  Blazars with redshifts z<0.1 are likely candidates for detection at energies
in the range 300 GeV - 50 TeV with Cerenkov telescopes and scintillator arrays.
We present gamma-ray flux predictions for a sample of 15 nearby flat-spectrum
radio sources fitting the proton blazar model of Mannheim (1993a) to their
observed broad-band spectral energy distributions. At high energies, we use
fluxes or flux limits measured by ROSAT, CGRO and the Whipple Observatory to
constrain their spectra. We take into account absorption of the gamma-rays by
pair production with low energy photons of the diffuse infrared-to-optical
photon background produced by galaxies (cosmic absorption) and with low energy
synchrotron photons of the blazar radiation field (internal absorption).
Typically, the theoretical spectra decrease much faster above TeV (photon index
s~3) than between GeV and TeV (s~2) owing to internal absorption. The predicted
fluxes are confronted with flux limits in the 20-50 TeV energy range obtained
by the High Energy Gamma Ray Astronomy (HEGRA) experiment. Without cosmic
absorption, the fluxes are about equal to the current sensitivity of HEGRA.
Improved gamma/hadron separation techniques could render a detection by HEGRA
possible, if cosmic absorption by the far-infrared background at wavelengths
~100 mu is not exceedingly strong.
