  Gamma-Ray Bursts are good candidates of the ``bottom up'' scenario for the
generation of the UHE Cosmic Rays. In the most discussed model of GRBs, namely
the ``fireball'' model, a highly relativistic shock forms and seems capable of
accelerating the cosmic rays up to the EeV range. However, only the first Fermi
cycle produces a large energy gain to particles coming from the external
medium. Thus, a complementary acceleration is proposed, downstream of the
external shock, in the relativistic plasma of the GRBs, where crossings of
relativistic fronts are likely to occur. Both forward and backward fronts are
necessary for the internal Fermi acceleration to work and the physical process
that generates them is presented. We found that there exists a relevant
physical process similar to Brillouin backscattering that redistributes the
incoming energy in the plasma shell. This redistribution occurs through the
generation of sound waves that heat the plasma shell and also through the
generation of both forward and backward relativistic Alfven fronts that
accelerate cosmic rays by the Fermi process. We show that this ensemble of
processes is able to account for the generation of UHE cosmic rays.
  There are two opportunities for these combined processes, first during the
``primary'' Gamma-Ray Burst where baryons are entrained by the relativistic
pair wind, second during the predeceleration and deceleration stages when the
fireball interacts with the interstellar medium. However, because of the
synchrotron losses, only the second stage can produce the UHE cosmic rays.
