  The actual potential of the next generation of Gamma Ray Telescopes in
improving the existing tests of an effective Quantum Gravity scale from the
study of the propagation delay for gamma rays of different energies coming from
a distant astrophysical source is discussed. It is shown that the existence of
a cosmological Gamma Ray Horizon, will impose very demanding conditions on the
observations of the telescopes to try to test a Quantum Gravity scale close to
the Planck mass.
