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Claims that the redshifts of galaxies are quantizied at intervals of []24, []36 or []72 kms^-1 are being subjected to rigorous statistical scrutiny using new, accurate redshift data. The results of this enquiry to date are reviewed. The presence of a global galactocentric periodicty []37.5[]0.2 kms^-1 is confirmed at a high confidence level. A strong redshift periodicity of []71.7[]1.3 kms^-1 also exists amongst the galaxies of the outer regions of the Virgo cluster.