The propagation of extragalactic particles within our Galaxy has been modelled. The flux of such particles is below the observed cosmic ray flux at most energies when their power-law spectrum is extrapolated back from the highest energies. Also, we expect that the propagation of extragalactic particles through static magnetic fields in the Galaxy will not result in a flux change to match the flux of particles measured here within the Galaxy. However, if we were to consider the observed cosmic rays to be of Galactic origin, there would be a remarkable similarity between the required Galactic injection flux and the extrapolated extragalactic flux. We consider here whether the scattering of extragalactic particles in the Galaxy together with an associated energy perturbation might be sufficient for the extragalactic beam to result in the production of ‘Galactic’ particles and, hence, essentially all of the observed cosmic rays. This appears to be possible.