  Based on the results of our previous study of the broad band synchrotron
emission of Cas A in the framework of a spatial inhomogeneous model, we
calculate the fluxes of gamma-radiation that can be expected from this
supernova remnant in different energy bands. We show that at energies below 10
GeV gamma-ray fluxes detectable by forthcoming space-borne detectors should be
produced due to bremsstrahlung of radio emitting electrons. We predict that the
power-law index of the photon flux in the GeV region should be hard, close to
the index ~2.2 expected for the acceleration spectrum of the electrons. Photon
fluxes accessible to future ground-based gamma-ray detectors could also be
expected at very high energies. The fluxes to be expected due to bremsstrahlung
and inverse Compton radiation of relativistic electrons at TeV energies should
be very steep, and strongly dependent on the characteristic magnetic fields in
Cas A. We could expect also significant fluxes of pi^0 -decay gamma-rays
produced by relativistic protons. These fluxes may extend with a hard spectrum
beyond TeV energies as far as the protons would be accelerated to energies
beyond 100 TeV. The hardness of the gamma-ray spectrum at TeV energies could in
principle allow one to distinguish between electronic and hadronic origins of
those gamma-rays. We discuss also other implications, such as relativistic
particle content, or physical parameters in the source, that could be derived
from future gamma-ray flux measurements in different energy bands.
