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We have studied the impact of cosmic-ray acceleration in SNR on the spectra of cosmic-ray nuclei in the Galaxy using a series expansion of the propagation equation, which allows us to use analytical solutions for part of the problem and an efficient numerical treatment of the remaining equations and thus accurately describes the cosmic-ray propagation on small scales around their sources in three spatial dimensions and time. We found strong variations of the cosmic-ray nuclei flux by typically 20% with occasional spikes of much higher amplitude, but only minor changes in the spectral distribution. The locally measured spectra of primary cosmic rays fit well into the obtained range of possible spectra. We further showed that the spectra of the secondary element Boron show almost no variations, so that the above findings also imply significant fluctuations of the Boron-to-Carbon ratio. Therefore the commonly used method of determining CR propagation parameters by fitting secondary-to-primary ratios appears flawed on account of the variations that these ratios would show throughout the Galaxy. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]