Blazars with redshifts z less than or equal to 0.1 are likely candidat
es for detection at energies in the range 300 GeV - 50 TeV with Cerenk
ov telescopes and scintillator arrays. We present gamma-ray flux predi
ctions for a sample of 15 nearby flat-spectrum radio sources fitting t
he proton blazar model of Mannheim (1993a) to their observed broad-ban
d spectral energy distributions. At high energies, we use fluxes or fl
ux limits measured by ROSAT, CGRO and the Whipple Observatory to const
rain 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 (in
ternal absorption). Typically, the theoretical spectra decrease much f
aster above TeV (photon index s approximate to 3) than between GeV and
TeV (s approximate to 2) owing to internal absorption. The predicted
fluxes are confronted with flux limits in the 20-50 TeV energy range o
btained by the High Energy Gamma Ray Astronomy (HEGRA) experiment. Wit
hout cosmic absorption, the fluxes are about equal to the current sens
itivity of HEGRA. Improved gamma/hadron separation techniques could re
nder a detection by HEGRA possible, if cosmic absorption by the far-in
frared background at wavelengths similar to 100 mu m is not exceedingl
y strong.