  Observations of minute-scale flares in TeV Blazars place constraints on
particle acceleration mechanisms in those objects. The implications for a
variety of radiation mechanisms have been addressed in the literature; in this
paper we compare four different acceleration mechanisms: diffusive shock
acceleration, second-order Fermi, shear acceleration and the converter
mechanism. When the acceleration timescales and radiative losses are taken into
account, we can exclude shear acceleration and the neutron-based converted
mechanism as possible acceleration processes in these systems. The first-order
Fermi process and the converter mechanism working via SSC photons are still
practically instantaneous, however, provided sufficient turbulence is generated
on the timescale of seconds. We propose stochastic acceleration as a promising
candidate for the energy-dependent time delays in recent gamma-ray flares of
Markarian 501.
