  We discuss the superluminal problem in the diffusion of ultra high energy
protons with energy losses taken into account. The phenomenological solution of
this problem is found with help of the generalized J\"uttner propagator,
originally proposed for relativization of the Maxwellian gas distribution. It
is demonstrated that the generalized J\"uttner propagator gives the correct
expressions in the limits of diffusive and rectilinear propagation of the
charged particles in the magnetic fields, together with the intermediate
regime, in all cases without superluminal velocities. This solution, very
general for the diffusion, is considered for two particular cases: diffusion
inside the stationary objects, like e.g. galaxies, clusters of galaxies etc,
and for expanding universe. The comparison with the previously obtained
solutions for propagation of UHE protons in magnetic fields is performed.
