfer of some of the relic photons upward along
the frequency axis (into the range > 217 GHz) upon their scattering. We have
computed the spectra of the expected CRB distortions for various clusters and
show that in many cases in the range 30 MHz - 3 GHz their measurement will be
hindered by the thermal bremsstrahlung from the intergalactic gas and the
scattered radio emission from cluster galaxies associated with their past
activity (and the synchrotron radiation from relativistic electrons). Below 20
MHz the scattering effect always dominates over the thermal gas radiation due
to the general increase in the CRB intensity. We have found the frequency
ranges that are optimal for searching for the Compton CRB excess and show that
hot (kTe > 8 keV) clusters at high (z > 0.5) redshifts are most promising for
its observation. Because of the strong concentration of the bremsstrahlung to
the cluster center, the peripheral observations of this excess must be more
preferable than the central ones. The transition from the 'negative' source on
the map of background fluctuations to the 'positive' one must occur not
gradually but through the stage of a 'hybrid source' (a bright spot surrounded
by a dark ring). This shape of the source in projection is explained by its
unusual three-dimensional shape (a narrow bremsstrahlung peak rising from the
center of a wide deep hole associated with the Compton scattering of the CMB).
