Recent experiments using extensive air shower techniques1–5 have given evidence for the presence of significant fluxes of cosmic γ rays, in the energy range 1015–1016 eV, from specific cosmic sources. We argue here that the flux from these sources, and others as yet unresolved, is probably sufficient to allow the explanation of a number of previously puzzling features of the cosmic radiation, in particular the way in which the amplitude and phase of the anisotropy of cosmic rays varies with energy. It is possible that the effects of cosmic γ rays will be detectable at energies as high as 1017 eV.