  We derive a relativistically covariant (although not manifestly so) equation
for the distribution function of particles accelerated at shocks, which applies
also to extremely relativistic shocks, and arbitrarily anisotropic particle
distributions. The theory is formulated for arbitrary pitch angle scattering,
and reduces to the well--known case for small angle scatterings via a
Fokker--Planck approximation. The boundary conditions for the problem are
completely reformulated introducing a physically motivated Green's function;
the new formulation allows derivation of the particle spectrum both close and
far away from the injection energy in an exact way, while it can be shown to
reduce to a power--law at large particle energies. The particle spectral index
is also recovered in a novel way. Contact is made with the Newtonian treatment.
