  The very high energy (VHE) $\gamma$-ray spectra of some TeV Blazars, after
being corrected for absorption in the extragalactic background light (EBL),
appear unusually hard, which poses challenges to conventional acceleration and
emission models. We investigate the parameter space that allows the production
of such hard TeV spectra within time-dependent leptonic models, both for
synchrotron self-Compton (SSC) and external Compton (EC) scenarios. In the
context of interpretation of very hard $\gamma$-ray spectra, time-dependent
considerations become crucial because even extremely hard, initial electron
distributions can be significantly deformed due to radiative energy losses. We
show that very steep VHE spectra can be avoided if adiabatic losses are taken
into account. Another way to keep extremely hard electron distributions in the
presence of radiative losses, is to assume stochastic acceleration models that
naturally lead to steady-state relativistic, Maxwellian-type particle
distributions. We demonstrate that in either case leptonic models can reproduce
TeV spectra as hard as $E_{\gamma} dN/dE_{\gamma} \propto E_{\gamma}$.
Unfortunately this limits, to a large extend, the potential of extracting EBL
from $\gamma$-ray observations of blazars.

High Energy Astrophysical Phenomena