  Decaying axion-like particles (ALP) with masses in the eV range which might
occupy dark matter halos of the Milky Way and other galaxies produce a
characteristic "bump" feature in the spectrum of extragalactic background light
(EBL). This feature leaves an imprint on the gamma-ray spectra of distant
extragalactic sources. We derive constraints on the ALP coupling to photons
based on analysis of spectra of very-high-energy gamma-ray loud blazars. We
combine gamma-ray spectral measurements by Fermi/LAT and Cherenkov telescopes
and fit a model in which the intrinsic source spectrum is modified by pair
production on photons produced by ALP decays. We constrain the amplitude of
gamma-ray flux suppression by this effect. We find that the combined Fermi/LAT
and VERITAS data set for the source 1ES 1218+304 currently provides the
tightest constraint on ALP-two-photon coupling which is complementary to the
constraints imposed by non-observation of excess energy loss in Horizontal
Branch stars, by the high-resolution spectroscopic observations of galaxy
clusters with optical telescopes and by the searches of ALP signal with CERN
Solar Axion Telescope. Our analysis favours existence of a bump in the EBL
spectrum which could be produced by ALPs in the mass range 2-3 eV and
axion-photon coupling $\sim 10^{-10}$ GeV$^{-1}$. We discuss possibilities for
verification of this hint with deeper Cherenkov telescope observations of large
number of blazars with current generation instruments and with the Cherenkov
Telescope Array.
