  Special relativity has been tested at low energy with great accuracy, but its
extrapolation to very high-energy phenomena is much less well established.
Introducing a critical distance scale, a , below 10E-25 cm (the wavelength
scale of the highest-energy observed cosmic rays) allows to consider models,
compatible with standard tests of special relativity, where a small violation
of Lorentz symmetry (a can, for instance, be the Planck length) produces
dramatic effects on the properties of high-energy cosmic rays. Not only the
Greisen-Zatsepin-Kuzmin (GZK) cutoff on very high-energy protons and nuclei
does no longer apply, but particles which are unstable at low energy (neutron,
several nuclei, some hadronic resonances like the Delta++...) would become
stable at very high energy. The muon would also become stable or very long
lived at very high energy if one of the two neutrinos associated to the light
charged leptons (electron, muon) has a mass. Similar considerations apply to
the tau lepton. We discuss several possible scenarios originating these
phenomena, as well as the cosmic ray energy range (well below the energy scale
associated to the fundamental length) and experiments where they could be
detected. Observable effects are predicted for the highest-energy cosmic rays.
