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 sever
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