A. TeV -rays
Hurley  reported on detection of 18 GeV photons from GRB 940217. Milagrito - A TeV detector - discovered a possible TeV signal coincident with GRB 970417 . González et al.  discovered a high energy tail that extended up to 200 MeV from GRB 941017.
A natural source for high energy -rays is the SSC (Synchrotron self Compton) component produced by IC from the burst itself or from the afterglow [235, 260]. The SSC photons energy should be e2 higher than the synchrotron photons. Typical random Lorentz factors of electrons, e, within internal shocks are of order a thousand (in the fluid's rest frame). This implies that if the observed -rays emission is produced by synchrotron in internal shocks then the IC emission would produce a second peak around a few hundred GeV. This would be the analogue of the high energy component observed in Blazars. Note that emission above ~ 10 - 100 GeV might be self absorbed by pair production with the source [150, 294, 303].
The SSC component would be even higher from the early afterglow. The synchrotron emission from the forward shock is expected to be around 10 keV (if the observed early afterglow is indeed produced by the external shocks). With a Lorentz factor of a typical electron around 105 the expected SSC component should be around 100 TeV. Finally the reverse shock emission is expected to produce 100 eV photons . With typical electrons Lorentz factor of a few thousand this should correspond to SSC photons with typical energy of 100 MeV. Depending on the relevant Y parameter the fluxes of these high energy components should be comparable or even larger than the prompt GRB -rays fluxes. This emission should be simultaneous with the GRB emission. It is also possible that the forward shock electrons will IC reverse shocks photons. It is likely that this is the cause of the high energy emission seen in GRB 941017 [295, 312].
Other mechanisms can produce high energy emission as well. Vietri97 suggested that as GRB can accelerate protons up to 1020eV (see Section VIIIC below). These protons can emit 0.01 of the GRB energy as high energy -rays with energies up to 300 GeV. Bottcher and Dermer  considered the synchrotron spectrum resulting from high energy protons and leptons produced in cascade initiated by photo-pion production. They predict a significant flux of 10 Mev-100 GeV photons.
While the high energy photons flux could be significant these photons might not be detectable on earth. The high energy photon flux above 1 TeV would be attenuated significantly due to pair production of such high energy photons with the intergalactic NIR flux . Dai and Lu  suggest that secondary emission produced via these interaction (upscattering of the CMB by the produced pairs) would still point towards the initial direction and hence might be detectable as a delayed GeV emission. However, even a tiny intergalactic magnetic field (> 10-22 G would be sufficient to deflect the electrons and dilute these signal .