  The implications of AUGER and HiRes results for patterns of Lorentz symmetry
violation (LSV) are examined, focusing on weak doubly special relativity
(WDSR). If the Greisen-Zatsepin-Kuzmin (GZK) cutoff is definitely confirmed,
the mass composition of the highest-energy cosmic-ray spectrum will be a
crucial issue to draw precise theoretical consequences from the experimental
results. Assuming that the observed flux suppression is due to the GZK
mechanism, data will allow in principle to exclude a significant range of LSV
models and parameters, but other important possibilities are expected to remain
open : Lorentz breaking can be weaker or occur at a scale higher than the
Planck scale, unconventional LSV effects can fake the GZK cutoff, threshold
phenomena can delay its appearance... Space experiments appear to be needed to
further test special relativity. We also examine the consequences of AUGER and
HiRes data for superbradyons. If such superluminal ultimate constituents of
matter exist in our Universe, they may provide new forms of dark matter and
dark energy.
