  Gamma-ray bursts (GRBs) and following afterglows are considered to be
produced by dissipation of kinetic energy of a relativistic fireball and
radiation process is widely believed as synchrotron radiation or inverse
Compton scattering of electrons. We argue that the transfer of kinetic energy
of ejecta into electrons may be inefficient process and hence the total energy
released by a GRB event is much larger than that emitted in soft gamma-rays, by
a factor of \sim (m_p/m_e). We show that, in this case, very strong emission of
TeV gamma-rays is possible due to synchrotron radiation of protons accelerated
up to \sim 10^{21} eV, which are trapped in the magnetic field of afterglow
shock and radiate their energy on an observational time scale of \sim day. This
suggests a possibility that GRBs are most energetic in TeV range and such TeV
gamma-rays may be detectable from GRBs even at cosmological distances, i.e., z
\sim 1, by currently working ground-based telescopes. Furthermore, this model
gives a quantitative explanation for the famous long-duration GeV photons
detected from GRB940217. If TeV gamma-ray emission which is much more energetic
than GRB photons is detected, it provides a strong evidence for acceleration of
protons up to \sim 10^{21} eV.
