  The question of the origin of ultra-high-energy cosmic rays at relativistic
shock waves is discussed in the light of results of recent Monte Carlo studies
of the first-order Fermi particle acceleration (Niemiec & Ostrowski 2006,
Niemiec et al. 2006). The models of the turbulent magnetic field near the shock
considered in these simulations include realistic features of the perturbed
magnetic field structures at the shock, which allow us to study all the field
and particle motion characteristics that are important for cosmic-ray
acceleration. Our results show that turbulent conditions near the shock, that
are consistent with the shock jump conditions, lead to substantial
modifications of the acceleration process with respect to the simplified
models, that produce wide-range power-law energy distributions, often with the
"universal" spectral index. Relativistic shocks are essentially always
superluminal, and thus they preferentially generate steep particle spectra with
cutoffs well below the maximum scattering energy, often not exceeding the
energy of the compressed background plasma ions. Thus, cosmic-ray acceleration
to very high energies at relativistic shock waves is inefficient, and such
shocks are not expected to be the sources of ultra-high-energy particles.
