  We calculate the spectra of inverse Compton (IC) emissions in gamma-ray burst
(GRB) shocks produced when relativistic ejecta encounters the external
interstellar medium, assuming a broken power-law approximation to the
synchrotron seed spectrum. Four IC processes, including the synchrotron
self-Compton (SSC) processes in GRB forward and reverse shocks, and two
combined-IC processes (i.e. scattering of reverse shock photons on the
electrons in forward shocks and forward shock photons on the electrons in
reverse shocks), are considered. We find that the SSC emission from reverse
shocks dominates over other emission processes in energy bands from tens of MeV
to tens of GeV, for a wide range of shock parameters. This mechanism may be
responsible for the prompt high energy gamma-rays detected by the Energetic
Gamma Ray Experiment Telescope (EGRET). At TeV energy bands, however, the
combined-IC emissions and/or the SSC emission from the forward shocks become
increasingly dominant for a moderately steep distribution of shocked electrons.
