  It was recently suggested that possible small volations of Lorentz invariance
could explain the existence of UHECR beyond the GZK cutoff and the observations
of multi-TeV gamma-rays from Mkn 501. Our analysis of Lorentz-violating
kinematics shows that in addition to the modified threshold conditions solving
cosmic ray puzzles we should expect a strong suppression of electromagnetic
processes like bremsstrahlung and pair creation. This leads to drastic effects
in electron-photon cascade development in the atmosphere and in detectors.
