We report on a numerical study of quantum diffusion over micron lengths in defect-free multi-walled nanotubes. The intershell coupling allows the electron spreading over several shells, and when their periodicities along the nanotube axis are incommensurate, which is likely in real materials, the electronic propagation is shown to be non ballistic. This results in magnetotransport properties which are exceptional for a disorder free system, and provides a new scenario to understand the experiments (A. Bachtold et al. Nature 397, 673 (1999)).