  The diffuse extragalactic gamma-ray background (EGRB) above 100 MeV encodes
unique information about high-energy processes in the universe. Numerous
sources for the EGRB have been proposed, but the two systems which are certain
to make some contribution are active galaxies (blazars) as well as normal
galaxies. In this paper, we evaluate the contribution to the background from
both sources. The active galaxy contribution arises from unresolved blazars. We
compute this contribution using the Stecker-Salamon model. For normal galaxies,
the emission is due to cosmic-ray interactions with diffuse gas. Our key
assumption here is that the cosmic-ray flux in a galaxy is proportional to the
supernova rate and thus the massive star formation rate, quantified
observationally by the cosmic star formation rate (CSFR). In addition, the
existence of stars today requires a considerably higher ISM mass in the past.
Using the CSFR to compute both these effects, we find that normal galaxies are
responsible for a significant portion (\sim 1/3) of the EGRB near 1 GeV, but
make a smaller contribution at other energies. Finally, we present a "minimal"
two-component model which includes contributions from both normal galaxies and
blazars. We show that the spectrum of the diffuse radiation is a key constraint
on this model: while neither the blazar spectra, nor the galactic spectra, are
separately optimal fits to the observed spectrum, the combined emission
provides an excellent fit. We close by noting key observational tests of this
two-component model, which can be probed by future gamma-ray observatories such
as GLAST.
