  We discuss here constraints on the particle acceleration models from the
observed gamma-ray bursts spectra. The standard synchrotron shock model assumes
that some fraction of available energy is given instantaneously to the
electrons which are injected at high Lorentz factor. The emitted spectrum in
that case corresponds to the spectrum of cooling electrons, F_\nu ~ \nu^{-1/2},
is much too soft to account for the majority of the observed spectral slopes.
We show that continuous heating of electrons over the life-time of a source is
needed to produce hard observed spectra. In this model, a prominent peak
develops in the electron distribution at energy which is a strong function of
Thomson optical depth \tau_T of heated electrons (pairs). At \tau_T>1, a
typical electron Lorentz factor \gamma ~ 1-2 and quasi-thermal Comptonization
operates. It produces spectrum peaking at a too high energy. Optical depths
below 10^{-4} would be difficult to imagine in any physical scenario. At \tau_T
=10^{-4}-10^{-2}, \gamma ~ 30-100 and synchrotron self-Compton radiation is the
main emission mechanism. The synchrotron peak should be observed at 10--100 eV,
while the self-absorbed low-energy tail with F_\nu ~ \nu^2 can produce the
prompt optical emission (like in the case of GRB 990123). The first Compton
scattering radiation by nearly monoenergetic electrons peaks in the BATSE
energy band and can be as hard as F_\nu ~ \nu^1 reproducing the hardness of
most of the observed GRB spectra. The second Compton peak should be observed in
the high-energy gamma-ray band, possibly being responsible for the 10-100 MeV
emission detected in GRB 941017. A significant electron-positron pair
production reduces the available energy per particle, moving spectral peaks to
lower energies as the burst progresses.
