  Detailed information on the physical parameters in the sources of
cosmological Gamma-Ray Bursts (GRBs) is obtained from few plausible assumptions
consistent with observations. Model-independent requirements posed by these
assumptions on the emission mechanism in GRBs are formulated. It is found that
the observed radiation in sub-MeV energy range is generated by the synchrotron
emission mechanism, though about ten per cent of the total GRB energy should be
converted via the inverse Compton process into ultra-hard spectral domain
(above 100 GeV). We estimate the magnetic field strength in the emitting
region, the Lorentz factor of accelerated electrons, and the typical energy of
IC photons.
  We show that there is a "line-of-death" relation for GRBs and derive from
this relation the lower limits on both GRB duration and GRB variability
timescale. The upper limit on the Lorentz factor of GRB fireballs is also
found. We demonstrate that steady-state electron distribution consistent with
the Compton losses may produce different spectral indices, e.g., 3/4 as opposed
to the figure 1/2 widely discussed in the literature. It is suggested that the
changes in the decline rate observed in the lightcurves of several GRB
afterglows may be due to the time evolution of spectral break, which appears in
the synchrotron emission generated by steady-state self-consistent electron
distribution.
