  We calculate the absorption of 10-500 GeV gamma-rays at high redshifts. This
calculation requires the determination of the high-redshift evolution of the
intergalactic starlight photon field, including its IR-UV spectral energy
distribution. To estimate this evolution, we have followed a recent analysis of
Fall, Charlot and Pei which gives results consistent with recent data. We give
our results for the gamma-ray opacity as a function of redshift out to a
redshift of 3. We also give predicted gamma-ray spectra for selected blazars
and give an extragalactic unresolved blazar background spectrum up to 500 GeV.
Our results indicate that this background should steepen significantly above 20
GeV owing to intergalactic absorption. Future observations of this steepening
would provide a test for the blazar background origin hypothesis. We have used
our results to discuss upper limits on the redshifts of gamma-ray bursts. We
note that the 17 Feb. 1994 burst observed by EGRET must have originated at a
redshift less than 2. We also use our estimates of the background to determine
the observability of multi-GeV gamma-ray lines from the annihilation of
supersymmetric dark matter particles in the galactic halo.
