  Most of the recent research on extragalactic $\gamma$-ray propagation focused
on the study of the $\gamma\gamma \rightarrow e^{+}e^{-}$ absorption process
("absorption-only model"). Starting from a possible anomaly at very high
energies (VHE, E >100 GeV), we briefly review several existing deviations from
this model. The exotic interpretation of the VHE anomaly is not supported by
the recent works. On the other hand, the process of intergalactic
electromagnetic cascade development naturally explains these effects. We
discuss phenomenology of intergalactic cascades and the main spectral
signatures of the electromagnetic cascade model. We also briefly consider the
hadronic cascade model; it also may explain the data, but requires low strength
of magnetic field around the source of primary protons or nuclei.
