  The principal paradigm for gamma-ray bursts suggest that the prompt transient
gamma-ray signal arises from multiple shocks internal to the relativistic
expansion. This paper illustrates some properties of diffusive acceleration at
relativistic shocks that pertain to GRB models, providing interpretation of the
BATSE/EGRET data. Using a standard Monte Carlo simulation, computations of the
spectral shape, and the range of spectral indices are presented, as functions
of the shock speed, magnetic field obliquity and the type of particle
scattering. It is clear that while quasi-parallel, relativistic shocks with
fields approximately normal to the shock plane can efficiently accelerate
particles, highly oblique and perpendicular ones cannot unless the particle
diffusion is almost isotropic, i.e. extremely close to the Bohm limit.
Accordingly, an array of distribution indices should be present in the burst
population, as is exhibited by the EGRET data, and even mildly-relativistic
internal shocks require strong field turbulence in order to model the >100 MeV
observations. In addition, recent spectral fitting to burst data in the BATSE
band is discussed, providing probes of the efficiency of injection of
non-thermal electrons.
