  A property common to several different astrophysical sources of high-energy
gamma-rays is the presence of bulk motion at relativistic speed. The intrinsic
spectra of the nonthermal radiating particles also show interesting
similarities, with a pronounced hardening towards lower energies. This suggests
two distinct acceleration mechanisms could be at work in these sources. At high
energies, the stochastic first-order Fermi process at shocks seems to provide a
reasonable explanation. I will briefly review the status of this mechanism
before discussing the possibility that, at lower energies, non-stochastic
acceleration in the induced electric field of a relativistic current sheet
plays a role.
