The intrinsic flux of very high-energy ( VHE , energy \gtrsim 100 GeV ) \gamma -rays from extragalactic sources is attenuated due to pair production in the interaction with photons of the extragalactic background light ( EBL ) . Depending on the distance of the source , the Universe should be opaque to VHE photons above a certain energy . However , indications exist that the Universe is more transparent than previously thought . A recent statistical analysis of a large sample of VHE spectra shows that the correction for absorption with current EBL models is too strong for the data points with the highest attenuation . An explanation might be the oscillation of VHE photons into hypothetical axionlike particles ( ALPs ) in ambient magnetic fields . This mechanism would decrease the opacity , as ALPs propagate unimpeded over cosmological distances . Here , a large sample of VHE \gamma -ray spectra obtained with imaging air Cherenkov telescopes is used to set , for the first time , lower limits on the photon-ALP coupling constant g _ { a \gamma } over a large range of ALP masses . The conversion in different magnetic field configurations , including intra-cluster and intergalactic magnetic fields together with the magnetic field of the Milky Way , is investigated taking into account the energy dependence of the oscillations . For optimistic scenarios of the intervening magnetic fields , a lower limit on g _ { a \gamma } of the order of 10 ^ { -12 } \mathrm { GeV } ^ { -1 } is obtained , whereas more conservative model assumptions result in g _ { a \gamma } \gtrsim 2 \times 10 ^ { -11 } \mathrm { GeV } ^ { -1 } . The latter value is within reach of future dedicated ALP searches .