After a short introduction on ultra-high-energy cosmic-ray (UHECR) physics, I will discuss the implications of the recent Fermi-LAT data regarding the extragalactic gamma-ray background, as well as IceCube very-high energy neutrino data, for the origin of UHECRs.
I will show how calculations of the diffuse flux of cosmogenic γ-rays and neutrinos, produced during the propagation UHECRs in the extragalactic medium, can provide constraints on the possible cosmological evolutions of UHECR sources. I will present in more details the mixed-composition scenario considered in several papers by Globus et al. (which is in agreement with most UHECR data) and show that this model is compatible with both the Fermi-LAT measurements and the current IceCube limits. I will finally discuss the possibility for future experiments to detect cosmogenic neutrinos and further constrain UHECR models,including possible subdominant UHECR proton sources.