Cascades from primary gamma rays and nuclei as a source of background in searches for oscillations between photons and axion-like particles

Methods of searching for oscillations of photons to axion-like particles (γ → ALP) in spectra of extragalactic sources are considered. It is shown that the secondary component from the cascades initiated by primary gamma rays or nuclei can produce an appreciable background in searches for ALPs in the optically thick region of the spectrum. Experiments with a high energy threshold (~1 TeV and higher) are insufficient for searching for γ → ALP oscillations; low-energy instruments (E < 100 GeV) like CTA should also be used.