  New high energy emission features have been recently discovered by the
Cherenkov telescopes from active galaxies e.g., a few minutes variability time
scale of TeV emission from Mrk 501 and PKS 2155-304, sub-TeV $\gamma$-ray
emission from GeV peaked blazar 3C 279, and TeV emission from two nearby active
galaxies, M87 and Cen A, which jets are inclined at a relatively large angle to
the line of sight. These results have put a new light on the high energy
processes occurring in central parts of active galaxies stimulating more
detailed studies of $\gamma$-ray emission models. Here we report the results of
a detailed analysis concerning the most general version of the model for the
$\gamma$-ray production by leptons injected in the jet which interact with the
thermal radiation from an accretion disk (the so called {\it external inverse
Compton model}). We investigate the $\gamma$-ray spectra produced in an
anisotropic Inverse Compton (IC) $e^\pm$ pair cascade in the whole volume above
the accretion disk. The cascade $\gamma$-ray spectra are obtained for different
locations of the observer in respect to the direction of the jet. We also study
the time evolution of this $\gamma$-ray emission caused by the propagation of
the relativistic leptons along the jet and the delays resulting from different
places of the origin of $\gamma$-rays above the accretion disk. We discuss the
main features of such a cascade model assuming constant injection rate of
electrons along the jet. We are investigating two models for their different
maximum energies: constant value independent on the distance along the jet or
limited by the synchrotron energy losses considered locally in the jet. The
model is discussed in the context of blazars observed at small and large
inclination angles taking as an example the parameters of the two famous
sources Cen A and 3C 279.
