  The arrival time coherence of particles in the Ultra High Energy Air Showers
where the center of mass energy of the interaction is of the order of $10^{15}
eV$, puts strict constraint on the propagation of particles in a hypothetical
extra-dimension. We first argue that at such high energies bulk modes and
massive KK-modes can be produced abundantly and in many models their phase
space volume is larger than confined modes. Then, we study the minimum
propagation time in one and two-brane models and show that a large part of the
parameter space of these models are ruled out unless the confinement of fields
is proteced by symmetries up to energies not accessible even to the high energy
tail of Ultar High Energy Cosmic Rays (UHECRs). As a by-product we confirm the
result obtained in some previous works about the close relation between a small
Cosmological Constant and the hierarchy problem.
