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Context. Most of the studies on extragalactic {\gamma}-ray propagationperformed up to now only accounted for primary gamma-ray absorption andadiabatic losses ("absorption-only model"). However, there is growing evidencethat this model is oversimplified and must be modified in some way. Inparticular, it was found that the intensity extrapolated from theoptically-thin energy range of some blazar spectra is insufficient to explainthe optically-thick part of these spectra. This effect was interpreted as anindication for {\gamma}-axion-like particle (ALP) oscillation. On the otherhand, there are many hints that a secondary component from electromagneticcascades initiated by primary {\gamma}-rays or nuclei may be observed in thespectra of some blazars. Aims. We study the impact of electromagnetic cascadesfrom primary {\gamma}-rays or protons on the physical interpretation of blazarspectra obtained with imaging Cherenkov telescopes. Methods. We use thepublicly-available code ELMAG to compute observable spectra of electromagneticcascades from primary {\gamma}-rays. For the case of primary proton, we developa simple, fast and reasonably accurate hybrid method to calculate theobservable spectrum. We perform the fitting of the observed spectral energydistributions (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 primaryproton). We distinguish the following species of hadronic cascade models: 1)"basic hadronic model", where it is assumed that the proton beam travelsundisturbed by extragalactic magnetic field and that all observable{\gamma}-rays are produced by primary protons through photohadronic processeswith subsequent development of electromagnetic cascades /abridged

Electromagnetic cascade masquerade: a way to mimic $\gamma$--axion-like particle mixing effects in blazar spectra