  We use of a hybrid matrix--Monte Carlo method to simulate the cascade through
the cosmic background radiation initiated by UHE particles and radiation
emitted by topological defects. We follow the cascade over cosmological
distances and calculate the intensities of hadrons, gamma-rays and neutrinos
produced. We compare our results with the observed cosmic ray intensity at 300
EeV and lower energies, and conclude that topological defects are most unlikely
to be the origin of the most energetic cosmic ray events.
