  We show that violation of the Lorentz symmetry in quantum electrodynamics can
suppress the rates of the interactions crucial for the formation of
photon-induced air showers, such as pair production on nuclei and in the
geomagnetic field. As a consequence, the allowed region in the space of
Lorentz-violating parameters will be seriously restricted if several photons
with energies $\gtrsim\,10^{19}\, {eV}$ are detected.
