  We study the production of cosmogenic neutrinos and photons during the
extragalactic propagation of ultra-high-energy cosmic rays (UHECRs). For a wide
range of models in cosmological evolution of source luminosity, composition and
maximum energy we calculate the expected flux of cosmogenic secondaries by
normalizing our cosmic ray output to experimental spectra and comparing the
diffuse flux of GeV-TeV gamma-rays to the experimental one measured by the
Fermi satellite. Most of these models yield significant neutrino fluxes for
current experiments like IceCube or Pierre Auger. Furthermore, we discuss the
possibilities of signing the presence of UHE proton sources either within or
outside the cosmic ray horizon using neutrinos or photons observations even if
the cosmic ray composition becomes heavier at the highest energies. We discuss
the possible constraints that could be brought on the UHECR origin from the
different messengers and energy ranges.

High Energy Astrophysical Phenomena;High Energy Physics - Phenomenology