In this paper we will discuss the problem of Ultra High Energy Cosmic Rays (UHECR) and show that the idea of a Single Source Model established by Erlykin and Wolfendale (1997) to explain the features seen in cosmic ray energy spectra around the 1015 eV region can be successfully applied also for the much higher energies. The propagation of UHECR (of energies higher than 1019 eV) in extragalactic magnetic fields can no longer be described as a random walk (diffusion) process and the transition to rectilinear propagation gives a possible explanation for the so-called Greisen-Zatzepin-Kuzmin (GZK) cut-off which still remains an open question after almost 40 years. A transient “single source” located at a particular distance and producing UHECR for a finite time is the proposed solution.
 A.D. Erlykin and A.W. Wolfendale: “A search for ‘structure’ in the energy spectra of cosmic ray protons and He-nuclei above 104 GeV”, Astroparticle Physics, Vol. 10, (1999), pp. 69–81; “Supernova remnants and the origin of the cosmic radiation: I. SNR acceleration models and their predictions”, Journal of Physics G, Vol. 27, (2001) pp. 941–958; “Supernova remnants and the origin of the cosmic radiation: II. Spectral variations in space and time”, Journal of Physics G, Vol. 27, (2001), pp. 959–976; “Supernova remnants and the origin of the cosmic radiation: III. Spectral differences for different nuclei”, Journal of Physics G, Vol. 27, (2001), pp. 1709–1721. http://dx.doi.org/10.1016/S0927-6505(98)00040-1
Financed by the National Centre for Research and Development under grant No. SP/I/1/77065/10 by the strategic scientific research and experimental development program:
SYNAT - “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information”.