The study of the interactions of cosmic rays (CR's) with universal diffuse
background radiation can provide very stringent rests of the validity of sp
ecial relativity. The interactions we consider are the ones characterized b
y well defined energy thresholds whose energy position can be predicted on
the basis of special relativity. We argue that the experimental confirmatio
n of the existence of these thresholds can in principle put very stringent
limits on the scale where special relativity and/or continuity of space-tim
e may possibly break down.