We calculate the spectra of inverse Compton (IC) emissions in gamma-ray bur
st (GRB) shocks produced when relativistic ejecta encounters the external i
nterstellar medium, assuming a broken power-law approximation to the synchr
otron seed spectrum. Four IC processes, including the synchrotron self-Comp
ton (SSC) processes in GRB forward and reverse shocks, and two combined-IC
processes (i.e., scattering of reverse shock photons on the electrons in fo
rward shocks and forward shock photons on the electrons in reverse shocks),
are considered. We find that the SSC emission from reverse shocks dominate
s 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 responsib
le for the prompt high-energy gamma rays detected by EGRET. At TeV energy b
ands, however, the combined-IC emissions and/or the SSC emission from the f
orward shocks become increasingly dominant for a moderately steep distribut
ion of shocked electrons.