  In this paper, we have made an accurate investigation of proton acceleration
in GRBs and we have predicted a possible signature of cosmic rays, in a
sufficiently baryon-loaded fireball, via GeV $\gamma$-ray emission produced by
$\pi^{0}$-meson decay. If two ungrounded assumptions are removed, namely,
Bohm's scaling and a slow magnetic field decrease, the usual Fermi processes
are unable to generate ultra high energy cosmic rays (UHECRs) in GRBs. We
propose to develop another scenario of relativistic Fermi acceleration in the
internal shock stage. We present the results of a realistic Monte-Carlo
simulation of a multi-front acceleration which clearly shows the possible
generation of UHECR. The amount of energy converted into UHECRs turns out to be
a sizeable fraction of the magnetic energy.
