  Context. Most of the studies on extragalactic {\gamma}-ray propagation
performed up to now only accounted for primary gamma-ray absorption and
adiabatic losses ("absorption-only model"). However, there is growing evidence
that this model is oversimplified and must be modified in some way. In
particular, it was found that the intensity extrapolated from the
optically-thin energy range of some blazar spectra is insufficient to explain
the optically-thick part of these spectra. This effect was interpreted as an
indication for {\gamma}-axion-like particle (ALP) oscillation. On the other
hand, there are many hints that a secondary component from electromagnetic
cascades initiated by primary {\gamma}-rays or nuclei may be observed in the
spectra of some blazars. Aims. We study the impact of electromagnetic cascades
from primary {\gamma}-rays or protons on the physical interpretation of blazar
spectra obtained with imaging Cherenkov telescopes. Methods. We use the
publicly-available code ELMAG to compute observable spectra of electromagnetic
cascades from primary {\gamma}-rays. For the case of primary proton, we develop
a simple, fast and reasonably accurate hybrid method to calculate the
observable spectrum. We perform the fitting of the observed spectral energy
distributions (SEDs) with various physical models: the absorption-only model,
the "electromagnetic cascade model" (for the case of primary {\gamma}-rays),
and several versions of the hadronic cascade model (for the case of primary
proton). We distinguish the following species of hadronic cascade models: 1)
"basic hadronic model", where it is assumed that the proton beam travels
undisturbed by extragalactic magnetic field and that all observable
{\gamma}-rays are produced by primary protons through photohadronic processes
with subsequent development of electromagnetic cascades /abridged
