We discuss on general grounds the possibility of testing specia relativity and the underlying small scale structure of space-time by studying the interactions of Cosmic Rays (CR) with universal diffuse background radiation.The interactions we consider are the ones characterized by well defined energy thresholds whose energy position can be predicted on the basis of special relativity.We argue that the experimental confirmation of the existence of these thresholds can in principle put very stringent limits on the energy (length) scale where special relativity and/or continuity of space-time break down.