  The spectra of very high energy gamma-radiation from distant extragalactic
objects suffer significant deformations during the passage of primary
gamma-rays through the intergalactic medium. The recently reported fluxes of
diffuse infrared background radiation indicate that we detect, most probably,
heavily absorbed TeV radiation from Mkn 421 and Mkn 501. This implies that the
absorption-corrected spectrum of Mkn 501 may contain a sharp pile-up which
contradicts to the predictions of the conventional models of TeV blazars, and
thus may leads to the so-called "IR background-TeV gamma-ray crisis". To
overcome this difficulty, in this paper we propose two independent hypotheses
assuming that (i) the TeV radiation from Mkn 501 has a secondary origin, i.e.
it is formed during the development of electron-photon cascades in the
intergalactic medium initiated by primary gamma-rays; (ii) the pile-up in the
source spectrum is a result of comptonization (in deep Klein-Nishina regime) of
ambient optical radiation by an ultrarelativistic conical cold outflow (jet)
with bulk motion Lorentz factor Gamma_0 >= 3 10^7. Within the uncertainties
caused by the limited energy resolution of spectral measurements, the observed
TeV radiation of Mkn 501 formally can be explained by the intergalactic cascade
gamma-rays, assuming however an extremely low intergalactic magnetic field in
the direction to the source at the level of < 10^{-18} G. We also demonstrate
that the "bulk motion comptonization" scenario can quite naturally reproduce
the unusual spectral features in the absorption-corrected TeV spectrum of Mkn
501, and briefly discuss the astrophysical implications of this hypothesis.
