  Clusters of galaxies are believed to be capable to accelerate protons at
accretion shocks to energies exceeding 10^18 eV. At these energies, the losses
caused by interactions of cosmic rays with photons of the Cosmic Microwave
Background Radiation (CMBR) become effective and determine the maximum energy
of protons and the shape of the energy spectrum in the cutoff region. The aim
of this work is the study of the formation of the energy spectrum of
accelerated protons at accretion shocks of galaxy clusters and of the
characteristics of their broad band emission. The proton energy distribution is
calculated self-consistently via a time-dependent numerical treatment of the
shock acceleration process which takes into account the proton energy losses
due to interactions with the CMBR. We calculate the energy distribution of
accelerated protons, as well as the flux of broad-band emission produced by
secondary electrons and positrons via synchrotron and inverse Compton
scattering processes. We find that the downstream and upstream regions
contribute almost at the same level to the emission. For the typical parameters
characterising galaxy clusters, the synchrotron and IC peaks in the spectral
energy distributions appear at comparable flux levels. For an efficient
acceleration, the expected emission components in the X-ray and gamma-ray band
are close to the detection threshold of current generation instruments, and
will be possibly detected with the future generation of detectors.
