  We show that inverse Compton scattering of cosmic-microwave-background and
starlight photons by cosmic-ray electrons in the interstellar and intergalactic
space explains well the spectrum and intensity of the diffuse gamma-ray
background radiation (GBR), which was measured by EGRET aboard the Compton
Gamma Ray Observatory (CGRO) in directions away from the Galactic disk and
centre. The Gamma Ray Large Area Space Telescope (GLAST) will be able to
separate the Galactic foreground from the extragalactic gamma-rays, and to
provide stringent tests of the theory.
